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From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
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+![netcal logo](img/logo/logo_long.png)
+
+# net:cal - Uncertainty Calibration
+
+<div style="text-align: justify">
+
+The **net:cal** calibration framework is a Python 3 library for measuring and mitigating miscalibration of uncertainty estimates, e.g., by a neural network. 
+For full API reference documentation, visit
+<https://fabiankueppers.github.io/calibration-framework>.
+
+Copyright &copy; 2019-2022 Ruhr West University of Applied Sciences,
+Bottrop, Germany AND e:fs TechHub GmbH, Gaimersheim, Germany.
+
+This Source Code Form is subject to the terms of the Apache License 2.0.
+If a copy of the APL2 was not distributed with this file, You can obtain
+one at <https://www.apache.org/licenses/LICENSE-2.0.txt>.
+
+**Important: updated references!** If you use this framework
+(*classification or detection*) or parts of it for your research, please
+cite it by:
+
+```
+@InProceedings{Kueppers_2020_CVPR_Workshops,
+   author = {Küppers, Fabian and Kronenberger, Jan and Shantia, Amirhossein and Haselhoff, Anselm},
+   title = {Multivariate Confidence Calibration for Object Detection},
+   booktitle = {The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
+   month = {June},
+   year = {2020}
+}
+```
+
+*If you use Bayesian calibration methods with uncertainty, please cite
+it by*:
+
+```
+@InProceedings{Kueppers_2021_IV,
+   author = {Küppers, Fabian and Kronenberger, Jan and Schneider, Jonas and Haselhoff, Anselm},
+   title = {Bayesian Confidence Calibration for Epistemic Uncertainty Modelling},
+   booktitle = {Proceedings of the IEEE Intelligent Vehicles Symposium (IV)},
+   month = {July},
+   year = {2021},
+}
+```
+
+*If you use Regression calibration methods, please cite it by*:
+
+```
+@InProceedings{Kueppers_2022_ECCV_Workshops,
+  author    = {Küppers, Fabian and Schneider, Jonas and Haselhoff, Anselm},
+  title     = {Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection},
+  booktitle = {European Conference on Computer Vision (ECCV) Workshops},
+  year      = {2022},
+  month     = {October},
+  publisher = {Springer},
+}
+```
+
+## Table of Contents
+
+- [Overview](#overview)
+  - [Update on version 1.3](#update-on-version-13)
+  - [Update on version 1.2](#update-on-version-12)
+  - [Update on version 1.1](#update-on-version-11)
+- [Installation](#installation)
+- [Requirements](#requirements)
+- [Calibration Metrics](#calibration-metrics)
+  - [Confidence Calibration Metrics](#confidence-calibration-metrics)
+  - [Regression Calibration Metrics](#regression-calibration-metrics)
+- [Methods](#methods)
+  - [Confidence Calibration Methods](#confidence-calibration-methods)
+    - [Binning](#binning)
+    - [Scaling](#scaling)
+    - [Regularization](#regularization)
+  - [Regression Calibration Methods](#regression-calibration-methods)
+    - [Non-parametric calibration](#non-parametric-calibration)
+    - [Parametric calibration](#parametric-calibration)
+- [Visualization](#visualization)
+- [Examples](#examples)
+  - [Classification](#classification)
+    - [Post-hoc Calibration for Classification](#post-hoc-calibration-for-classification)
+    - [Measuring Miscalibration for Classification](#measuring-miscalibration-for-classification)
+    - [Visualizing Miscalibration for Classification](#visualizing-miscalibration-for-classification)
+  - [Detection (Confidence of Objects)](#detection-confidence-of-objects)
+    - [Post-hoc Calibration for Detection](#post-hoc-calibration-for-detection)
+    - [Measuring Miscalibration for Detection](#measuring-miscalibration-for-detection)
+    - [Visualizing Miscalibration for Detection](#visualizing-miscalibration-for-detection)
+  - [Uncertainty in Confidence Calibration](#uncertainty-in-confidence-calibration)
+    - [Post-hoc Calibration with Uncertainty](#post-hoc-calibration-with-uncertainty)
+    - [Measuing Miscalibration with Uncertainty](#measuring-miscalibration-with-uncertainty)
+  - [Probabilistic Regression](#probabilistic-regression)
+    - [Post-hoc Calibration (Parametric)](#post-hoc-calibration-parametric)
+    - [Post-hoc Calibration (Non-Parametric)](#post-hoc-calibration-non-parametric)
+    - [Correlation Estimation and Recalibration](#correlation-estimation-and-recalibration)
+    - [Measuring Miscalibration for Regression](#measuring-miscalibration-for-regression)
+    - [Visualizing Miscalibration for Regression](#visualizing-miscalibration-for-regression)
+- [References](#references)
+
+## Overview
+
+This framework is designed to calibrate the confidence estimates of
+classifiers like neural networks. Modern neural networks are likely to
+be overconfident with their predictions. However, reliable confidence
+estimates of such classifiers are crucial especially in safety-critical
+applications.
+
+For example: given 100 predictions with a confidence of 80% of each
+prediction, the observed accuracy should also match 80% (neither more
+nor less). This behaviour is achievable with several calibration
+methods.
+
+### Update on version 1.3
+
+TL;DR:
+
+- Regression calibration methods: train and infer methods to rescale the uncertainty of probabilistic regression models
+- New package: *netcal.regression* with regression calibration methods:   
+  - Isotonic Regression (*netcal.regression.IsotonicRegression*)
+  - Variance Scaling (*netcal.regression.VarianceScaling*)
+  - GP-Beta (*netcal.regression.GPBeta*)
+  - GP-Normal (*netcal.regression.GPNormal*)
+  - GP-Cauchy (*netcal.regression.GPCauchy*)
+- Implement *netcal.regression.GPNormal* method with correlation estimation and recalibration
+- Restructured *netcal.metrics* package to distinguish between (semantic) confidence calibration in *netcal.confidence* and regression uncertainty calibration in *netcal.regression*:
+  - Expected Calibration Error (ECE - *netcal.confidence.ECE*)
+  - Maximum Calibration Error (MCE - *netcal.confidence.MCE*)
+  - Average Calibration Error (ACE - *netcal.confidence.ACE*)
+  - Maximum Mean Calibration Error (MMCE - *netcal.confidence.MMCE*)
+  - Negative Log Likelihood (NLL - *netcal.regression.NLL*)
+  - Prediction Interval Coverage Probability (PICP - *netcal.regression.PICP*)
+  - Pinball loss (*netcal.regression.PinballLoss*)
+  - Uncertainty Calibration Error (UCE - *netcal.regression.UCE*)
+  - Expected Normalized Calibration Error (ENCE - *netcal.regression.ENCE*)
+  - Quantile Calibration Error (QCE - *netcal.regression.QCE*)
+
+- Added new types of reliability diagrams to visualize regression calibration properties:   
+  - Reliability Regression diagram to visualize calibration for different quantile levels (preferred - *netcal.presentation.ReliabilityRegression*)
+  - Reliability QCE diagram to visualize QCE over stddev (*netcal.presentation.QCE*)
+- Updated examples
+- Minor bugfixes
+- Use library [tikzplotlib](https://github.com/texworld/tikzplotlib) within the *netcal.presentation* package to enable a direct conversion of *matplotlib.Figure* objects to Tikz-Code (e.g., can be used for LaTeX figures)
+
+Within this release, we provide a new package *netcal.regression* to
+enable recalibration of probabilistic regression tasks. Within
+probabilistic regression, a regression model does not output a single
+score for each prediction but rather a probability distribution (e.g.,
+Gaussian with mean/variance) that targets the true output score. Similar
+to (semantic) confidence calibration, regression calibration requires
+that the estimated uncertainty matches the observed error distribution.
+There exist several definitions for regression calibration which the
+provided calibration methods aim to mitigate (cf. README within the
+*netcal.regression* package). We distinguish the provided calibration
+methods into non-parametric and parametric methods. Non-parametric
+calibration methods take a probability distribution as input and apply
+recalibration in terms of quantiles on the cumulative (CDF). This leads
+to a recalibrated probability distribution that, however, has no
+analytical representation but is given by certain points defining a CDF
+distribution. Non-parametric calibration methods are
+*netcal.regression.IsotonicRegression* and *netcal.regression.GPBeta*.
+
+In contrast, parametric calibration methods also take a probability
+distribution as input and provide a recalibrated distribution that has
+an analytical expression (e.g., Gaussian). Parametric calibration
+methods are *netcal.regression.VarianceScaling*,
+*netcal.regression.GPNormal*, and *netcal.regression.GPCauchy*.
+
+The calibration methods are designed to also work with multiple
+independent dimensions. The methods
+*netcal.regression.IsotonicRegression* and
+*netcal.regression.VarianceScaling* apply a recalibration of each
+dimension independently of each other. In contrast, the GP methods
+*netcal.regression.GPBeta*, *netcal.regression.GPNormal*, and
+*netcal.regression.GPCauchy* use a single GP to apply recalibration.
+Furthermore, the GP-Normal *netcal.regression.GPNormal* is can model
+possible correlations within the training data to transform multiple
+univariate probability distributions of a single sample to a joint
+multivariate (normal) distribution with possible correlations. This
+calibration scheme is denoted as *correlation estimation*. Additionally,
+the GP-Normal is also able to take a multivariate (normal) distribution
+with correlations as input and applies a recalibration of the whole
+covariance matrix. This is referred to as *correlation recalibration*.
+
+Besides the recalibration methods, we restructured the *netcal.metrics*
+package which now also holds several metrics for regression calibration
+(cf. *netcal.metrics* package documentation for detailed information).
+Finally, we provide several ways to visualize regression miscalibration
+within the *netcal.presentation* package.
+
+All plot-methods within the *netcal.presentation* package now support
+the option "tikz=True" which switches from standard
+*matplotlib.Figure* objects to strings with Tikz-Code. Tikz-code can be
+directly used for LaTeX documents to render images as vector graphics
+with high quality. Thus, this option helps to improve the quality of
+your reliability diagrams if you are planning to use this library for
+any type of publication/document
+
+### Update on version 1.2
+
+TL;DR:
+
+- Bayesian confidence calibration: train and infer scaling methods using variational inference (VI) and MCMC sampling
+- New metrics: MMCE [[13]](#ref13) and PICP [[14]](#ref14) (*netcal.metrics.MMCE* and *netcal.metrics.PICP*)
+- New regularization methods: MMCE [[13]](#ref13) and DCA [[15]](#ref15) (*netcal.regularization.MMCEPenalty* and *netcal.regularization.DCAPenalty*)
+- Updated examples
+- Switched license from MPL2 to APL2
+
+Now you can also use Bayesian methods to obtain uncertainty within a
+calibration mapping mainly in the *netcal.scaling* package. We adapted
+Markov-Chain Monte-Carlo sampling (MCMC) as well as Variational
+Inference (VI) on common calibration methods. It is also easily possible
+to bring the scaling methods to CUDA in order to speed-up the
+computations. We further provide new metrics to evaluate confidence
+calibration (MMCE) and to evaluate the quality of prediction intervals
+(PICP). Finally, we updated our framework by new regularization methods
+that can be used during model training (MMCE and DCA).
+
+### Update on version 1.1
+
+This framework can also be used to calibrate object detection models. It
+has recently been shown that calibration on object detection also
+depends on the position and/or scale of a predicted object [[12]](#ref12). We
+provide calibration methods to perform confidence calibration w.r.t. the
+additional box regression branch. For this purpose, we extended the
+commonly used Histogram Binning [[3]](#ref3), Logistic Calibration alias Platt
+scaling [[10]](#ref10) and the Beta Calibration method [[2]](#ref2) to also include the
+bounding box information into a calibration mapping. Furthermore, we
+provide two new methods called the *Dependent Logistic Calibration* and
+the *Dependent Beta Calibration* that are not only able to perform a
+calibration mapping w.r.t. additional bounding box information but also
+to model correlations and dependencies between all given quantities [[12]](#ref12).
+Those methods should be preffered over their counterparts in object
+detection mode.
+
+The framework is structured as follows:
+
+    netcal
+      .binning         # binning methods (confidence calibration)
+      .scaling         # scaling methods (confidence calibration)
+      .regularization  # regularization methods (confidence calibration)
+      .presentation    # presentation methods (confidence/regression calibration)
+      .metrics         # metrics for measuring miscalibration (confidence/regression calibration)
+      .regression      # methods for regression uncertainty calibration (regression calibration)
+
+    examples           # example code snippets
+
+## Installation
+
+The installation of the calibration suite is quite easy as it registered
+in the Python Package Index (PyPI). You can either install this
+framework using PIP:
+```shell
+    $ python3 -m pip install netcal
+```
+Or simply invoke the following command to install the calibration suite when installing from source:
+```shell
+    $ git clone https://github.com/fabiankueppers/calibration-framework.git
+    $ cd calibration-framework
+    $ python3 -m pip install .
+```
+
+Note: with update 1.3, we switched from *setup.py* to *pyproject.toml*
+according to PEP-518. The *setup.py* is only for backwards
+compatibility.
+
+### Requirements
+According to *requierments.txt*:
+
+-   numpy\>=1.18
+-   scipy\>=1.4
+-   matplotlib\>=3.3
+-   scikit-learn\>=0.24
+-   torch\>=1.9
+-   torchvision\>=0.10.0
+-   tqdm\>=4.40
+-   pyro-ppl\>=1.8
+-   tikzplotlib\>=0.9.8
+-   tensorboard\>=2.2
+-   gpytorch\>=1.5.1
+
+## Calibration Metrics
+
+We further distinguish between *onfidence calibration* which aims to
+recalibrate confidence estimates in the [0, 1] interval, and
+*regression uncertainty calibration* which addresses the problem of
+calibration in probabilistic regression settings.
+
+### Confidence Calibration Metrics
+
+The most common metric to determine miscalibration in the scope of
+classification is the *Expected Calibration Error* (ECE) [[1]](#ref1). This
+metric divides the confidence space into several bins and measures the
+observed accuracy in each bin. The bin gaps between observed accuracy
+and bin confidence are summed up and weighted by the amount of samples
+in each bin. The *Maximum Calibration Error* (MCE) denotes the highest
+gap over all bins. The *Average Calibration Error* (ACE) [[11]](#ref11) denotes
+the average miscalibration where each bin gets weighted equally. For
+object detection, we implemented the *Detection Calibration Error*
+(D-ECE) [[12]](#ref12) that is the natural extension of the ECE to object
+detection tasks. The miscalibration is determined w.r.t. the bounding
+box information provided (e.g. box location and/or scale). For this
+purpose, all available information gets binned in a multidimensional
+histogram. The accuracy is then calculated in each bin separately to
+determine the mean deviation between confidence and accuracy.
+
+- (Detection) Expected Calibration Error [[1]](#ref1), [[12]](#ref12) (*netcal.metrics.ECE*)
+- (Detection) Maximum Calibration Error [[1]](#ref1), [[12]](#ref12)  (*netcal.metrics.MCE*)
+- (Detection) Average Calibration Error [[11]](#ref11), [[12]](#ref12) (*netcal.metrics.ACE*)
+- Maximum Mean Calibration Error (MMCE) [[13]](#ref13) (*netcal.metrics.MMCE*) (no position-dependency)
+
+### Regression Calibration Metrics
+
+In regression calibration, the most common metric is the *Negative Log
+Likelihood* (NLL) to measure the quality of a predicted probability
+distribution w.r.t. the ground-truth:
+
+- Negative Log Likelihood (NLL) (*netcal.metrics.NLL*)
+
+The metrics *Pinball Loss*, *Prediction Interval Coverage Probability*
+(PICP), and *Quantile Calibration Error* (QCE) evaluate the estimated
+distributions by means of the predicted quantiles. For example, if a
+forecaster makes 100 predictions using a probability distribution for
+each estimate targeting the true ground-truth, we can measure the
+coverage of the ground-truth samples for a certain quantile level (e.g.,
+95% quantile). If the relative amount of ground-truth samples falling
+into a certain predicted quantile is above or below the specified
+quantile level, a forecaster is told to be miscalibrated in terms of
+*quantile calibration*. Appropriate metrics in this context are
+
+- Pinball Loss (*netcal.metrics.PinballLoss*)
+- Prediction Interval Coverage Probability (PICP) [[14]](#ref14) (*netcal.metrics.PICP*)
+- Quantile Calibration Error (QCE) [[15]](#ref15) (*netcal.metrics.QCE*)
+
+Finally, if we work with normal distributions, we can measure the
+quality of the predicted variance/stddev estimates. For *variance
+calibration*, it is required that the predicted variance mathes the
+observed error variance which is equivalent to then Mean Squared Error
+(MSE). Metrics for *variance calibration* are
+
+- Expected Normalized Calibration Error (ENCE) [[17]](#ref17) (*netcal.metrics.ENCE*)
+- Uncertainty Calibration Error (UCE) [[18]](#ref18) (*netcal.metrics.UCE*)
+
+## Methods
+
+We further give an overview about the post-hoc calibration methods for
+(semantic) confidence calibration as well as about the methods for
+regression uncertainty calibration.
+
+### Confidence Calibration Methods
+
+The post-hoc calibration methods are separated into binning and scaling
+methods. The binning methods divide the available information into
+several bins (like ECE or D-ECE) and perform calibration on each bin.
+The scaling methods scale the confidence estimates or logits directly to
+calibrated confidence estimates - on detection calibration, this is done
+w.r.t. the additional regression branch of a network.
+
+Important: if you use the detection mode, you need to specifiy the flag
+"detection=True" in the constructor of the according method (this is
+not necessary for *netcal.scaling.LogisticCalibrationDependent* and
+*netcal.scaling.BetaCalibrationDependent*).
+
+Most of the calibration methods are designed for binary classification
+tasks. For binning methods, multi-class calibration is performed in
+"one vs. all" by default.
+
+Some methods such as "Isotonic Regression" utilize methods from the
+scikit-learn API [[9]](#ref9).
+
+Another group are the regularization tools which are added to the loss
+during the training of a Neural Network.
+
+#### Binning
+
+Implemented binning methods are:
+
+- Histogram Binning for classification [[3]](#ref3), [[4]](#ref4) and object detection [[12]](#ref12) (*netcal.binning.HistogramBinning*)
+- Isotonic Regression [[4]](#ref4),[[5]](#ref5) (*netcal.binning.IsotonicRegression*)
+- Bayesian Binning into Quantiles (BBQ) [[1]](#ref1) (*netcal.binning.BBQ*)
+- Ensemble of Near Isotonic Regression (ENIR) [[6]](#ref6) (*netcal.binning.ENIR*)
+
+#### Scaling
+
+Implemented scaling methods are:
+
+- Logistic Calibration/Platt Scaling for classification [[10]](#ref10) and object detection [[12]](#ref12) (*netcal.scaling.LogisticCalibration*)
+- Dependent Logistic Calibration for object detection [[12]](#ref12) (*netcal.scaling.LogisticCalibrationDependent*) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Logistic Calibration for object detection
+- Temperature Scaling for classification [[7]](#ref7) and object detection [[12]](#ref12) (*netcal.scaling.TemperatureScaling*)
+- Beta Calibration for classification [[2]](#ref2) and object detection [[12]](#ref12) (*netcal.scaling.BetaCalibration*)
+- Dependent Beta Calibration for object detection [[12]](#ref12) (*netcal.scaling.BetaCalibrationDependent*) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Beta Calibration for object detection
+
+**New on version 1.2:** you can provide a parameter named "method" to
+the constructor of each scaling method. This parameter could be one of
+the following: - 'mle': use the method feed-forward with maximum
+likelihood estimates on the calibration parameters (standard) -
+'momentum': use non-convex momentum optimization (e.g. default on
+dependent beta calibration) - 'mcmc': use Markov-Chain Monte-Carlo
+sampling to obtain multiple parameter sets in order to quantify
+uncertainty in the calibration - 'variational': use Variational
+Inference to obtain multiple parameter sets in order to quantify
+uncertainty in the calibration
+
+#### Regularization
+
+With some effort, it is also possible to push the model training towards
+calibrated confidences by regularization. Implemented regularization
+methods are:
+
+- Confidence Penalty [[8]](#ref8) (*netcal.regularization.confidence\_penalty* and *netcal.regularization.ConfidencePenalty* - the latter one is a PyTorch implementation that might be used as a regularization term)
+- Maximum Mean Calibration Error (MMCE) [[13]](#ref13) (*netcal.regularization.MMCEPenalty* - PyTorch regularization module)
+- DCA [[15]](#ref15) (*netcal.regularization.DCAPenalty* - PyTorch regularization module)
+
+### Regression Calibration Methods
+
+The *netcal* library provides post-hoc methods to recalibrate the
+uncertainty of probabilistic regression tasks. We distinguish the
+calibration methods into non-parametric and parametric methods.
+Non-parametric calibration methods take a probability distribution as
+input and apply recalibration in terms of quantiles on the cumulative
+(CDF). This leads to a recalibrated probability distribution that,
+however, has no analytical representation but is given by certain points
+defining a CDF distribution. In contrast, parametric calibration methods
+also take a probability distribution as input and provide a recalibrated
+distribution that has an analytical expression (e.g., Gaussian).
+
+#### Non-parametric calibration
+
+The common non-parametric recalibration methods use the predicted
+cumulative (CDF) distribution functions to learn a mapping from the
+uncalibrated quantiles to the observed quantile coverage. Using a
+recalibrated CDF, it is possible to derive the respective density
+functions (PDF) or to extract statistical moments such as mean and
+variance. Non-parametric calibration methods within the
+*netcal.regression* package are
+
+- Isotonic Regression [[19]](#ref19) which applies a (marginal) recalibration of the CDF (*netcal.regression.IsotonicRegression*)
+- GP-Beta [[20]](#ref20) which applies an input-dependent recalibration of the CDF using a Gaussian process for parameter estimation (*netcal.regression.GPBeta*)
+
+#### Parametric calibration
+
+The parametric recalibration methods apply a recalibration of the
+estimated distributions so that the resulting distribution is given in
+terms of a distribution with an analytical expression (e.g., a
+Gaussian). These methods are suitable for applications where a
+parametric distribution is required for subsequent applications, e.g.,
+within Kalman filtering. We implemented the following parametric
+calibration methods:
+
+- Variance Scaling [[17]](#ref17), [[18]](#ref18) which is nothing else but a temperature scaling for the predicted variance (*netcal.regression.VarianceScaling*)
+- GP-Normal [[16]](#ref16) which applies an input-dependent rescaling of the predicted variance (*netcal.regression.GPNormal*). Note: this method is also able to capture correlations between multiple input dimensions and can return a joint multivariate normal distribution as calibration output (cf. examples section).
+- GP-Cauchy [[16]](#ref16) is similar to GP-Normal but utilizes a Cauchy distribution as calibration output (*netcal.regression.GPCauchy*)
+
+## Visualization
+
+For visualization of miscalibration, one can use a Confidence Histograms
+& Reliability Diagrams for (semantic) confidence calibration as well as
+for regression uncertainty calibration. Within confidence calibration,
+these diagrams are similar to ECE. The output space is divided into
+equally spaced bins. The calibration gap between bin accuracy and bin
+confidence is visualized as a histogram.
+
+For detection calibration, the miscalibration can be visualized either
+along one additional box information (e.g. the x-position of the
+predictions) or distributed over two additional box information in terms
+of a heatmap.
+
+For regression uncertainty calibration, the reliability diagram shows
+the relative prediction interval coverage of the ground-truth samples
+for different quantile levels.
+
+- Reliability Diagram [[1]](#ref1), [[12]](#ref12) (*netcal.presentation.ReliabilityDiagram*)
+- Reliability Diagram for regression calibration (*netcal.presentation.ReliabilityRegression*)
+- Reliability QCE Diagram [[16]](#ref16) shows the Quantile Calibration Error (QCE) for different variance levels (*netcal.presentation.ReliabilityQCE*)
+
+**New on version 1.3:** All plot-methods within the
+*netcal.presentation* package now support the option "tikz=True" which
+switches from standard *matplotlib.Figure* objects to strings with
+Tikz-Code. Tikz-code can be directly used for LaTeX documents to render
+images as vector graphics with high quality. Thus, this option helps to
+improve the quality of your reliability diagrams if you are planning to
+use this library for any type of publication/document
+
+## Examples
+
+The calibration methods work with the predicted confidence estimates of
+a neural network and on detection also with the bounding box regression
+branch.
+
+### Classification
+
+This is a basic example which uses softmax predictions of a
+classification task with 10 classes and the given NumPy arrays:
+
+```python
+ground_truth  # this is a NumPy 1-D array with ground truth digits between 0-9 - shape: (n_samples,)
+confidences   # this is a NumPy 2-D array with confidence estimates between 0-1 - shape: (n_samples, n_classes)
+```
+
+#### Post-hoc Calibration for Classification
+
+This is an example for *netcal.scaling.TemperatureScaling* but also
+works for every calibration method (remind different constructor
+parameters):
+
+```python
+import numpy as np
+from netcal.scaling import TemperatureScaling
+
+temperature = TemperatureScaling()
+temperature.fit(confidences, ground_truth)
+calibrated = temperature.transform(confidences)
+```
+
+#### Measuring Miscalibration for Classification
+
+The miscalibration can be determined with the ECE:
+
+```python
+from netcal.metrics import ECE
+
+n_bins = 10
+
+ece = ECE(n_bins)
+uncalibrated_score = ece.measure(confidences, ground_truth)
+calibrated_score = ece.measure(calibrated, ground_truth)
+```
+
+#### Visualizing Miscalibration for Classification
+
+The miscalibration can be visualized with a Reliability Diagram:
+
+```python
+from netcal.presentation import ReliabilityDiagram
+
+n_bins = 10
+
+diagram = ReliabilityDiagram(n_bins)
+diagram.plot(confidences, ground_truth)  # visualize miscalibration of uncalibrated
+diagram.plot(calibrated, ground_truth)   # visualize miscalibration of calibrated
+
+# you can also use this method to create a tikz file with tikz code
+# that can be directly used within LaTeX documents:
+diagram.plot(confidences, ground_truth, tikz=True, filename="diagram.tikz")
+```
+
+### Detection (Confidence of Objects)
+
+In this example we use confidence predictions of an object detection
+model with the according x-position of the predicted bounding boxes. Our
+ground-truth provided to the calibration algorithm denotes if a bounding
+box has matched a ground-truth box with a certain IoU and the correct
+class label.
+
+```python
+matched                # binary NumPy 1-D array (0, 1) that indicates if a bounding box has matched a ground truth at a certain IoU with the right label - shape: (n_samples,)
+confidences            # NumPy 1-D array with confidence estimates between 0-1 - shape: (n_samples,)
+relative_x_position    # NumPy 1-D array with relative center-x position between 0-1 of each prediction - shape: (n_samples,)
+```
+
+#### Post-hoc Calibration for Detection
+
+This is an example for *netcal.scaling.LogisticCalibration* and
+*netcal.scaling.LogisticCalibrationDependent* but also works for every
+calibration method (remind different constructor parameters):
+
+```python
+import numpy as np
+from netcal.scaling import LogisticCalibration, LogisticCalibrationDependent
+
+input = np.stack((confidences, relative_x_position), axis=1)
+
+lr = LogisticCalibration(detection=True, use_cuda=False)    # flag 'detection=True' is mandatory for this method
+lr.fit(input, matched)
+calibrated = lr.transform(input)
+
+lr_dependent = LogisticCalibrationDependent(use_cuda=False) # flag 'detection=True' is not necessary as this method is only defined for detection
+lr_dependent.fit(input, matched)
+calibrated = lr_dependent.transform(input)
+```
+
+#### Measuring Miscalibration for Detection
+
+The miscalibration can be determined with the D-ECE:
+
+```python
+from netcal.metrics import ECE
+
+n_bins = [10, 10]
+input_calibrated = np.stack((calibrated, relative_x_position), axis=1)
+
+ece = ECE(n_bins, detection=True)           # flag 'detection=True' is mandatory for this method
+uncalibrated_score = ece.measure(input, matched)
+calibrated_score = ece.measure(input_calibrated, matched)
+```
+
+#### Visualizing Miscalibration for Detection
+
+The miscalibration can be visualized with a Reliability Diagram:
+
+```python
+from netcal.presentation import ReliabilityDiagram
+
+n_bins = [10, 10]
+
+diagram = ReliabilityDiagram(n_bins, detection=True)    # flag 'detection=True' is mandatory for this method
+diagram.plot(input, matched)                # visualize miscalibration of uncalibrated
+diagram.plot(input_calibrated, matched)     # visualize miscalibration of calibrated
+
+# you can also use this method to create a tikz file with tikz code
+# that can be directly used within LaTeX documents:
+diagram.plot(input, matched, tikz=True, filename="diagram.tikz")
+```
+
+### Uncertainty in Confidence Calibration
+
+We can also quantify the uncertainty in a calibration mapping if we use
+a Bayesian view on the calibration models. We can sample multiple
+parameter sets using MCMC sampling or VI. In this example, we reuse the
+data of the previous detection example.
+
+```python
+matched                # binary NumPy 1-D array (0, 1) that indicates if a bounding box has matched a ground truth at a certain IoU with the right label - shape: (n_samples,)
+confidences            # NumPy 1-D array with confidence estimates between 0-1 - shape: (n_samples,)
+relative_x_position    # NumPy 1-D array with relative center-x position between 0-1 of each prediction - shape: (n_samples,)
+```
+
+#### Post-hoc Calibration with Uncertainty
+
+This is an example for *netcal.scaling.LogisticCalibration* and
+*netcal.scaling.LogisticCalibrationDependent* but also works for every
+calibration method (remind different constructor parameters):
+
+```python
+import numpy as np
+from netcal.scaling import LogisticCalibration, LogisticCalibrationDependent
+
+input = np.stack((confidences, relative_x_position), axis=1)
+
+# flag 'detection=True' is mandatory for this method
+# use Variational Inference with 2000 optimization steps for creating this calibration mapping
+lr = LogisticCalibration(detection=True, method'variational', vi_epochs=2000, use_cuda=False)
+lr.fit(input, matched)
+
+# 'num_samples=1000': sample 1000 parameter sets from VI
+# thus, 'calibrated' has shape [1000, n_samples]
+calibrated = lr.transform(input, num_samples=1000)
+
+# flag 'detection=True' is not necessary as this method is only defined for detection
+# this time, use Markov-Chain Monte-Carlo sampling with 250 warm-up steps, 250 parameter samples and one chain
+lr_dependent = LogisticCalibrationDependent(method='mcmc',
+                                            mcmc_warmup_steps=250, mcmc_steps=250, mcmc_chains=1,
+                                            use_cuda=False)
+lr_dependent.fit(input, matched)
+
+# 'num_samples=1000': although we have only sampled 250 different parameter sets,
+# we can randomly sample 1000 parameter sets from MCMC
+calibrated = lr_dependent.transform(input)
+```
+
+#### Measuring Miscalibration with Uncertainty
+
+You can directly pass the output to the D-ECE and PICP instance to
+measure miscalibration and mask quality:
+
+```python
+from netcal.metrics import ECE
+from netcal.metrics import PICP
+
+n_bins = 10
+ece = ECE(n_bins, detection=True)
+picp = PICP(n_bins, detection=True)
+
+# the following function calls are equivalent:
+miscalibration = ece.measure(calibrated, matched, uncertainty="mean")
+miscalibration = ece.measure(np.mean(calibrated, axis=0), matched)
+
+# now determine uncertainty quality
+uncertainty = picp.measure(calibrated, matched, kind="confidence")
+
+print("D-ECE:", miscalibration)
+print("PICP:", uncertainty.picp) # prediction coverage probability
+print("MPIW:", uncertainty.mpiw) # mean prediction interval width
+```
+
+If we want to measure miscalibration and uncertainty quality by means of
+the relative x position, we need to broadcast the according information:
+
+```python
+# broadcast and stack x information to calibrated information
+broadcasted = np.broadcast_to(relative_x_position, calibrated.shape)
+calibrated = np.stack((calibrated, broadcasted), axis=2)
+
+n_bins = [10, 10]
+ece = ECE(n_bins, detection=True)
+picp = PICP(n_bins, detection=True)
+
+# the following function calls are equivalent:
+miscalibration = ece.measure(calibrated, matched, uncertainty="mean")
+miscalibration = ece.measure(np.mean(calibrated, axis=0), matched)
+
+# now determine uncertainty quality
+uncertainty = picp.measure(calibrated, matched, uncertainty="mean")
+
+print("D-ECE:", miscalibration)
+print("PICP:", uncertainty.picp) # prediction coverage probability
+print("MPIW:", uncertainty.mpiw) # mean prediction interval width
+```
+
+### Probabilistic Regression
+
+The following example shows how to use the post-hoc calibration methods
+for probabilistic regression tasks. Within probabilistic regression, a
+forecaster (e.g. with Gaussian prior) outputs a mean and a variance
+targeting the true ground-truth score. Thus, the following information
+is required to construct the calibration methods:
+
+```python
+mean          # NumPy n-D array holding the estimated mean of shape (n, d) with n samples and d dimensions
+stddev        # NumPy n-D array holding the estimated stddev (independent) of shape (n, d) with n samples and d dimensions
+ground_truth  # NumPy n-D array holding the ground-truth scores of shape (n, d) with n samples and d dimensions
+```
+
+#### Post-hoc Calibration (Parametric)
+
+These information might result e.g. from object detection where the
+position information of the objects (bounding boxes) are parametrized by
+normal distributions. We start by using parametric calibration methods
+such as Variance Scaling:
+
+```python
+from netcal.regression import VarianceScaling, GPNormal
+
+# the initialization of the Variance Scaling method is pretty simple
+varscaling = VarianceScaling()
+
+# the GP-Normal requires a little bit more parameters to parametrize the underlying GP
+gpnormal = GPNormal(
+    n_inducing_points=12,    # number of inducing points
+    n_random_samples=256,    # random samples used for likelihood
+    n_epochs=256,            # optimization epochs
+    use_cuda=False,          # can also use CUDA for computations
+)
+
+# fit the Variance Scaling
+# note that we need to pass the first argument as tuple as the input distributions
+# are parametrized by mean and variance
+varscaling.fit((mean, stddev), ground_truth)
+
+# fit GP-Normal - similar parameters here!
+gpnormal.fit((mean, stddev), ground_truth)
+
+# transform distributions to obtain recalibrated stddevs
+stddev_varscaling = varscaling.transform((mean, stddev))  # NumPy array with stddev - has shape (n, d)
+stddev_gpnormal = gpnormal.transform((mean, stddev))  # NumPy array with stddev - has shape (n, d)
+```
+
+#### Post-hoc Calibration (Non-Parametric)
+
+We can also use non-parametric calibration methods. In this case, the
+calibrated distributions are defined by their density (PDF) and
+cumulative (CDF) functions:
+
+```python
+from netcal.regression import IsotonicRegression, GPBeta
+
+# the initialization of the Isotonic Regression method is pretty simple
+isotonic = IsotonicRegression()
+
+# the GP-Normal requires a little bit more parameters to parametrize the underlying GP
+gpbeta = GPBeta(
+    n_inducing_points=12,    # number of inducing points
+    n_random_samples=256,    # random samples used for likelihood
+    n_epochs=256,            # optimization epochs
+    use_cuda=False,          # can also use CUDA for computations
+)
+
+# fit the Isotonic Regression
+# note that we need to pass the first argument as tuple as the input distributions
+# are parametrized by mean and variance
+isotonic.fit((mean, stddev), ground_truth)
+
+# fit GP-Beta - similar parameters here!
+gpbeta.fit((mean, stddev), ground_truth)
+
+# transform distributions to obtain recalibrated distributions
+t_isotonic, pdf_isotonic, cdf_isotonic = varscaling.transform((mean, stddev))
+t_gpbeta, pdf_gpbeta, cdf_gpbeta = gpbeta.transform((mean, stddev))
+
+# Note: the transformation results are NumPy n-d arrays with shape (t, n, d)
+# with t as the number of points that define the PDF/CDF,
+# with n as the number of samples, and
+# with d as the number of dimensions.
+
+# The resulting variables can be interpreted as follows:
+# - t_isotonic/t_gpbeta: x-values of the PDF/CDF with shape (t, n, d)
+# - pdf_isotonic/pdf_gpbeta: y-values of the PDF with shape (t, n, d)
+# - cdf_isotonic/cdf_gpbeta: y-values of the CDF with shape (t, n, d)
+```
+
+You can visualize the non-parametric distribution of a single sample
+within a single dimension using Matplotlib:
+
+```python
+from matplotlib import pyplot as plt
+
+fig, (ax1, ax2) = plt.subplots(2, 1)
+
+# plot the recalibrated PDF within a single axis after calibration
+ax1.plot(
+    t_isotonic[:, 0, 0], pdf_isotonic[:, 0, 0],
+    t_gpbeta[:, 0, 0], pdf_gpbeta[:, 0, 0],
+)
+
+# plot the recalibrated PDF within a single axis after calibration
+ax2.plot(
+    t_isotonic[:, 0, 0], cdf_isotonic[:, 0, 0],
+    t_gpbeta[:, 0, 0], cdf_gpbeta[:, 0, 0],
+)
+
+plt.show()
+```
+
+We provide a method to extract the statistical moments expectation and
+variance from the recalibrated cumulative (CDF). Note that we advise to
+use one of the parametric calibration methods if you need e.g. a
+Gaussian for subsequent applications such as Kalman filtering.
+
+```python
+from netcal import cumulative_moments
+
+# extract the expectation (mean) and the variance from the recalibrated CDF
+ymean_isotonic, yvar_isotonic = cumulative_moments(t_isotonic, cdf_isotonic)
+ymean_gpbeta, yvar_gpbeta = cumulative_moments(t_gpbeta, cdf_gpbeta)
+
+# each of these variables has shape (n, d) and holds the
+# mean/variance for each sample and in each dimension
+```
+
+#### Correlation Estimation and Recalibration
+
+With the GP-Normal *netcal.regression.GPNormal*, it is also possible to
+detect possible correlations between multiple input dimensions that have
+originally been trained/modelled independently from each other:
+
+```python
+from netcal.regression import GPNormal
+
+# the GP-Normal requires a little bit more parameters to parametrize the underlying GP
+gpnormal = GPNormal(
+    n_inducing_points=12,    # number of inducing points
+    n_random_samples=256,    # random samples used for likelihood
+    n_epochs=256,            # optimization epochs
+    use_cuda=False,          # can also use CUDA for computations
+    correlations=True,       # enable correlation capturing between the input dimensions
+)
+
+# fit GP-Normal
+# note that we need to pass the first argument as tuple as the input distributions
+# are parametrized by mean and variance
+gpnormal.fit((mean, stddev), ground_truth)
+
+# transform distributions to obtain recalibrated covariance matrices
+cov = gpnormal.transform((mean, stddev))  # NumPy array with covariance - has shape (n, d, d)
+
+# note: if the input is already given by multivariate normal distributions
+# (stddev is covariance and has shape (n, d, d)), the methods works similar
+# and simply applies a covariance recalibration of the input
+```
+
+#### Measuring Miscalibration for Regression
+
+Measuring miscalibration is as simple as the training of the methods:
+
+```python
+import numpy as np
+from netcal.metrics import NLL, PinballLoss, QCE
+
+# define the quantile levels that are used to evaluate the pinball loss and the QCE
+quantiles = np.linspace(0.1, 0.9, 9)
+
+# initialize NLL, Pinball, and QCE objects
+nll = NLL()
+pinball = PinballLoss()
+qce = QCE(marginal=True)  # if "marginal=False", we can also measure the QCE by means of the predicted variance levels (realized by binning the variance space)
+
+# measure miscalibration with the initialized metrics
+# Note: the parameter "reduction" has a major influence to the return shape of the metrics
+# see the method docstrings for detailed information
+nll.measure((mean, stddev), ground_truth, reduction="mean")
+pinball.measure((mean, stddev), ground_truth, q=quantiles, reduction="mean")
+qce.measure((mean, stddev), ground_truth, q=quantiles, reduction="mean")
+```
+
+#### Visualizing Miscalibration for Regression
+
+Example visualization code block using the
+*netcal.presentation.ReliabilityRegression* class:
+
+```python
+from netcal.presentation import ReliabilityRegression
+
+# define the quantile levels that are used for the quantile evaluation
+quantiles = np.linspace(0.1, 0.9, 9)
+
+# initialize the diagram object
+diagram = ReliabilityRegression(quantiles=quantiles)
+
+# visualize miscalibration with the initialized object
+diagram.plot((mean, stddev), ground_truth)
+
+# you can also use this method to create a tikz file with tikz code
+# that can be directly used within LaTeX documents:
+diagram.plot((mean, stddev), ground_truth, tikz=True, filename="diagram.tikz")
+```
+</div>
+
+## References
+
+<a name="ref1">[1]</a> Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht: "Obtaining well calibrated probabilities using bayesian binning." Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
+
+<a name="ref2">[2]</a> Kull, Meelis, Telmo Silva Filho, and Peter Flach: "Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers." Artificial Intelligence and Statistics, PMLR 54:623-631, 2017.
+
+<a name="ref3">[3]</a> Zadrozny, Bianca and Elkan, Charles: "Obtaining calibrated probability estimates from decision trees and naive bayesian classifiers." In ICML, pp. 609–616, 2001.
+
+<a name="ref4">[4]</a> Zadrozny, Bianca and Elkan, Charles: "Transforming classifier scores into accurate multiclass probability estimates." In KDD, pp. 694–699, 2002.
+
+<a name="ref5">[5]</a> Ryan J Tibshirani, Holger Hoefling, and Robert Tibshirani: "Nearly-isotonic regression." Technometrics, 53(1):54–61, 2011.
+
+<a name="ref6">[6]</a> Naeini, Mahdi Pakdaman, and Gregory F. Cooper: "Binary classifier calibration using an ensemble of near isotonic regression models." 2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE, 2016.
+
+<a name="ref7">[7]</a> Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger: "On Calibration of Modern Neural Networks." Proceedings of the 34th International Conference on Machine Learning, 2017.
+
+<a name="ref8">[8]</a> Pereyra, G., Tucker, G., Chorowski, J., Kaiser, L. and Hinton, G.: “Regularizing neural networks by penalizing confident output distributions.” CoRR, 2017.
+
+<a name="ref9">[9]</a> Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. and Duchesnay, E.: "Scikit-learn: Machine Learning in Python." In Journal of Machine Learning Research, volume 12 pp 2825-2830, 2011.
+
+<a name="ref10">[10]</a> Platt, John: "Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods." Advances in large margin classifiers, 10(3): 61–74, 1999.
+
+<a name="ref11">[11]</a> Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi: "Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection." Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.
+
+<a name="ref12">[12]</a> Fabian Küppers, Jan Kronenberger, Amirhossein Shantia, and Anselm Haselhoff: "Multivariate Confidence Calibration for Object Detection"." The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020
+
+<a name="ref13">[13]</a> Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain: "Trainable calibration measures for neural networks from _kernel mean embeddings." International Conference on Machine Learning. 2018
+
+<a name="ref14">[14]</a> Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez: "Quality of Uncertainty Quantification for Bayesian Neural Network Inference." Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019
+
+<a name="ref15">[15]</a> Liang, Gongbo, et al.: "Improved trainable calibration method for neural networks on medical imaging classification." arXiv preprint arXiv:2009.04057 (2020)
+
+<a name="ref16">[16]</a> Fabian Küppers, Jonas Schneider, Jonas, and Anselm Haselhoff: "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection." In: Proceedings of the European Conference on Computer Vision (ECCV) Workshops, Springer, October 2022
+
+<a name="ref17">[17]</a> Levi, Dan, et al.: "Evaluating and calibrating uncertainty prediction in regression tasks." arXiv preprint arXiv:1905.11659 (2019).
+
+<a name="ref18">[18]</a> Laves, Max-Heinrich, et al.: "Well-calibrated regression uncertainty in medical imaging with deep learning." Medical Imaging with Deep Learning. PMLR, 2020.
+
+<a name="ref19">[19]</a> Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon: "Accurate uncertainties for deep learning using calibrated regression." International Conference on Machine Learning. PMLR, 2018.
+
+<a name="ref20">[20]</a> Hao Song, Tom Diethe, Meelis Kull and Peter Flach: "Distribution calibration for regression." International Conference on Machine Learning. PMLR, 2019.
diff --git a/README.rst b/README.rst
deleted file mode 100644
index 2bb283c..0000000
--- a/README.rst
+++ /dev/null
@@ -1,362 +0,0 @@
-Calibration Framework
-=====================
-Calibration framework in Python 3 for Neural Networks.
-For full API reference documentation, visit https://fabiankueppers.github.io/calibration-framework.
-
-Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-AND Elektronische Fahrwerksysteme GmbH, Gaimersheim, Germany
-
-This Source Code Form is subject to the terms of the Apache License 2.0.
-If a copy of the APL2 was not distributed with this
-file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
-
-**Important: updated references!** If you use this framework (*classification or detection*) or parts of it for your research, please cite it by::
-
-    @InProceedings{Kueppers_2020_CVPR_Workshops,
-       author = {Küppers, Fabian and Kronenberger, Jan and Shantia, Amirhossein and Haselhoff, Anselm},
-       title = {Multivariate Confidence Calibration for Object Detection},
-       booktitle = {The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
-       month = {June},
-       year = {2020}
-    }
-
-*If you use Bayesian calibration methods with uncertainty, please cite it by*::
-
-    @InProceedings{Kueppers_2021_IV,
-           author = {Küppers, Fabian and Kronenberger, Jan and Schneider, Jonas and Haselhoff, Anselm},
-           title = {Bayesian Confidence Calibration for Epistemic Uncertainty Modelling},
-           booktitle = {Proceedings of the IEEE Intelligent Vehicles Symposium (IV)},
-           month = {July},
-           year = {2021},
-        }
-
-.. contents:: Table of Contents
-   :depth: 2
-
-Overview
-===============
-
-This framework is designed to calibrate the confidence estimates of classifiers like neural networks. Modern neural networks are likely to be overconfident with their predictions. However, reliable confidence estimates of such classifiers are crucial especially in safety-critical applications.
-
-For example: given 100 predictions with a confidence of 80% of each prediction, the observed accuracy should also match 80% (neither more nor less). This behaviour is achievable with several calibration methods.
-
-Update on version 1.2
----------------------
-TL;DR:
-- Bayesian confidence calibration: train and infer scaling methods using variational inference (VI) and MCMC sampling
-- New metrics: MMCE [13]_ and PICP [14]_ (*netcal.metrics.MMCE* and *netcal.metrics.PICP*)
-- New regularization methods: MMCE [13]_ and DCA [15]_ (*netcal.regularization.MMCEPenalty* and *netcal.regularization.DCAPenalty*)
-- Updated examples
-- Switched license from MPL2 to APL2
-
-Now you can also use Bayesian methods to obtain uncertainty within a calibration mapping mainly in the *netcal.scaling* package. We adapted Markov-Chain Monte-Carlo sampling (MCMC) as well as Variational Inference (VI) on common calibration methods.
-It is also easily possible to bring the scaling methods to CUDA in order to speed-up the computations. We further provide new metrics to evaluate confidence calibration (MMCE) and to evaluate the quality of prediction intervals (PICP).
-Finally, we updated our framework by new regularization methods that can be used during model training (MMCE and DCA).
-
-Update on version 1.1
----------------------
-This framework can also be used to calibrate object detection models. It has recently been shown that calibration on object detection also depends on the position and/or scale of a predicted object [12]_. We provide calibration methods to perform confidence calibration w.r.t. the additional box regression branch.
-For this purpose, we extended the commonly used Histogram Binning [3]_, Logistic Calibration alias Platt scaling [10]_ and the Beta Calibration method [2]_ to also include the bounding box information into a calibration mapping.
-Furthermore, we provide two new methods called the *Dependent Logistic Calibration* and the *Dependent Beta Calibration* that are not only able to perform a calibration mapping
-w.r.t. additional bounding box information but also to model correlations and dependencies between all given quantities [12]_. Those methods should be preffered over their counterparts in object detection mode.
-
-The framework is structured as follows::
-
-    netcal
-      .binning         # binning methods
-      .scaling         # scaling methods
-      .regularization  # regularization methods
-      .presentation    # presentation methods
-      .metrics         # metrics for measuring miscalibration
-
-    examples           # example code snippets
-
-Installation
-===============
-The installation of the calibration suite is quite easy with setuptools. You can either install this framework using PIP::
-
-    pip3 install netcal
-
-Or simply invoke the following command to install the calibration suite::
-
-    python3 setup.py install
-
-Requirements
-------------
-- numpy>=1.17
-- scipy>=1.3
-- matplotlib>=3.1
-- scikit-learn>=0.21
-- torch>=1.4
-- torchvision>=0.5.0
-- tqdm>=4.40
-- pyro-ppl>=1.3
-- tikzplotlib>=0.9.8
-- tensorboard>=2.2
-
-
-Calibration Metrics
-======================
-The most common metric to determine miscalibration in the scope of classification is the *Expected Calibration Error* (ECE) [1]_. This metric divides the confidence space into several bins and measures the observed accuracy in each bin. The bin gaps between observed accuracy and bin confidence are summed up and weighted by the amount of samples in each bin. The *Maximum Calibration Error* (MCE) denotes the highest gap over all bins. The *Average Calibration Error* (ACE) [11]_ denotes the average miscalibration where each bin gets weighted equally.
-For object detection, we implemented the *Detection Calibration Error* (D-ECE) [12]_ that is the natural extension of the ECE to object detection tasks. The miscalibration is determined w.r.t. the bounding box information provided (e.g. box location and/or scale). For this purpose, all available information gets binned in a multidimensional histogram. The accuracy is then calculated in each bin separately to determine the mean deviation between confidence and accuracy.
-
-- (Detection) Expected Calibration Error [1]_, [12]_ (*netcal.metrics.ECE*)
-- (Detection) Maximum Calibration Error [1]_, [12]_  (*netcal.metrics.MCE*)
-- (Detection) Average Calibration Error [11]_, [12]_ (*netcal.metrics.ACE*)
-- Maximum Mean Calibration Error (MMCE) [13]_ (*netcal.metrics.MMCE*) (no position-dependency)
-- Prediction interval coverage probability (PICP) (*netcal.metrics.PICP*) - this score is not a direct measure of confidence calibration but rather to measure the quality of uncertainty prediction intervals.
-
-Methods
-=======
-The post-hoc calibration methods are separated into binning and scaling methods. The binning methods divide the available information into several bins (like ECE or D-ECE) and perform calibration on each bin. The scaling methods scale the confidence estimates or logits directly to calibrated confidence estimates - on detection calibration, this is done w.r.t. the additional regression branch of a network.
-
-Important: if you use the detection mode, you need to specifiy the flag "detection=True" in the constructor of the according method (this is not necessary for *netcal.scaling.LogisticCalibrationDependent* and *netcal.scaling.BetaCalibrationDependent*).
-
-Most of the calibration methods are designed for binary classification tasks. For binning methods, multi-class calibration is performed in "one vs. all" by default.
-
-Some methods like "Isotonic Regression" utilize methods from the scikit-learn API [9]_.
-
-Another group are the regularization tools which are added to the loss during the training of a Neural Network.
-
-Binning
--------
-Implemented binning methods are:
-
-- Histogram Binning for classification [3]_, [4]_ and object detection [12]_ (*netcal.binning.HistogramBinning*)
-- Isotonic Regression [4]_, [5]_ (*netcal.binning.IsotonicRegression*)
-- Bayesian Binning into Quantiles (BBQ) [1]_ (*netcal.binning.BBQ*)
-- Ensemble of Near Isotonic Regression (ENIR) [6]_ (*netcal.binning.ENIR*)
-
-Scaling
--------
-Implemented scaling methods are:
-
-- Logistic Calibration/Platt Scaling for classification [10]_, [12]_ and object detection [12]_ (*netcal.scaling.LogisticCalibration*)
-- Dependent Logistic Calibration for object detection [12]_ (*netcal.scaling.LogisticCalibrationDependent*) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Logistic Calibration for object detection
-- Temperature Scaling for classification [7]_ and object detection [12]_ (*netcal.scaling.TemperatureScaling*)
-- Beta Calibration for classification [2]_ and object detection [12]_ (*netcal.scaling.BetaCalibration*)
-- Dependent Beta Calibration for object detection [12]_ (*netcal.scaling.BetaCalibrationDependent*) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Beta Calibration for object detection
-
-**New on version 1.2:**: you can provide a parameter named "method" to the constructor of each scaling method. This parameter could be one of the following:
-- 'mle': use the method feed-forward with maximum likelihood estimates on the calibration parameters (standard)
-- 'momentum': use non-convex momentum optimization (e.g. default on dependent beta calibration)
-- 'mcmc': use Markov-Chain Monte-Carlo sampling to obtain multiple parameter sets in order to quantify uncertainty in the calibration
-- 'variational': use Variational Inference to obtain multiple parameter sets in order to quantify uncertainty in the calibration
-
-Regularization
---------------
-With some effort, it is also possible to push the model training towards calibrated confidences by regularization. Implemented regularization methods are:
-
-- Confidence Penalty [8]_ (*netcal.regularization.confidence_penalty* and *netcal.regularization.ConfidencePenalty* - the latter one is a PyTorch implementation that might be used as a regularization term)
-- Maximum Mean Calibration Error (MMCE) [13]_ (*netcal.regularization.MMCEPenalty* - PyTorch regularization module)
-- DCA [15]_ (*netcal.regularization.DCAPenalty* - PyTorch regularization module)
-
-Visualization
-=============
-For visualization of miscalibration, one can use a Confidence Histograms & Reliability Diagrams. These diagrams are similar to ECE, the output space is divided into equally spaced bins. The calibration gap between bin accuracy and bin confidence is visualized as a histogram.
-
-On detection calibration, the miscalibration can be visualized either along one additional box information (e.g. the x-position of the predictions) or distributed over two additional box information in terms of a heatmap.
-
-- Reliability Diagram [1]_, [12]_ (*netcal.presentation.ReliabilityDiagram*)
-
-Examples
-========
-The calibration methods work with the predicted confidence estimates of a neural network and on detection also with the bounding box regression branch.
-
-Classification
---------------
-This is a basic example which uses softmax predictions of a classification task with 10 classes and the given NumPy arrays:
-
-.. code-block:: python
-
-    ground_truth  # this is a NumPy 1-D array with ground truth digits between 0-9 - shape: (n_samples,)
-    confidences   # this is a NumPy 2-D array with confidence estimates between 0-1 - shape: (n_samples, n_classes)
-
-This is an example for *netcal.scaling.TemperatureScaling* but also works for every calibration method (remind different constructor parameters):
-
-.. code-block:: python
-
-    import numpy as np
-    from netcal.scaling import TemperatureScaling
-
-    temperature = TemperatureScaling()
-    temperature.fit(confidences, ground_truth)
-    calibrated = temperature.transform(confidences)
-
-The miscalibration can be determined with the ECE:
-
-.. code-block:: python
-
-    from netcal.metrics import ECE
-
-    n_bins = 10
-
-    ece = ECE(n_bins)
-    uncalibrated_score = ece.measure(confidences)
-    calibrated_score = ece.measure(calibrated)
-
-The miscalibration can be visualized with a Reliability Diagram:
-
-.. code-block:: python
-
-    from netcal.presentation import ReliabilityDiagram
-
-    n_bins = 10
-
-    diagram = ReliabilityDiagram(n_bins)
-    diagram.plot(confidences, ground_truth)  # visualize miscalibration of uncalibrated
-    diagram.plot(calibrated, ground_truth)   # visualize miscalibration of calibrated
-
-Detection
----------
-In this example we use confidence predictions of an object detection model with the according x-position of the predicted bounding boxes. Our ground-truth provided to the calibration algorithm denotes if a bounding box has matched a ground-truth box with a certain IoU and the correct class label.
-
-.. code-block:: python
-
-    matched                # binary NumPy 1-D array (0, 1) that indicates if a bounding box has matched a ground truth at a certain IoU with the right label - shape: (n_samples,)
-    confidences            # NumPy 1-D array with confidence estimates between 0-1 - shape: (n_samples,)
-    relative_x_position    # NumPy 1-D array with relative center-x position between 0-1 of each prediction - shape: (n_samples,)
-
-This is an example for *netcal.scaling.LogisticCalibration* and *netcal.scaling.LogisticCalibrationDependent* but also works for every calibration method (remind different constructor parameters):
-
-.. code-block:: python
-
-    import numpy as np
-    from netcal.scaling import LogisticCalibration, LogisticCalibrationDependent
-
-    input = np.stack((confidences, relative_x_position), axis=1)
-
-    lr = LogisticCalibration(detection=True, use_cuda=False)    # flag 'detection=True' is mandatory for this method
-    lr.fit(input, matched)
-    calibrated = lr.transform(input)
-
-    lr_dependent = LogisticCalibrationDependent(use_cuda=False) # flag 'detection=True' is not necessary as this method is only defined for detection
-    lr_dependent.fit(input, matched)
-    calibrated = lr_dependent.transform(input)
-
-The miscalibration can be determined with the D-ECE:
-
-.. code-block:: python
-
-    from netcal.metrics import ECE
-
-    n_bins = [10, 10]
-    input_calibrated = np.stack((calibrated, relative_x_position), axis=1)
-
-    ece = ECE(n_bins, detection=True)           # flag 'detection=True' is mandatory for this method
-    uncalibrated_score = ece.measure(input, matched)
-    calibrated_score = ece.measure(input_calibrated, matched)
-
-The miscalibration can be visualized with a Reliability Diagram:
-
-.. code-block:: python
-
-    from netcal.presentation import ReliabilityDiagram
-
-    n_bins = [10, 10]
-
-    diagram = ReliabilityDiagram(n_bins, detection=True)    # flag 'detection=True' is mandatory for this method
-    diagram.plot(input, matched)                # visualize miscalibration of uncalibrated
-    diagram.plot(input_calibrated, matched)     # visualize miscalibration of calibrated
-
-Uncertainty in Calibration
---------------------------
-We can also quantify the uncertainty in a calibration mapping if we use a Bayesian view on the calibration models. We can sample multiple parameter sets using MCMC sampling or VI. In this example, we reuse the data of the previous detection example.
-
-.. code-block:: python
-
-    matched                # binary NumPy 1-D array (0, 1) that indicates if a bounding box has matched a ground truth at a certain IoU with the right label - shape: (n_samples,)
-    confidences            # NumPy 1-D array with confidence estimates between 0-1 - shape: (n_samples,)
-    relative_x_position    # NumPy 1-D array with relative center-x position between 0-1 of each prediction - shape: (n_samples,)
-
-This is an example for *netcal.scaling.LogisticCalibration* and *netcal.scaling.LogisticCalibrationDependent* but also works for every calibration method (remind different constructor parameters):
-
-.. code-block:: python
-
-    import numpy as np
-    from netcal.scaling import LogisticCalibration, LogisticCalibrationDependent
-
-    input = np.stack((confidences, relative_x_position), axis=1)
-
-    # flag 'detection=True' is mandatory for this method
-    # use Variational Inference with 2000 optimization steps for creating this calibration mapping
-    lr = LogisticCalibration(detection=True, method'variational', vi_epochs=2000, use_cuda=False)
-    lr.fit(input, matched)
-
-    # 'num_samples=1000': sample 1000 parameter sets from VI
-    # thus, 'calibrated' has shape [1000, n_samples]
-    calibrated = lr.transform(input, num_samples=1000)
-
-    # flag 'detection=True' is not necessary as this method is only defined for detection
-    # this time, use Markov-Chain Monte-Carlo sampling with 250 warm-up steps, 250 parameter samples and one chain
-    lr_dependent = LogisticCalibrationDependent(method='mcmc',
-                                                mcmc_warmup_steps=250, mcmc_steps=250, mcmc_chains=1,
-                                                use_cuda=False)
-    lr_dependent.fit(input, matched)
-
-    # 'num_samples=1000': although we have only sampled 250 different parameter sets,
-    # we can randomly sample 1000 parameter sets from MCMC
-    calibrated = lr_dependent.transform(input)
-
-You can directly pass the output to the D-ECE and PICP instance to measure miscalibration and mask quality:
-
-.. code-block:: python
-
-    from netcal.metrics import ECE
-    from netcal.metrics import PICP
-
-    n_bins = 10
-    ece = ECE(n_bins, detection=True)
-    picp = PICP(n_bins, detection=True)
-
-    # the following function calls are equivalent:
-    miscalibration = ece.measure(calibrated, matched, uncertainty="mean")
-    miscalibration = ece.measure(np.mean(calibrated, axis=0), matched)
-
-    # now determine uncertainty quality
-    uncertainty = picp.measure(calibrated, matched, uncertainty="mean")
-
-    print("D-ECE:", miscalibration)
-    print("PICP:", uncertainty.picp) # prediction coverage probability
-    print("MPIW:", uncertainty.mpiw) # mean prediction interval width
-
-If we want to measure miscalibration and uncertainty quality by means of the relative x position, we need to broadcast the according information:
-
-.. code-block:: python
-
-    # broadcast and stack x information to calibrated information
-    broadcasted = np.broadcast_to(relative_x_position, calibrated.shape)
-    calibrated = np.stack((calibrated, broadcasted), axis=2)
-
-    n_bins = [10, 10]
-    ece = ECE(n_bins, detection=True)
-    picp = PICP(n_bins, detection=True)
-
-    # the following function calls are equivalent:
-    miscalibration = ece.measure(calibrated, matched, uncertainty="mean")
-    miscalibration = ece.measure(np.mean(calibrated, axis=0), matched)
-
-    # now determine uncertainty quality
-    uncertainty = picp.measure(calibrated, matched, uncertainty="mean")
-
-    print("D-ECE:", miscalibration)
-    print("PICP:", uncertainty.picp) # prediction coverage probability
-    print("MPIW:", uncertainty.mpiw) # mean prediction interval width
-
-References
-==========
-.. [1] Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht: "Obtaining well calibrated probabilities using bayesian binning." Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
-.. [2] Kull, Meelis, Telmo Silva Filho, and Peter Flach: "Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers." Artificial Intelligence and Statistics, PMLR 54:623-631, 2017.
-.. [3] Zadrozny, Bianca and Elkan, Charles: "Obtaining calibrated probability estimates from decision trees and naive bayesian classifiers." In ICML, pp. 609–616, 2001.
-.. [4] Zadrozny, Bianca and Elkan, Charles: "Transforming classifier scores into accurate multiclass probability estimates." In KDD, pp. 694–699, 2002.
-.. [5] Ryan J Tibshirani, Holger Hoefling, and Robert Tibshirani: "Nearly-isotonic regression." Technometrics, 53(1):54–61, 2011.
-.. [6] Naeini, Mahdi Pakdaman, and Gregory F. Cooper: "Binary classifier calibration using an ensemble of near isotonic regression models." 2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE, 2016.
-.. [7] Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger: "On Calibration of Modern Neural Networks." Proceedings of the 34th International Conference on Machine Learning, 2017.
-.. [8] Pereyra, G., Tucker, G., Chorowski, J., Kaiser, L. and Hinton, G.: “Regularizing neural networks by penalizing confident output distributions.” CoRR, 2017.
-.. [9] Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. and Duchesnay, E.: "Scikit-learn: Machine Learning in Python." In Journal of Machine Learning Research, volume 12 pp 2825-2830, 2011.
-.. [10] Platt, John: "Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods." Advances in large margin classifiers, 10(3): 61–74, 1999.
-.. [11] Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi: "Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection." Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.
-.. [12] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff: "Multivariate Confidence Calibration for Object Detection"." The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020
-.. [13] Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain: "Trainable calibration measures for neural networks from _kernel mean embeddings." International Conference on Machine Learning. 2018
-.. [14] Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez: "Quality of Uncertainty Quantification for Bayesian Neural Network Inference." Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019
-.. [15] Liang, Gongbo, et al.: "Improved trainable calibration method for neural networks on medical imaging classification." arXiv preprint arXiv:2009.04057 (2020)
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diff --git a/pyproject.toml b/pyproject.toml
new file mode 100644
index 0000000..53f99e2
--- /dev/null
+++ b/pyproject.toml
@@ -0,0 +1,74 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+[build-system]
+requires = ['setuptools']
+build-backend = "setuptools.build_meta"
+
+[project]
+name = "netcal"
+description = "The net:cal calibration framework is a Python 3 library for measuring and mitigating miscalibration of uncertainty estimates, e.g., by a neural network."
+requires-python = ">=3.6"
+authors = [
+  {email = "fabian.kueppers@efs-auto.com"},
+  {name = "Fabian Küppers"}
+]
+maintainers = [
+  {email = "fabian.kueppers@efs-auto.com"},
+  {name = "Fabian Küppers"}
+]
+
+keywords = [
+    "netcal",
+    "calibration",
+    "uncertainty",
+    "neural",
+    "network",
+    "confidence",
+    "classification",
+    "object",
+    "detection",
+    "regression"
+]
+
+classifiers = [
+    "Programming Language :: Python :: 3",
+    "License :: OSI Approved :: Apache Software License",
+    "Operating System :: OS Independent",
+    "Development Status :: 5 - Production/Stable",
+    "Topic :: Scientific/Engineering :: Artificial Intelligence",
+]
+
+dependencies = [
+    "numpy>=1.18",
+    "scipy>=1.4",
+    "matplotlib>=3.3",
+    "scikit-learn>=0.24",
+    "torch>=1.9",
+    "torchvision>=0.10.0",
+    "tqdm>=4.40",
+    "pyro-ppl>=1.8",
+    "tikzplotlib==0.9.8",
+    "tensorboard>=2.2",
+    "gpytorch>=1.5.1"
+]
+
+dynamic = ["version", "readme"]
+
+[project.urls]
+homepage = "https://github.com/fabiankueppers/calibration-framework"
+documentation = "https://fabiankueppers.github.io/calibration-framework"
+
+[project.license]
+file = "LICENSE.txt"
+
+[tool.setuptools]
+packages = ["netcal"]
+
+[tool.setuptools.dynamic]
+version = {attr = "netcal.__version__"}
+readme = {file = ["README.md"]}
diff --git a/requirements.txt b/requirements.txt
new file mode 100644
index 0000000..a637345
--- /dev/null
+++ b/requirements.txt
@@ -0,0 +1,11 @@
+numpy>=1.18
+scipy>=1.4
+matplotlib>=3.3
+scikit-learn>=0.24
+torch>=1.9
+torchvision>=0.10.0
+tqdm>=4.40
+pyro-ppl>=1.8
+tikzplotlib==0.9.8
+tensorboard>=2.2
+gpytorch>=1.5.1
\ No newline at end of file
diff --git a/setup.cfg b/setup.cfg
deleted file mode 100644
index 5aef279..0000000
--- a/setup.cfg
+++ /dev/null
@@ -1,2 +0,0 @@
-[metadata]
-description-file = README.rst
diff --git a/setup.py b/setup.py
index 6469528..0ed50f6 100644
--- a/setup.py
+++ b/setup.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -7,25 +7,4 @@
 
 import setuptools
 
-with open("README.rst", "r") as fh:
-    long_description = fh.read()
-
-setuptools.setup(
-    name="netcal",
-    version="1.2.1",
-    author="Fabian Kueppers",
-    author_email="fabian.kueppers@hs-ruhrwest.de",
-    description="Python Framework to calibrate confidence estimates of classifiers like Neural Networks",
-    long_description=long_description,
-    long_description_content_type="text/x-rst",
-    url="https://github.com/fabiankueppers/calibration-framework",
-    packages=setuptools.find_packages(),
-    install_requires = ['numpy>=1.17', 'scipy>=1.3', 'matplotlib>=3.1', 'scikit-learn>=0.21', 'torch>=1.4', 'torchvision>=0.5.0', 'tqdm>=4.40', 'pyro-ppl>=1.3', 'tikzplotlib>=0.9.8', 'tensorboard>=2.2'],
-    classifiers=[
-        "Programming Language :: Python :: 3",
-        "License :: OSI Approved :: Apache Software License",
-        "Operating System :: OS Independent",
-        "Development Status :: 5 - Production/Stable",
-        "Topic :: Scientific/Engineering :: Artificial Intelligence",
-    ],
-)
+setuptools.setup()

From b7e48c37b5d288f61215fbfa931a797cfbf8d467 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:39:05 +0200
Subject: [PATCH 02/21] Add README.md files to each subpackage

---
 netcal/README.md                |  3 ++
 netcal/binning/README.md        |  5 +++
 netcal/metrics/README.md        | 19 +++++++++++
 netcal/presentation/README.md   | 15 +++++++++
 netcal/regression/README.md     | 58 +++++++++++++++++++++++++++++++++
 netcal/regularization/README.md |  6 ++++
 netcal/scaling/README.md        | 10 ++++++
 7 files changed, 116 insertions(+)
 create mode 100644 netcal/README.md
 create mode 100644 netcal/binning/README.md
 create mode 100644 netcal/metrics/README.md
 create mode 100644 netcal/presentation/README.md
 create mode 100644 netcal/regression/README.md
 create mode 100644 netcal/regularization/README.md
 create mode 100644 netcal/scaling/README.md

diff --git a/netcal/README.md b/netcal/README.md
new file mode 100644
index 0000000..64d8ff2
--- /dev/null
+++ b/netcal/README.md
@@ -0,0 +1,3 @@
+# API Reference of net:cal
+
+For a detailed API reference, visit <https://fabiankueppers.github.io/calibration-framework>.
\ No newline at end of file
diff --git a/netcal/binning/README.md b/netcal/binning/README.md
new file mode 100644
index 0000000..12105ed
--- /dev/null
+++ b/netcal/binning/README.md
@@ -0,0 +1,5 @@
+# Binning Methods for Confidence Calibration
+
+This package consists of several methods for confidence calibration which use binning to approximate
+confidence estimates to the measured accuracy. The most common calibration methods within this package
+are *netcal.binning.HistogramBinning* and *netcal.binning.IsotonicRegression*.
\ No newline at end of file
diff --git a/netcal/metrics/README.md b/netcal/metrics/README.md
new file mode 100644
index 0000000..748dc33
--- /dev/null
+++ b/netcal/metrics/README.md
@@ -0,0 +1,19 @@
+# Metrics Package to Measure Miscalibration
+
+Methods for measuring miscalibration in the context of confidence calibration and regression uncertainty calibration.
+
+The common methods for confidence calibration evaluation are given with the
+*netcal.metrics.confidence.ECE* (ECE), *netcal.metrics.confidence.MCE* (MCE), and
+*netcal.metrics.confidence.ACE* (ACE). Each method bins the samples by their confidence and measures the
+accuracy in each bin. The ECE gives the mean gap between confidence and observed accuracy in each bin weighted by the
+number of samples. The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights
+each bin equally.
+
+The common methods for regression uncertainty evaluation are *netcal.metrics.regression.PinballLoss* (Pinball
+loss), the *netcal.metrics.regression.NLL* (NLL), and the *netcal.metrics.regression.QCE* (M-QCE and
+C-QCE). The Pinball loss as well as the Marginal/Conditional Quantile Calibration Error (M-QCE and C-QCE) evaluate
+the quality of the estimated quantiles compared to the observed ground-truth quantile coverage. The NLL is a proper
+scoring rule to measure the overall quality of the predicted probability distributions.
+
+For a detailed description of the available metrics within regression calibration, see the module doc of
+*netcal.regression*.
\ No newline at end of file
diff --git a/netcal/presentation/README.md b/netcal/presentation/README.md
new file mode 100644
index 0000000..9cf7a3b
--- /dev/null
+++ b/netcal/presentation/README.md
@@ -0,0 +1,15 @@
+# Visualization Package
+
+Methods for the visualization of miscalibration in the scope of confidence calibration and regression uncertainty
+calibration.
+
+This package consists of a *netcal.presentation.ReliabilityDiagram* (Reliability Diagram) method used to
+visualize the calibration properties for confidence
+calibration in the scope of classification, object detection (semantic label confidence) or segmentation.
+Similar to the ACE or ECE, this method bins the samples in equally sized bins by their confidence and
+displays the gap between confidence and observed accuracy in each bin.
+
+For regression uncertainty calibration, this package also holds the *netcal.presentation.ReliabilityRegression*
+method that is able to visualize the quantile calibration properties of probabilistic regression models, e.g., within
+probabilistic regression or object detection (spatial position uncertainty).
+A complementary diagram is the *netcal.presentation.ReliabilityQCE* that visualizes the computation of the *netcal.metrics.regression.QCE* (C-QCE) metric.
\ No newline at end of file
diff --git a/netcal/regression/README.md b/netcal/regression/README.md
new file mode 100644
index 0000000..0972f24
--- /dev/null
+++ b/netcal/regression/README.md
@@ -0,0 +1,58 @@
+# Probabilistic Regression Calibration Package
+
+Methods for uncertainty calibration of probabilistic regression tasks.
+A probabilistic regression model does not only provide a continuous estimate but also an according uncertainty
+(commonly a Gaussian standard deviation/variance).
+The methods within this package are able to recalibrate this uncertainty by means of *quantile calibration* [1],
+*distribution calibration* [2], or *variance calibration* [3], [4].
+
+*Quantile calibration* [1] requires that a predicted quantile for a quantile level *t* covers
+approx. *100t%* of the ground-truth samples.
+
+Methods for *quantile calibration*:
+
+- *IsotonicRegression* [1].
+
+*Distribution calibration* [2] requires that a predicted probability distribution should be equal to the observed
+error distribution. This must hold for all statistical moments.
+
+Methods for *distribution calibration*:
+
+- *GPBeta* [2].
+- *GPNormal* [5].
+- *GPCauchy* [5].
+
+*Variance calibration* [3], [4] requires that the predicted variance of a Gaussian distribution should match the
+observed error variance which is equivalent to the root mean squared error.
+
+Methods for *variance calibration*:
+
+- *VarianceScaling* [3], [4].
+- *GPNormal* [5].
+
+## References
+
+[1] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+   "Accurate uncertainties for deep learning using calibrated regression."
+   International Conference on Machine Learning. PMLR, 2018.
+   [Get source online](http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf)
+
+[2] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+   "Distribution calibration for regression."
+   International Conference on Machine Learning. PMLR, 2019.
+   [Get source online](http://proceedings.mlr.press/v97/song19a/song19a.pdf)
+
+[3] Levi, Dan, et al.:
+   "Evaluating and calibrating uncertainty prediction in regression tasks."
+   arXiv preprint arXiv:1905.11659 (2019).
+   [Get source online](https://arxiv.org/pdf/1905.11659.pdf)
+
+[4] Laves, Max-Heinrich, et al.:
+   "Well-calibrated regression uncertainty in medical imaging with deep learning."
+   Medical Imaging with Deep Learning. PMLR, 2020.
+   [Get source online](http://proceedings.mlr.press/v121/laves20a/laves20a.pdf)
+
+[5] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+   "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+   ArXiv preprint arXiv:2207.01242, 2022.
+   [Get source online](https://arxiv.org/pdf/2207.01242.pdf)
\ No newline at end of file
diff --git a/netcal/regularization/README.md b/netcal/regularization/README.md
new file mode 100644
index 0000000..601171b
--- /dev/null
+++ b/netcal/regularization/README.md
@@ -0,0 +1,6 @@
+# Regularization Methods for Confidence Calibration
+
+Regularization methods which are applied during model training. These methods should achieve a
+confidence calibration during model training. For example, the Confidence Penalty
+penalizes confident predictions and prohibits over-confident estimates.
+Use the functions to obtain the regularization and callback instances with prebuild parameters.
\ No newline at end of file
diff --git a/netcal/scaling/README.md b/netcal/scaling/README.md
new file mode 100644
index 0000000..7b065c0
--- /dev/null
+++ b/netcal/scaling/README.md
@@ -0,0 +1,10 @@
+# Scaling Methods for Confidence Calibration
+
+This package consists of several methods for confidence calibration which use confidence scaling to approximate
+confidence estimates to observed accuracy. The most common scaling methods are
+*netcal.scaling.TemperatureScaling*, *netcal.scaling.LogisticCalibration*, and *netcal.scaling.BetaCalibration*.
+Note that all methods can also be applied to object detection and are capable of additional influenting factors
+such as object position and/or shape.
+The advanced methods *netcal.scaling.LogisticCalibrationDependent* and *netcal.scaling.BetaCalibrationDependent*
+are able to better represent possible correlations as the underlying probability distributions are joint
+multivariate distributions with possible correlations.
\ No newline at end of file

From 815e2f559fffa93a558ff0f3ed6cbe07aef8d96f Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:40:28 +0200
Subject: [PATCH 03/21] Update helper files with new statistical methods and
 helper functions.

---
 netcal/AbstractCalibration.py |  46 +--
 netcal/Context.py             |   4 +-
 netcal/Decorator.py           |   4 +-
 netcal/Helper.py              | 560 ++++++++++++++++++++++++++++++++++
 netcal/Stats.py               |  44 ++-
 5 files changed, 614 insertions(+), 44 deletions(-)
 create mode 100644 netcal/Helper.py

diff --git a/netcal/AbstractCalibration.py b/netcal/AbstractCalibration.py
index a07aec1..74ae1bd 100644
--- a/netcal/AbstractCalibration.py
+++ b/netcal/AbstractCalibration.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -7,13 +7,14 @@
 
 import abc, os
 import numpy as np
-from typing import Union, Tuple, Iterable, List
+from typing import Tuple, List, Dict
 from sklearn.base import BaseEstimator, TransformerMixin
 
 import torch
 import torch.nn.functional as F
 
 from netcal import __version__ as version
+from .Helper import squeeze_generic
 from .Decorator import accepts, dimensions
 
 
@@ -68,7 +69,8 @@ def __init__(self, detection: bool = False, independent_probabilities: bool = Fa
             class are treated as independent of each other (sigmoid).
         """
 
-        super().__init__()
+        BaseEstimator.__init__(self)
+        TransformerMixin.__init__(self)
 
         self.detection = detection
         self.num_classes = None
@@ -124,7 +126,7 @@ def fit(self, X: np.ndarray, y: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
         # preprocessing of confidence values given with X
 
         # remove single-dimensional entries if present
-        X = self.squeeze_generic(X, axes_to_keep=0)
+        X = squeeze_generic(X, axes_to_keep=0)
 
         # check shape of input array X and determine number of classes
         # first case: confidence array is 1-D: binary classification problem
@@ -169,7 +171,7 @@ def fit(self, X: np.ndarray, y: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
         # preprocessing of ground truth values given with y
 
         # remove single-dimensional entries if present
-        y = self.squeeze_generic(y, axes_to_keep=0)
+        y = squeeze_generic(y, axes_to_keep=0)
 
         # check shape of ground truth array y
         # array is 2-D: assume one-hot encoded
@@ -244,7 +246,7 @@ def transform(self, X: np.ndarray) -> np.ndarray:
         # preprocessing of confidence values given with X
 
         # remove single-dimensional entries if present
-        X = self.squeeze_generic(X, axes_to_keep=0)
+        X = squeeze_generic(X, axes_to_keep=0)
 
         # got only 1-D array but model was fit for more than 2 classes?
         if len(X.shape) == 1:
@@ -283,7 +285,7 @@ def clear(self):
         self.num_classes = 2 if self.detection else None
         self.independent_probabilities = self._default_independent_probabilities
 
-    def get_params(self, deep=True):
+    def get_params(self, deep=True) -> Dict:
         """
         Get parameters for this estimator.
 
@@ -386,34 +388,6 @@ def load_model(self, filename):
         self.set_params(**params)
         return self
 
-    @classmethod
-    def squeeze_generic(cls, a: np.ndarray, axes_to_keep: Union[int, Iterable[int]]) -> np.ndarray:
-        """
-        Squeeze input array a but keep axes defined by parameter 'axes_to_keep' even if the dimension is
-        of size 1.
-
-        Parameters
-        ----------
-        a : np.ndarray
-            NumPy array that should be squeezed.
-        axes_to_keep : int or iterable
-            Axes that should be kept even if they have a size of 1.
-
-        Returns
-        -------
-        np.ndarray
-            Squeezed array.
-
-        """
-
-        # if type is int, convert to iterable
-        if type(axes_to_keep) == int:
-            axes_to_keep = (axes_to_keep, )
-
-        # iterate over all axes in a and check if dimension is in 'axes_to_keep' or of size 1
-        out_s = [s for i, s in enumerate(a.shape) if i in axes_to_keep or s != 1]
-        return a.reshape(out_s)
-
     @accepts(np.ndarray, np.ndarray, list, str)
     def _calc_model_scores(self, confidences: np.ndarray, ground_truth: np.ndarray,
                            model_list: List['AbstractCalibration'], score_function: str = 'BIC') -> np.ndarray:
diff --git a/netcal/Context.py b/netcal/Context.py
index 2b15013..f8f5f47 100644
--- a/netcal/Context.py
+++ b/netcal/Context.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/netcal/Decorator.py b/netcal/Decorator.py
index 269aaef..69ddc42 100644
--- a/netcal/Decorator.py
+++ b/netcal/Decorator.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/netcal/Helper.py b/netcal/Helper.py
new file mode 100644
index 0000000..9aba5a5
--- /dev/null
+++ b/netcal/Helper.py
@@ -0,0 +1,560 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Union, Iterable, Tuple
+import multiprocessing as mp
+import numpy as np
+
+from scipy.stats import norm, cauchy, chi2
+from scipy.interpolate import interp1d
+
+from .Decorator import global_accepts, global_dimensions
+from .Stats import hpdi
+
+
+@global_accepts((tuple, list))
+def _extract_input(X: Iterable[np.ndarray]) -> Tuple[np.ndarray, np.ndarray, bool]:
+    """
+    Extract input tuple or list. Assert that the input consists of two Numpy arrays containing mean and stddev.
+
+    Parameters
+    ----------
+    X : tuple of two np.ndarray, each of shape (n,)
+        Input data obtained by a model that performs inference with uncertainty.
+        Assert X as a tuple of two NumPy arrays with shape (n,) for each array, where the
+        first array is interpreted as mean and the second one as the according stddev predictions.
+    cov : bool, optional, default: False
+        If True, extract covariance matrix on input instead of single independent variances.
+
+    Returns
+    -------
+    tuple of two np.ndarray and bool
+        Return unpacked mean and stddev/cov and flag if covariance matrix is returned.
+    """
+
+    # assert input data and std dev as input
+    assert len(X) == 2, "If \'X\' is provided with type of {list, tuple}, this methods asserts a length of 2 " \
+                        "with X[0] as the predicted mean and X[1] as the predicted stddev."
+
+    # extract mean and stddev of parameter X
+    mean, stddev = X[0], X[1]
+
+    # if both are passed as lists, convert to numpy arrays
+    mean = squeeze_generic(np.array(mean), axes_to_keep=0)
+    stddev = squeeze_generic(np.array(stddev), axes_to_keep=0)
+
+    assert len(mean) == len(stddev), "Different amount of samples passed for mean and stddev."
+
+    cov = mean.ndim == stddev.ndim - 1
+    if not cov:
+        assert (stddev > 0).all(), "Found zero or negative stddev."
+    else:
+        assert mean.ndim == stddev.ndim - 1, "Asserted covariance matrix, but invalid amount of dimensions passed for mean and cov."
+        assert (np.diagonal(stddev, axis1=-2, axis2=-1) > 0).all(), "Asserted covariance matrix, but found zero or negative variances in cov."
+
+    return mean, stddev, cov
+
+
+def squeeze_generic(a: np.ndarray, axes_to_keep: Union[int, Iterable[int]]) -> np.ndarray:
+    """
+    Squeeze input array a but keep axes defined by parameter 'axes_to_keep' even if the dimension is
+    of size 1.
+
+    Parameters
+    ----------
+    a : np.ndarray
+        NumPy array that should be squeezed.
+    axes_to_keep : int or iterable
+        Axes that should be kept even if they have a size of 1.
+
+    Returns
+    -------
+    np.ndarray
+        Squeezed array.
+    """
+
+    # if type is int, convert to iterable
+    if type(axes_to_keep) == int:
+        axes_to_keep = (axes_to_keep, )
+
+    # iterate over all axes in a and check if dimension is in 'axes_to_keep' or of size 1
+    out_s = [s for i, s in enumerate(a.shape) if i in axes_to_keep or s != 1]
+    return a.reshape(out_s)
+
+
+def meanvar(
+        X: Union[Iterable[np.ndarray], np.ndarray],
+        y: np.ndarray = None
+) -> Union[Tuple[np.ndarray, np.ndarray, bool], Tuple[Tuple[np.ndarray, np.ndarray], np.ndarray, bool]]:
+    """
+    Convert input X to mean and variance. The input might be given either as tuple consisting of NumPy arrays
+    containing mean and stddev. Alternatively, the input might also consist of multiple stochastic samples obtained
+    by a sampling algorithm (e.g. MC dropout).
+
+    It is also possible to convert target y scores in {0, 1} to observed frequencies in [0, 1] to convert a
+    classification to a regression task. For this purpose, the parameters 'classification' and 'bins' control the
+    conversion of the target scores.
+
+    Parameters
+    ----------
+    X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+        Input data for calibration regression obtained by a model that performs inference with uncertainty.
+        Depending on the input format, this method handles the input differently:
+        If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+        first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+        If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+        inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+        case, the mean and stddev is computed automatically.
+    y : np.ndarray of shape (n, [d])
+        Target scores for each prediction estimate in X.
+
+    Returns
+    -------
+    tuple of np.ndarray (mean, var) if y=None or (mean, var), y if y is given, with additional bool
+        Mean and variance obtained by X. If y is given, also return the (probably) converted target scores.
+        Also, always return boolean flag if covariance matrix has been found in input data.
+    """
+
+    # extract input if X is given as iterable
+    if isinstance(X, (tuple, list)):
+        mean, stddev, cov = _extract_input(X)
+
+        # if covariance matrix estimation is enabled, do not square matrix
+        if cov:
+            variance = stddev
+        else:
+            variance = np.square(stddev)
+
+    elif isinstance(X, np.ndarray):
+        # assert input data of multiple stochastic forward passes per sample (e.g. by MC dropout)
+        assert X.ndim >= 2, "If \'X\' is provided as NumPy array, this methods asserts values obtained by " \
+                            "multiple stochastic forward passes (e.g. by MC dropout) of shape (R, N, [D]) with " \
+                            "R forward passes, N number of samples and D dimensions (optional)."
+
+        # TODO: in general, it should be possible to capture covariance matrices here!
+        mean = np.mean(X, axis=0)  # (n, [d])
+        variance = np.var(X, axis=0)  # (n, [d])
+        cov = False
+
+    else:
+        raise ValueError("Parameter \'X\' must be either of type {list, tuple} with mean and stddev passed or "
+                         "of NumPy array of shape (R, N, [D]) with N number of samples, R stochastic forward "
+                         "passes (e.g. by MC dropout) and D dimensions (optional).")
+
+    # remove data dim if d=1
+    mean = squeeze_generic(mean, axes_to_keep=0)
+    variance = squeeze_generic(variance, axes_to_keep=0)
+    if y is not None:
+        y = squeeze_generic(y, axes_to_keep=0)
+        return (mean, variance), y, cov
+    else:
+        return mean, variance, cov
+
+
+@global_dimensions(None, (2, 3))
+def cumulative(X: Union[Iterable[np.ndarray], np.ndarray], y: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
+    """
+    Get cumulative distribution function at y using the moments passed in X. The input X might be given either as tuple
+    consisting of NumPy arrays containing mean and stddev. Alternatively, the input might also consist of multiple
+    stochastic samples obtained by a sampling algorithm (e.g. MC dropout).
+
+    It is also possible to convert target y scores in {0, 1} to observed frequencies in [0, 1] to convert a
+    classification to a regression task. For this purpose, the parameters 'classification' and 'bins' control the
+    conversion of the target scores.
+
+    Parameters
+    ----------
+    X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+        Input data obtained by a model that performs inference with uncertainty.
+        Depending on the input format, this method handles the input differently:
+        If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+        first array as mean and the second one as the according stddev predictions for d dimensions.
+        If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+        inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+        case, the mean and stddev is computed automatically.
+    y : np.ndarray of shape (t, n, [d])
+        Target scores for each prediction estimate in X. If y has dim t, interpret this dimension as multiple
+        points on the CDF curve for each sample.
+
+    Returns
+    -------
+    tuple of np.ndarray (t/y, n, d)
+        Cumulative distribution function of shape (t, n, d). Also return the (probably) converted target scores y.
+    """
+
+    # make y at least 3d (with feature dim if not given)
+    y = np.expand_dims(y, axis=2) if y.ndim == 2 else y  # (t, n, d)
+
+    # extract input if X is given as iterable
+    if isinstance(X, (tuple, list)):
+        mean, stddev, cov = _extract_input(X)
+
+        # catch covariance input
+        if cov:
+            raise RuntimeError("Covariance input is currently not supported for quantile computation.")
+
+        # make mean and stddev at least 2d
+        mean = mean.reshape((-1, 1)) if mean.ndim == 1 else mean  # (n, d)
+        stddev = stddev.reshape((-1, 1)) if stddev.ndim == 1 else stddev  # (n, d)
+
+        # get CDF for the corresponding target scores
+        ret = norm.cdf(y, loc=mean[None, ...], scale=stddev[None, ...])  # (t, n, d)
+
+    elif isinstance(X, np.ndarray):
+        # assert input data of multiple stochastic forward passes per sample (e.g. by MC dropout)
+        assert X.ndim >= 2, "If \'X\' is provided as NumPy array, this methods asserts values obtained by " \
+                            "multiple stochastic forward passes (e.g. by MC dropout) of shape (R, N, [D]) with " \
+                            "R forward passes, N number of samples and D dimensions (optional)."
+
+        # make X at least 3d
+        X = np.expand_dims(X, axis=2) if X.ndim == 2 else X  # (r, n, d)
+
+        # get CDF of each distribution by measuring the fraction of samples below target y
+        ret = np.mean(
+            X[None, ...] <= y[:, None, ...],  # (t, r, n, d)
+            axis=1,
+        )  # (t, n, d)
+
+    else:
+        raise ValueError("Parameter \'X\' must be either of type {list, tuple} with mean and stddev passed or "
+                         "of NumPy array of shape (R, N, [D]) with N number of samples, R stochastic forward "
+                         "passes (e.g. by MC dropout) and D dimensions (optional).")
+
+    return ret, y
+
+
+def _get_density(t, t_mid, pdf):
+    """
+    Helper function for "density_from_cumulative" that performs interpolation for a single sample in a single dim.
+    """
+
+    return interp1d(
+        t_mid,
+        pdf,
+        kind="cubic",
+        bounds_error=False,
+        fill_value="extrapolate",
+    )(t)  # (t,)
+
+
+def density_from_cumulative(t: np.ndarray, cdf: np.ndarray):
+    """
+    Return the probability density function (PDF) given the respective cumulative (CDF) function.
+
+    Parameters
+    ----------
+    t : np.ndarray of shape (t, n, [d])
+        NumPy array that defines the base points (x-axis) of the cumulative distribution function with
+        t sampling points, n samples and d dimensions.
+    cdf : np.ndarray of shape (t, n, [d])
+        NumPy array with actual cumulative scores for each t with t sampling points, n samples and d dimensions.
+
+    Returns
+    -------
+    np.ndarray of shape (t, n, d)
+        Probability density function at points t.
+    """
+
+    t = np.expand_dims(t, axis=2) if t.ndim == 2 else t
+    cdf = np.expand_dims(cdf, axis=2) if cdf.ndim == 2 else cdf
+
+    _, n_samples, n_dims = t.shape
+
+    # instead of using diffs built-in prepend method, we manually repeat the first PDF score to obtain
+    # the same dimension as for CDF
+    delta_t = np.clip(np.diff(t, axis=0), a_min=np.finfo(np.float32).eps, a_max=None)  # (t-1, n, d)
+    pdf = np.diff(cdf, axis=0) / delta_t  # (t-1, n, d)
+
+    # at this point, the density is defined between the sampling points. Use interpolation to scale them back
+    t_mid = (t[:-1, ...] + t[1:, ...]) / 2  # (t-1, n, d)
+
+    density = []
+    for d in range(n_dims):
+        results = [_get_density(t[:, n, d], t_mid[:, n, d], pdf[:, n, d]) for n in range(n_samples)]
+
+        results = np.stack(results, axis=1)  # (t, n)
+        density.append(results)
+
+    density = np.stack(density, axis=2)  # (t, n, d)
+
+    return density
+
+
+def cumulative_moments(t: np.ndarray, cdf: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
+    """
+    Return mean and variance of a probability distribution that is defined by a cumulative distribution.
+
+    Parameters
+    ----------
+    t : np.ndarray of shape (t, n, [d])
+        NumPy array that defines the base points (x-axis) of the cumulative distribution function with
+        t sampling points, n samples and d dimensions.
+    cdf : np.ndarray of shape (t, n, [d])
+        NumPy array with actual cumulative scores for each t with t sampling points, n samples and d dimensions.
+
+    Returns
+    -------
+    Tuple of 2 np.ndarray, both of shape (n, d)
+        Mean and variance for each input sample and for each dimension.
+    """
+
+    t = np.expand_dims(t, axis=2) if t.ndim == 2 else t
+    cdf = np.expand_dims(cdf, axis=2) if cdf.ndim == 2 else cdf
+
+    delta_cdf = np.diff(cdf, axis=0)  # (t-1, n, [d])
+    t = (t[:-1, ...] + t[1:, ...]) / 2  # (t-1, n, [d])
+
+    mean = np.sum(t * delta_cdf, axis=0)
+    var = np.sum(np.square(t) * delta_cdf, axis=0) - np.square(mean)
+
+    return mean, var
+
+
+def is_in_quantile(
+        X: Union[Iterable[np.ndarray], np.ndarray],
+        y: np.ndarray,
+        q: Union[float, Iterable[float], np.ndarray],
+        kind: str
+) -> Tuple[np.ndarray, np.ndarray, Tuple[np.ndarray, np.ndarray], np.ndarray, np.ndarray]:
+    """
+    Determine if the ground-truth information :math:`Y` is in the prediction interval of a predicted probabilitiy
+    distribution specified by :math:`X` for q certain quantile level :math:`\\tau`.
+
+    Parameters
+    ----------
+    X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+        Input data obtained by a model that performs inference with uncertainty.
+        See parameter "kind" for input format descriptions.
+    y : np.ndarray of shape (n, [d])
+        Target scores for each prediction estimate in X.
+    q : np.ndarray of shape (q,)
+        Quantile scores in [0, 1] of size q to compute the x-valued quantile boundaries for.
+    kind : str, either "meanstd" or "cumulative"
+        Specify the kind of the input data. Might be one of:
+        - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+                   first array as mean and the second one as the according stddev predictions for d dimensions.
+                   If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                   inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes.
+                   In this case, the mean and stddev is computed automatically.
+        - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                      for sample n (and optionally d dimensions).
+
+    Returns
+    -------
+    tuple of 4 np.ndarray
+        Tuple with four NumPy arras:
+        (1) Boolean flag for each input sample if ground-truth y is in a certain prediction interval
+            specified by quantile level q.
+        (2) Quantile boundaries for each quantile q w.r.t. distributions given by X. Note that we're working with
+            two-sided quantiles. Thus, we return either the lower or the upper quantile boundary, depending on its
+            distance to the target score given by Y.
+        (3) Tuple with lower and upper quantile boundaries.
+        (4) Parametric mean.
+        (5) Parametric variance/covariance.
+    """
+    assert kind in ['meanstd', 'cauchy', 'cumulative'], 'Parameter \'kind\' must be either \'meanstd\', or \'cumulative\'.'
+
+    # if quantiles are given as list or float, convert to numpy array
+    q = squeeze_generic(np.array(q), axes_to_keep=0).reshape((-1,))  # (q,)
+    alpha = 1. - q  # (q,)
+
+    # make y at least 2d
+    y = np.expand_dims(y, axis=1) if y.ndim == 1 else y  # (n, d)
+
+    if kind == 'cumulative':
+
+        t, cdf = X[0], X[1]  # (t, n, [d])
+
+        # make CDF at least 3d
+        t = np.expand_dims(t, axis=2) if t.ndim == 2 else t  # (t, n, d)
+        cdf = np.expand_dims(cdf, axis=2) if cdf.ndim == 2 else cdf  # (t, n, d)
+
+        alpha = alpha.reshape((-1, 1, 1, 1))  # (q, 1, 1, 1)
+
+        # for the moment, use the nearest point of the curve
+        # cdf has shape (t, n), q has shape (q,)
+        nearest_min = np.argmin(
+            np.abs(cdf[None, ...] - (alpha / 2.)),  # (q, t, n, d)
+            axis=1
+        )  # (q, n, d)
+
+        nearest_max = np.argmin(
+            np.abs(cdf[None, ...] - (1. - (alpha / 2.))),  # (q, t, n, d)
+            axis=1
+        )  # (q, n, d)
+
+        # extract the interval boundaries and check if y is within prediction interval
+        qbounds_min = np.take_along_axis(t, nearest_min, axis=0)  # (q, n, d)
+        qbounds_max = np.take_along_axis(t, nearest_max, axis=0)  # (q, n, d)
+
+        in_quantile = (y[None, ...] >= qbounds_min) & (y[None, ...] <= qbounds_max)  # (q, n, d)
+
+        # now choose the quantile boundaries that are closer to our ground-truth Y
+        qbounds_next = np.where(
+            np.abs(qbounds_min - y[None, ...]) < np.abs(qbounds_max - y[None, ...]),
+            qbounds_min,
+            qbounds_max
+        )  # (q, n, d)
+
+        qbounds = (qbounds_min, qbounds_max)
+
+        # calculate mean and variance from cumulative
+        mean, var = cumulative_moments(t, cdf)
+
+    # Cauchy distribution is given - check if samples are within two-sided quantile boundaries
+    elif kind == 'cauchy':
+
+        mode, scale = X[0], X[1]  # (t, n, [d])
+
+        # catch if multivariate Cauchy with correlations is given
+        if scale.ndim > mode.ndim:
+            raise RuntimeError("Multivariate Cauchy with correlations is currently not supported.")
+
+        # make mode and scale at least 2d
+        mode = mode.reshape((-1, 1)) if mode.ndim == 1 else mode  # (n, d)
+        scale = scale.reshape((-1, 1)) if scale.ndim == 1 else scale  # (n, d)
+
+        alpha = alpha.reshape((-1, 1, 1))  # (q, 1, 1)
+        qbounds_min = cauchy.ppf(alpha / 2., loc=mode[None, ...], scale=scale[None, ...])  # (q, n, d)
+        qbounds_max = cauchy.ppf(1. - (alpha / 2.), loc=mode[None, ...], scale=scale[None, ...])  # (q, n, d)
+
+        in_quantile = (y[None, ...] >= qbounds_min) & (y[None, ...] <= qbounds_max)  # (q, n, d)
+
+        # now choose the quantile boundaries that are closer to our ground-truth Y
+        qbounds_next = np.where(
+            np.abs(qbounds_min - y[None, ...]) < np.abs(qbounds_max - y[None, ...]),
+            qbounds_min,
+            qbounds_max
+        )  # (q, n, d)
+
+        qbounds = (qbounds_min, qbounds_max)
+
+        # TODO: surrogate fix, edit names!
+        mean = mode
+        var = scale ** 2
+
+    else:
+
+        # get quantile bounds and convert q to numpy array (if not already given)
+        # extract input if X is given as iterable
+        if isinstance(X, (tuple, list)):
+            mean, stddev, cov = _extract_input(X)
+
+            # make mean and stddev at least 2d
+            mean = mean.reshape((-1, 1)) if mean.ndim == 1 else mean  # (n, d)
+
+            # if covariance matrix is given in input, compute the multivariate HDR using the
+            # Mahalanobis distance and the chi2 test for multivariate normal
+            if cov:
+
+                # get number of dimensions (necessary for chi2 distribution)
+                ndims = mean.shape[-1]
+
+                # reshape cov to the right dimensions
+                cov = np.expand_dims(stddev, axis=-1) if stddev.ndim == 2 else stddev  # (n, d, d)
+                var = cov
+
+                # try matrix inversion and get eigenvalues and eigenvectors to determine the isolines
+                # of multivariate normal
+                try:
+                    invcov = np.linalg.inv(cov)  # (n, d, d)
+                except np.linalg.LinAlgError:
+                    raise RuntimeError("Input covariance matrices are not positive semidefinite.")
+
+                # reshape diff to the right dimensions and compute Mahalanobis distance
+                diff = np.expand_dims(y - mean, axis=-1)  # (n, d, 1)
+                mahalanobis = np.transpose(diff, axes=(0, 2, 1)) @ invcov @ diff  # (n, 1, 1)
+                mahalanobis = np.squeeze(mahalanobis, axis=(1, 2))  # (n,)
+
+                # currently, qbounds is not defined/implemented for multivariate normal distributions
+                qbounds_next = None
+                qbounds = (None, None)
+
+            # in the independent case, we also use the Mahalanobis distance but for each dimension separately
+            else:
+
+                ndims = 1
+                stddev = stddev.reshape((-1, 1)) if stddev.ndim == 1 else stddev  # (n, d)
+
+                # use the variance to compute the Mahalanobis distance
+                # in the _extract_input function, we already guarantee nonzero variances
+                var = np.square(stddev)  # (n, d)
+                mahalanobis = np.divide(np.square(y - mean), var)  # (n, d)
+
+                # since we're working with two-sided quantiles, we choose the quantile boundaries that
+                # are closer to our ground-truth target Y
+                qbounds_min = norm.ppf(
+                    np.expand_dims(alpha / 2., axis=(1, 2)),  # (q, 1, 1)
+                    loc=mean[None, ...],  # (1, n, d)
+                    scale=stddev[None, ...]  # (1, n, d)
+                )  # (q, n, d)
+
+                qbounds_max = norm.ppf(
+                    np.expand_dims(1. - (alpha / 2.), axis=(1, 2)),  # (q, 1, 1)
+                    loc=mean[None, ...],  # (1, n, d)
+                    scale=stddev[None, ...]  # (1, n, d)
+                )  # (q, n, d)
+
+                # now choose the quantile boundaries that are closer to our ground-truth Y
+                qbounds_next = np.where(
+                    np.abs(qbounds_min - y[None, ...]) < np.abs(qbounds_max - y[None, ...]),
+                    qbounds_min,
+                    qbounds_max
+                )
+
+                qbounds = (qbounds_min, qbounds_max)
+
+            # to test for a two-sided quantile coverage, use the (single-sided) chi2 quantile
+            # and compare with Mahalanobis distance
+            chi2_bounds = chi2.ppf(q, df=ndims)  # (q,)
+            chi2_bounds = np.expand_dims(chi2_bounds, axis=list(np.array(range(mahalanobis.ndim)) + 1))  # (q, 1, [1])
+
+            # finally, check if mahalanobis distance is below requested chi2 quantile boundary
+            # this is valid for two-sided Gaussian quantiles
+            in_quantile = mahalanobis[None, ...] <= chi2_bounds  # (q, n, [d])
+
+        elif isinstance(X, np.ndarray):
+
+            # assert input data of multiple stochastic forward passes per sample (e.g. by MC dropout)
+            assert X.ndim >= 2, "If \'X\' is provided as NumPy array, this methods asserts values obtained by " \
+                                "multiple stochastic forward passes (e.g. by MC dropout) of shape (R, N, [D]) with " \
+                                "R forward passes, N number of samples and D dimensions (optional)."
+
+            # make X at least 3d
+            X = np.expand_dims(X, axis=2) if X.ndim == 2 else X  # (r, n, d)
+
+            # on inference mode, get two-sided quantile bounds for remapped CDF scores
+            # use HPDI to get the quantile bounds
+            qbounds_min, qbounds_max = [], []
+            for prob in q:
+                qbounds_next = hpdi(X, prob=prob, axis=0)  # (2, n, d)
+                qbounds_min.append(qbounds_next[0])
+                qbounds_max.append(qbounds_next[1])
+
+            qbounds_min = np.stack(qbounds_min, axis=0)  # (q, n, d)
+            qbounds_max = np.stack(qbounds_max, axis=0)  # (q, n, d)
+
+            in_quantile = (y[None, ...] >= qbounds_min) & (y[None, ...] <= qbounds_max)  # (q, n, d)
+
+            # now choose the quantile boundaries that are closer to our ground-truth Y
+            qbounds_next = np.where(
+                np.abs(qbounds_min - y[None, ...]) < np.abs(qbounds_max - y[None, ...]),
+                qbounds_min,
+                qbounds_max
+            )
+
+            qbounds = (qbounds_min, qbounds_max)
+
+            mean = np.mean(X, axis=0)  # (n, d)
+            var = np.var(X, axis=0)  # (n, d)
+
+        else:
+            raise ValueError("Parameter \'X\' must be either of type {list, tuple} with mean and stddev passed or "
+                             "of NumPy array of shape (R, N, [D]) with N number of samples, R stochastic forward "
+                             "passes (e.g. by MC dropout) and D dimensions (optional).")
+
+    return in_quantile, qbounds_next, qbounds, mean, var
diff --git a/netcal/Stats.py b/netcal/Stats.py
index 7684d02..264e859 100644
--- a/netcal/Stats.py
+++ b/netcal/Stats.py
@@ -1,7 +1,5 @@
-# Copyright (C) 2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
-# Copyright (C) 2019-2020 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Visteon Electronics Germany GmbH, Kerpen, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -10,6 +8,7 @@
 # Parts of this file have been adapted from NumPyro: https://github.com/pyro-ppl/numpyro/blob/master/numpyro/diagnostics.py
 
 import numpy as np
+import torch
 
 
 def hpdi(x, prob=0.90, axis=0):
@@ -47,3 +46,40 @@ def hpdi(x, prob=0.90, axis=0):
     hpd_right = np.swapaxes(hpd_right, axis, 0)
 
     return np.concatenate([hpd_left, hpd_right], axis=axis)
+
+
+def mv_cauchy_log_density(value: torch.Tensor, loc: torch.Tensor, cov: torch.Tensor):
+    """
+    Computes the log of the density function of a multivariate Cauchy distribution at vector "value" for a Cauchy
+    distribution that is specified by "loc" and "cov".
+
+    Parameters
+    ----------
+    value : torch.Tensor of shape (n, d)
+        Location at which the log density is calcualted for each sample n with d dimensions.
+    loc : torch.Tensor of shape (n, d)
+        Mode/location parameter of the multivariate Cauchy for each sample n with d dimensions.
+    cov : torch.Tensor of shape (n, d, d)
+        Covariance matrix of the multivariate Cauchy for each sample n with d dimensions.
+
+    Returns
+    -------
+    torch.Tensor of shape (n,)
+        Log density of the multivariate Cauchy for each sample n.
+    """
+
+    diff = torch.unsqueeze(value - loc, dim=-1)  # ([1], n, d, 1)
+    invcov = torch.linalg.inv(cov)
+
+    n_dims = torch.tensor(loc.shape[-1], dtype=diff.dtype)
+
+    const = torch.lgamma((n_dims + 1) / 2.) - \
+            torch.lgamma(torch.tensor(0.5)) - \
+            (n_dims / 2) * torch.log(torch.tensor(np.pi))  # scalar
+
+    logdet = 0.5 * torch.logdet(cov)  # ([r], n)
+    mahalanobis = torch.transpose(diff, dim0=-2, dim1=-1) @ invcov @ diff  # ([r], n, 1, 1)
+
+    log_density = const - logdet - ((n_dims + 1) / 2.) * torch.log(1. + mahalanobis[..., 0, 0])  # ([r], n)
+
+    return log_density

From 965757f6ddf3604276ab7241f87381b15f620b72 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:41:33 +0200
Subject: [PATCH 04/21] Update copyright in binning package. Minor bugfixes in
 documentation.

---
 netcal/binning/BBQ.py                    | 10 ++++++----
 netcal/binning/ENIR.py                   | 10 ++++++----
 netcal/binning/HistogramBinning.py       | 14 ++++++++------
 netcal/binning/IsotonicRegression.py     | 10 ++++++----
 netcal/binning/NearIsotonicRegression.py |  7 ++++---
 netcal/binning/__init__.py               |  9 ++++-----
 6 files changed, 34 insertions(+), 26 deletions(-)

diff --git a/netcal/binning/BBQ.py b/netcal/binning/BBQ.py
index a2ea290..17abf89 100644
--- a/netcal/binning/BBQ.py
+++ b/netcal/binning/BBQ.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -15,7 +15,9 @@
 
 class BBQ(AbstractCalibration):
     """
-    Bayesian Binning into Quantiles (BBQ) [1]_. This method utilizes multiple :class:`HistogramBinning`
+    Bayesian Binning into Quantiles (BBQ).
+    This method has been proposed by [1]_.
+    This method utilizes multiple :class:`HistogramBinning`
     instances with different amounts of bins and computes a weighted sum of all methods to obtain a
     well-calibrated confidence estimate. The scoring function "BDeu", which is proposed in the original paper,
     is currently not supported.
@@ -78,7 +80,7 @@ class are treated as independent of each other (sigmoid).
     .. [1] Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
        "Obtaining well calibrated probabilities using bayesian binning."
        Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
-       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`_
+       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`__
 
     """
 
diff --git a/netcal/binning/ENIR.py b/netcal/binning/ENIR.py
index 3645b2a..aa29388 100644
--- a/netcal/binning/ENIR.py
+++ b/netcal/binning/ENIR.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -12,7 +12,9 @@
 
 class ENIR(AbstractCalibration):
     """
-    Ensemble of Near Isotonic Regression (ENIR) models [1]_. These models allow - in contrast to standard
+    Ensemble of Near Isotonic Regression (ENIR) models.
+    This method has initially been proposed by [1]_.
+    These models allow - in contrast to standard
     :class:`IsotonicRegression` method - a violation of the monotony restrictions. Using the *modified
     Pool-Adjacent-Violators Algorithm (mPAVA)*, this method build multiple Near Isotonic Regression models
     and weights them by a certain score function.
@@ -74,7 +76,7 @@ class are treated as independent of each other (sigmoid).
     .. [1] Naeini, Mahdi Pakdaman, and Gregory F. Cooper:
        "Binary classifier calibration using an ensemble of near isotonic regression models."
        2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE, 2016.
-       `Get source online <https://ieeexplore.ieee.org/iel7/7837023/7837813/07837860.pdf>`_
+       `Get source online <https://ieeexplore.ieee.org/iel7/7837023/7837813/07837860.pdf>`__
     """
 
     @accepts(str, bool, bool, bool)
diff --git a/netcal/binning/HistogramBinning.py b/netcal/binning/HistogramBinning.py
index 4f050ee..4293d12 100644
--- a/netcal/binning/HistogramBinning.py
+++ b/netcal/binning/HistogramBinning.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -13,7 +13,9 @@
 
 class HistogramBinning(AbstractCalibration):
     """
-    Simple Histogram Binning calibration method [1]_. Each prediction is sorted into a bin
+    Simple Histogram Binning calibration method.
+    This method has been proposed by [1]_.
+    Each prediction is sorted into a bin
     and assigned its calibrated confidence estimate. This method normally works for binary
     classification. For multiclass classification, this method is applied into a 1-vs-all manner [2]_.
 
@@ -46,16 +48,16 @@ class are treated as independent of each other (sigmoid).
     .. [1] Zadrozny, Bianca and Elkan, Charles:
        "Obtaining calibrated probability estimates from decision trees and naive bayesian classifiers."
        In ICML, pp. 609–616, 2001.
-       `Get source online <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.3039&rep=rep1&type=pdf>`_
+       `Get source online <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.3039&rep=rep1&type=pdf>`__
 
     .. [2] Zadrozny, Bianca and Elkan, Charles:
        "Transforming classifier scores into accurate multiclass probability estimates."
        In KDD, pp. 694–699, 2002.
-       `Get source online <https://www.researchgate.net/profile/Charles_Elkan/publication/2571315_Transforming_Classifier_Scores_into_Accurate_Multiclass_Probability_Estimates/links/0fcfd509ae852a8bb9000000.pdf>`_
+       `Get source online <https://www.researchgate.net/profile/Charles_Elkan/publication/2571315_Transforming_Classifier_Scores_into_Accurate_Multiclass_Probability_Estimates/links/0fcfd509ae852a8bb9000000.pdf>`__
 
     .. [3] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
-       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.
+       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
     """
 
     @accepts((int, tuple, list), bool, bool, bool)
diff --git a/netcal/binning/IsotonicRegression.py b/netcal/binning/IsotonicRegression.py
index f26d85d..12b4ada 100644
--- a/netcal/binning/IsotonicRegression.py
+++ b/netcal/binning/IsotonicRegression.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -12,7 +12,9 @@
 
 class IsotonicRegression(AbstractCalibration):
     """
-    Isotonic Regression method [1]_. This method is similar to :class:`HistogramBinning` but with dynamic bin sizes
+    Isotonic Regression method.
+    This method has initially been proposed by [1]_.
+    This method is similar to :class:`HistogramBinning` but with dynamic bin sizes
     and boundaries. A piecewise constant function gets fit to ground truth labels sorted by
     given confidence estimates.
 
@@ -33,7 +35,7 @@ class are treated as independent of each other (sigmoid).
     .. [1] Zadrozny, Bianca and Elkan, Charles:
        "Transforming classifier scores into accurate multiclass probability estimates."
        In KDD, pp. 694–699, 2002.
-       `Get source online <https://www.researchgate.net/profile/Charles_Elkan/publication/2571315_Transforming_Classifier_Scores_into_Accurate_Multiclass_Probability_Estimates/links/0fcfd509ae852a8bb9000000.pdf>`_
+       `Get source online <https://www.researchgate.net/profile/Charles_Elkan/publication/2571315_Transforming_Classifier_Scores_into_Accurate_Multiclass_Probability_Estimates/links/0fcfd509ae852a8bb9000000.pdf>`__
     """
 
     @accepts(bool, bool)
diff --git a/netcal/binning/NearIsotonicRegression.py b/netcal/binning/NearIsotonicRegression.py
index d957f85..081b85a 100644
--- a/netcal/binning/NearIsotonicRegression.py
+++ b/netcal/binning/NearIsotonicRegression.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -12,7 +12,8 @@
 
 class NearIsotonicRegression(AbstractCalibration):
     """
-    Near Isotonic Regression Calibration method [1]_ (commonly used by :class:`ENIR` [2]_).
+    Near Isotonic Regression Calibration method.
+    Has been proposed by [1]_ and is commonly used by :class:`ENIR` [2]_.
 
     Parameters
     ----------
diff --git a/netcal/binning/__init__.py b/netcal/binning/__init__.py
index 7d5c0e4..2f6a139 100644
--- a/netcal/binning/__init__.py
+++ b/netcal/binning/__init__.py
@@ -1,14 +1,13 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
 """
-Binning methods for confidence calibration.
-This package consists of several methods for confidence calibration which use binning to approximate
-confidence estimates to the measured accuracy.
+.. include:: /../../netcal/binning/README.md
+   :parser: myst_parser.sphinx_
 
 Available classes
 =================

From 4ee2c3971c418a3d8cb8979788662ccfee343630 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:43:59 +0200
Subject: [PATCH 05/21] Make flexible data precision in scaling package
 depending on the provided data. Update copyright. Minor bugfixes in
 documentation.

---
 netcal/scaling/AbstractLogisticRegression.py  | 42 +++++++------
 netcal/scaling/BetaCalibration.py             | 45 +++++++++-----
 netcal/scaling/BetaCalibrationDependent.py    | 38 ++++++++----
 netcal/scaling/LogisticCalibration.py         | 38 +++++++-----
 .../scaling/LogisticCalibrationDependent.py   | 62 ++++++++++---------
 netcal/scaling/TemperatureScaling.py          | 19 +++---
 netcal/scaling/__init__.py                    |  9 ++-
 7 files changed, 146 insertions(+), 107 deletions(-)

diff --git a/netcal/scaling/AbstractLogisticRegression.py b/netcal/scaling/AbstractLogisticRegression.py
index 4020d7a..f07b936 100644
--- a/netcal/scaling/AbstractLogisticRegression.py
+++ b/netcal/scaling/AbstractLogisticRegression.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -28,7 +28,7 @@
 from pyro.optim import Adam, SGD
 import pyro.distributions as dist
 
-from netcal import AbstractCalibration, dimensions, accepts, manual_seed
+from netcal import AbstractCalibration, dimensions, accepts, manual_seed, squeeze_generic
 
 
 class AbstractLogisticRegression(AbstractCalibration):
@@ -209,10 +209,15 @@ def prepare(self, X: np.ndarray) -> torch.Tensor:
         return torch.Tensor(X).to(self._device)
 
     @abc.abstractmethod
-    def prior(self):
+    def prior(self, dtype: torch.dtype):
         """
         Prior definition of the weights and intercept used for log regression. This function has to set the
         sites at least for "weights" and "bias".
+
+        Parameters
+        ----------
+        dtype: torch.dtype
+            Data type of the input data so that the priors are initialized with the same precision.
         """
 
         raise NotImplementedError()
@@ -361,7 +366,7 @@ def fit(self, X: np.ndarray, y: np.ndarray, random_state: int = None, tensorboar
         self.num_features = X.shape[1] if self.detection else 1
 
         # initialize priors
-        self.prior()
+        self.prior(dtype=data.dtype)
 
         # mark first dimension as independent
         for site in self._sites.values():
@@ -447,7 +452,7 @@ def log(kernel, samples, stage, i):
                     warmup_steps=self.mcmc_warmup,
                     num_chains=self.mcmc_chains,
                     hook_fn=log)
-        mcmc.run(data.float(), y.float())
+        mcmc.run(data, y.to(dtype=data.dtype))
 
         # get samples from MCMC chains and store weights
         samples = mcmc.get_samples()
@@ -468,14 +473,10 @@ def variational(self, data: torch.Tensor, y: torch.Tensor, tensorboard: bool, lo
             NumPy array with ground truth labels as 1-D vector (binary).
         """
 
-        # explicitly define datatype
-        data = data.float()
-        y = y.float()
-
         num_samples = data.shape[0]
 
         # create dataset
-        lr_dataset = torch.utils.data.TensorDataset(data, y)
+        lr_dataset = torch.utils.data.TensorDataset(data, y.to(dtype=data.dtype))
         data_loader = DataLoader(dataset=lr_dataset, batch_size=1024, pin_memory=False)
 
         # define optimizer
@@ -553,7 +554,7 @@ def MLE(w, x, y):
         # this might be necessary for the optimizer
         data = data.double()
         initial_weights = np.concatenate(
-            [site['init']['mean'].cpu().numpy().astype(np.float64) for site in self._sites.values()]
+            [site['init']['mean'].cpu().numpy() for site in self._sites.values()]
         )
 
         # on detection or binary classification, use binary cross entropy loss and convert target vector to double
@@ -581,7 +582,7 @@ def loss_op(x, y):
         start = 0
         for name, site in self._sites.items():
             num_weights = len(site['init']['mean'])
-            site['values'] = result.x[start:start + num_weights].astype(np.float32)
+            site['values'] = result.x[start:start + num_weights]
             start += num_weights
 
         # on some methods like Beta calibration, it is necessary to repeat the optimization
@@ -599,7 +600,7 @@ def loss_op(x, y):
         start = 0
         for name, site in self._sites.items():
             num_weights = len(site['init']['mean'])
-            site['values'] = result.x[start:start + num_weights].astype(np.float32)
+            site['values'] = result.x[start:start + num_weights]
             start += num_weights
 
     def momentum(self, data: torch.Tensor, y: torch.Tensor, tensorboard: bool, log_dir: str):
@@ -624,7 +625,7 @@ def momentum(self, data: torch.Tensor, y: torch.Tensor, tensorboard: bool, log_d
         criterion = nn.BCEWithLogitsLoss(reduction='mean')
 
         # create dataset
-        lr_dataset = torch.utils.data.TensorDataset(data.double(), y.double())
+        lr_dataset = torch.utils.data.TensorDataset(data, y.to(dtype=data.dtype))
         data_loader = DataLoader(dataset=lr_dataset, batch_size=batch_size, pin_memory=False)
 
         # init model and optimizer
@@ -739,7 +740,8 @@ def process_model(weights: dict) -> torch.Tensor:
         self.to(self._device)
 
         # convert input data and weights to torch (and possibly to CUDA)
-        data = self.prepare(X).float().to(self._device)
+        data = self.prepare(X).to(self._device)
+        num_data = data.shape[0]
 
         # if weights is 2-D matrix, we are in sampling mode
         # treat each row as a separate weights vector
@@ -766,7 +768,7 @@ def process_model(weights: dict) -> torch.Tensor:
 
                 # on MLE without uncertainty, only return the single model estimate
                 calibrated = process_model(weights).cpu().numpy()
-                calibrated = self.squeeze_generic(calibrated, axes_to_keep=0)
+                calibrated = squeeze_generic(calibrated, axes_to_keep=0)
             else:
 
                 parameter = []
@@ -791,7 +793,7 @@ def process_model(weights: dict) -> torch.Tensor:
                     raise ValueError("Internal error: neither MCMC nor variational model given.")
 
                 # remove unnecessary dims that possibly occur on MCMC or VI
-                samples = {k: torch.reshape(v, (num_samples, -1)) for k, v in samples.items()}
+                samples = {k: torch.squeeze(v, dim=1) for k, v in samples.items()}
 
                 # iterate over all parameter sets
                 for i in range(num_samples):
@@ -812,7 +814,7 @@ def process_model(weights: dict) -> torch.Tensor:
 
                 # stack all calibrated estimates along axis 0 and calculate stddev as well as mean
                 calibrated = torch.stack(calibrated, dim=0).cpu().numpy()
-                calibrated = self.squeeze_generic(calibrated, axes_to_keep=(0, 1))
+                calibrated = squeeze_generic(calibrated, axes_to_keep=(0, 1))
         else:
 
             # extract all weight values of sites and store into single dict
@@ -822,7 +824,7 @@ def process_model(weights: dict) -> torch.Tensor:
 
             # on MLE without uncertainty, only return the single model estimate
             calibrated = process_model(weights).cpu().numpy()
-            calibrated = self.squeeze_generic(calibrated, axes_to_keep=0)
+            calibrated = squeeze_generic(calibrated, axes_to_keep=0)
 
         # delete torch data tensor
         del data
diff --git a/netcal/scaling/BetaCalibration.py b/netcal/scaling/BetaCalibration.py
index 15d3990..cc6c6d3 100644
--- a/netcal/scaling/BetaCalibration.py
+++ b/netcal/scaling/BetaCalibration.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -78,6 +78,8 @@ class BetaCalibration(AbstractLogisticRegression):
     :math:`c=\\sum_k \\log B(\\alpha_k^-, \\beta_k^-) - \\log B(\\alpha_k^+, \\beta_k^+)`.
     We utilize standard optimization methods to determine the calibration mapping :math:`g(s)`.
 
+    Capturing epistemic uncertainty of the calibration method is also able with this implementation [3]_.
+
     Parameters
     ----------
     method : str, default: "mle"
@@ -115,11 +117,11 @@ class are treated as independent of each other (sigmoid).
     .. [1] Kull, Meelis, Telmo Silva Filho, and Peter Flach:
        "Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers"
        Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
-       `Get source online <http://proceedings.mlr.press/v54/kull17a/kull17a.pdf>`_
+       `Get source online <http://proceedings.mlr.press/v54/kull17a/kull17a.pdf>`__
 
     .. [2] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
-       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.
+       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 
     .. [3] Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
        "Bayesian Confidence Calibration for Epistemic Uncertainty Modelling."
@@ -200,12 +202,17 @@ def prepare(self, X: np.ndarray) -> torch.Tensor:
             data_input = np.log(data_input)
             data_input[..., 1] *= -1
 
-        return torch.tensor(data_input)
+        return torch.from_numpy(data_input)
 
-    def prior(self):
+    def prior(self, dtype: torch.dtype):
         """
         Prior definition of the weights used for log regression. This function has to set the
         variables 'self.weight_prior_dist', 'self.weight_mean_init' and 'self.weight_stddev_init'.
+
+        Parameters
+        ----------
+        dtype: torch.dtype
+            Data type of the input data so that the priors are initialized with the same precision.
         """
 
         self._sites = OrderedDict()
@@ -224,10 +231,10 @@ def prior(self):
                     'values': None,
                     'constraint': constraints.real,
                     'init': {
-                        'mean': torch.ones(feature_weights),
-                        'scale': torch.ones(feature_weights)
+                        'mean': torch.ones(feature_weights, dtype=dtype),
+                        'scale': torch.ones(feature_weights, dtype=dtype)
                     },
-                    'prior': dist.Normal(torch.ones(feature_weights), 10 * torch.ones(feature_weights), validate_args=True),
+                    'prior': dist.Normal(torch.ones(feature_weights, dtype=dtype), 10 * torch.ones(feature_weights, dtype=dtype), validate_args=True),
                 }
 
         # on multiclass classification, we have one weight and one bias for each class separately
@@ -236,8 +243,8 @@ def prior(self):
             num_weights = 2*self.num_classes
 
         # initialize weight mean by ones and set prior distribution
-        init_mean = torch.ones(num_weights)
-        init_scale = torch.ones(num_weights)
+        init_mean = torch.ones(num_weights, dtype=dtype)
+        init_scale = torch.ones(num_weights, dtype=dtype)
         prior = dist.Normal(init_mean, 10 * init_scale, validate_args=True)
 
         # we have constraints on the weights for the confidence
@@ -266,10 +273,10 @@ def prior(self):
             'values': None,
             'constraint': constraints.real,
             'init': {
-                'mean': torch.zeros(num_bias),
-                'scale': torch.ones(num_bias)
+                'mean': torch.zeros(num_bias, dtype=dtype),
+                'scale': torch.ones(num_bias, dtype=dtype)
             },
-            'prior': dist.Normal(torch.zeros(num_bias), 10 * torch.ones(num_bias), validate_args=True)
+            'prior': dist.Normal(torch.zeros(num_bias, dtype=dtype), 10 * torch.ones(num_bias, dtype=dtype), validate_args=True)
         }
 
     def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
@@ -302,7 +309,13 @@ def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
 
             # on MCMC sampling, extreme values might occur and can cause an 'inf'
             # this will result in invalid prob values - catch infs and set to log of max value
-            weights[torch.isinf(weights)] = torch.log(torch.tensor(torch.finfo(weights.dtype).max))
+            weights[torch.isinf(weights)] = torch.log(
+                torch.tensor(
+                    torch.finfo(weights.dtype).max,
+                    dtype=weights.dtype,
+                    device=weights.device
+                )
+            )
 
         # additional weights are extra weights for extra features (on detection mode)
         if "feature_weights" in self._sites.keys():
@@ -316,7 +329,7 @@ def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
                 weights = torch.reshape(weights, (-1, 1))
 
                 # compute logits and remove unnecessary dimensions
-                logit = torch.squeeze(torch.matmul(X, weights) + bias)
+                logit = torch.squeeze(torch.matmul(X, weights) + bias, dim=1)
                 probs = torch.sigmoid(logit)
                 dist_op = dist.Bernoulli
 
diff --git a/netcal/scaling/BetaCalibrationDependent.py b/netcal/scaling/BetaCalibrationDependent.py
index 28e6710..84719b9 100644
--- a/netcal/scaling/BetaCalibrationDependent.py
+++ b/netcal/scaling/BetaCalibrationDependent.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -84,6 +84,7 @@ class BetaCalibrationDependent(AbstractLogisticRegression):
     This is optimized by an Adam optimizer with a learning rate of 1e-3 and a batch size of 256 for
     1000 iterations (default).
 
+    Capturing epistemic uncertainty of the calibration method is also able with this implementation [3]_.
 
     Parameters
     ----------
@@ -116,7 +117,7 @@ class are treated as independent of each other (sigmoid).
     ----------
     .. [1] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
-       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.
+       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 
     .. [2] Libby, David L., and Melvin R. Novick:
        "Multivariate generalized beta distributions with applications to utility assessment"
@@ -197,12 +198,17 @@ def prepare(self, X: np.ndarray) -> torch.Tensor:
 
         # clip seperately due to numerical stability
         data = np.clip(X, self.epsilon, 1. - self.epsilon) / np.clip((1. - X), self.epsilon, 1. - self.epsilon)
-        return torch.tensor(data)
+        return torch.from_numpy(data)
 
-    def prior(self):
+    def prior(self, dtype: torch.dtype):
         """
         Prior definition of the weights used for log regression. This function has to set the
         variables 'self.weight_prior_dist', 'self.weight_mean_init' and 'self.weight_stddev_init'.
+
+        Parameters
+        ----------
+        dtype: torch.dtype
+            Data type of the input data so that the priors are initialized with the same precision.
         """
 
         # number of weights
@@ -210,8 +216,8 @@ def prior(self):
         self._sites = OrderedDict()
 
         # initial values for mean, scale and prior dist
-        init_mean = torch.ones(num_weights).uniform_(1. + self.epsilon, 2.)
-        init_scale = torch.ones(num_weights)
+        init_mean = torch.ones(num_weights, dtype=dtype).uniform_(1. + self.epsilon, 2.)
+        init_scale = torch.ones(num_weights, dtype=dtype)
         prior = dist.Normal(init_mean, 10 * init_scale, validate_args=True)
 
         # we have constraints on the weights to be positive
@@ -242,10 +248,10 @@ def prior(self):
             'values': None,
             'constraint': constraints.real,
             'init': {
-                'mean': torch.ones(1) * self.epsilon,
-                'scale': torch.ones(1)
+                'mean': torch.ones(1, dtype=dtype) * self.epsilon,
+                'scale': torch.ones(1, dtype=dtype)
             },
-            'prior': dist.Normal(torch.zeros(1), 10 * torch.ones(1), validate_args=True),
+            'prior': dist.Normal(torch.zeros(1, dtype=dtype), 10 * torch.ones(1, dtype=dtype), validate_args=True),
         }
 
     def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
@@ -283,7 +289,13 @@ def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
 
             # on MCMC sampling, extreme values might occur and can cause an 'inf'
             # this will result in invalid prob values - catch infs and set to log of max value
-            weights[torch.isinf(weights)] = torch.log(torch.tensor(torch.finfo(weights.dtype).max))
+            weights[torch.isinf(weights)] = torch.log(
+                torch.tensor(
+                    torch.finfo(weights.dtype).max,
+                    dtype=weights.dtype,
+                    device=weights.device
+                )
+            )
 
         # the first dimension of the given input data is the "independent" sample dimension
         with pyro.plate("data", X.shape[0]):
@@ -315,8 +327,8 @@ def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
             log_sum_lower_neg = torch.log(1. + torch.sum(lambda_neg * X, dim=1))
             lower_part = (sum_alpha_neg * log_sum_lower_neg) - (sum_alpha_pos * log_sum_lower_pos)
 
-            # combine both parts and bias to logits
-            logit = torch.squeeze(bias + upper_part + lower_part)
+            # combine both parts and bias to logitsŝ
+            logit = bias + upper_part + lower_part
 
             # if MLE, (slow) sampling is not necessary. However, this is needed for 'variational' and 'mcmc'
             if self.method in ['variational', 'mcmc']:
diff --git a/netcal/scaling/LogisticCalibration.py b/netcal/scaling/LogisticCalibration.py
index f7120ae..c0e06aa 100644
--- a/netcal/scaling/LogisticCalibration.py
+++ b/netcal/scaling/LogisticCalibration.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -69,6 +69,9 @@ class LogisticCalibration(AbstractLogisticRegression):
     with bias :math:`c \\in \\mathbb{R}`.
     We utilize standard optimization methods to determine the calibration mapping :math:`g(s)`.
 
+    Capturing epistemic uncertainty of the calibration method is also able with this implementation [4]_.
+
+
     Parameters
     ----------
     temperature_only : bool, default: False
@@ -108,16 +111,16 @@ class are treated as independent of each other (sigmoid).
     .. [1] Platt, John:
        "Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods."
        Advances in large margin classifiers 10.3: 61-74, 1999
-       `Get source online <https://www.researchgate.net/profile/John_Platt/publication/2594015_Probabilistic_Outputs_for_Support_Vector_Machines_and_Comparisons_to_Regularized_Likelihood_Methods/links/004635154cff5262d6000000.pdf>`_
+       `Get source online <https://www.researchgate.net/profile/John_Platt/publication/2594015_Probabilistic_Outputs_for_Support_Vector_Machines_and_Comparisons_to_Regularized_Likelihood_Methods/links/004635154cff5262d6000000.pdf>`__
 
     .. [2] Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
        "On Calibration of Modern Neural Networks."
        Proceedings of the 34th International Conference on Machine Learning-Volume 70. JMLR. org, 2017.
-       `Get source online <https://arxiv.org/abs/1706.04599>`_
+       `Get source online <https://arxiv.org/abs/1706.04599>`__
 
     .. [3] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
-       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.
+       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 
     .. [4] Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
        "Bayesian Confidence Calibration for Epistemic Uncertainty Modelling."
@@ -185,12 +188,17 @@ def prepare(self, X: np.ndarray) -> torch.Tensor:
         else:
             data_input = self._inverse_softmax(X)
 
-        return torch.Tensor(data_input)
+        return torch.from_numpy(data_input)
 
-    def prior(self):
+    def prior(self, dtype: torch.dtype):
         """
         Prior definition of the weights used for log regression. This function has to set the
         variables 'self.weight_prior_dist', 'self.weight_mean_init' and 'self.weight_stddev_init'.
+
+        Parameters
+        ----------
+        dtype: torch.dtype
+            Data type of the input data so that the priors are initialized with the same precision.
         """
 
         self._sites = OrderedDict()
@@ -201,10 +209,10 @@ def prior(self):
                 'values': None,
                 'constraint': constraints.real,
                 'init': {
-                    'mean': torch.ones(1),
-                    'scale': torch.ones(1)
+                    'mean': torch.ones(1, dtype=dtype),
+                    'scale': torch.ones(1, dtype=dtype)
                     },
-                'prior': dist.Normal(torch.ones(1), 10 * torch.ones(1), validate_args=True)
+                'prior': dist.Normal(torch.ones(1, dtype=dtype), 10 * torch.ones(1, dtype=dtype), validate_args=True)
             }
 
         else:
@@ -225,10 +233,10 @@ def prior(self):
                 'values': None,
                 'constraint': constraints.real,
                 'init': {
-                    'mean': torch.ones(num_weights),
-                    'scale': torch.ones(num_weights)
+                    'mean': torch.ones(num_weights, dtype=dtype),
+                    'scale': torch.ones(num_weights, dtype=dtype)
                 },
-                'prior': dist.Normal(torch.ones(num_weights), 10 * torch.ones(num_weights), validate_args=True),
+                'prior': dist.Normal(torch.ones(num_weights, dtype=dtype), 10 * torch.ones(num_weights, dtype=dtype), validate_args=True),
             }
 
             # set properties for "bias"
@@ -239,7 +247,7 @@ def prior(self):
                     'mean': torch.zeros(num_bias),
                     'scale': torch.ones(num_bias)
                 },
-                'prior': dist.Normal(torch.zeros(num_bias), 10 * torch.ones(num_bias), validate_args=True),
+                'prior': dist.Normal(torch.zeros(num_bias, dtype=dtype), 10 * torch.ones(num_bias, dtype=dtype), validate_args=True),
             }
 
     def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
@@ -279,7 +287,7 @@ def logit_op(x, w, b): return torch.squeeze(torch.sum(torch.mul(x, w), dim=1))
             # platt scaling: one weight for each feature given
             else:
                 weights = torch.reshape(weights, (-1, 1))
-                def logit_op(x, w, b): return torch.squeeze(torch.matmul(x, w) + b)
+                def logit_op(x, w, b): return torch.squeeze(torch.matmul(x, w) + b, dim=1)
 
             # define as probabilistic output the sigmoid and a bernoulli distribution
             prob_op = torch.sigmoid
diff --git a/netcal/scaling/LogisticCalibrationDependent.py b/netcal/scaling/LogisticCalibrationDependent.py
index 40c9e25..9c78d6a 100644
--- a/netcal/scaling/LogisticCalibrationDependent.py
+++ b/netcal/scaling/LogisticCalibrationDependent.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -58,8 +58,8 @@ class LogisticCalibrationDependent(AbstractLogisticRegression):
 
     .. math::
 
-       \\ell r(s) = \\log \\frac{\\Sigma^-}{\\Sigma^+}
-       + \\frac{1}{2} (s_-^T \\Sigma_-^{-1}s^-) - (s_+^T \\Sigma_+^{-1}s^+),
+       \\ell r(s) = \\log \\frac{|\\Sigma^-|}{|\\Sigma^+|}
+       + \\frac{1}{2} \\Big[ (s_-^T \\Sigma_-^{-1}s^-) - (s_+^T \\Sigma_+^{-1}s^+) \\Big],
 
     with :math:`s^+ = s - \\mu^+` and :math:`s^- = s - \\mu^-`.
 
@@ -71,6 +71,8 @@ class LogisticCalibrationDependent(AbstractLogisticRegression):
 
     instead of estimating :math:`\\Sigma` directly. This guarantees both requirements.
 
+    Capturing epistemic uncertainty of the calibration method is also able with this implementation [3]_.
+
     Parameters
     ----------
     method : str, default: "mle"
@@ -102,12 +104,12 @@ class are treated as independent of each other (sigmoid).
     ----------
     .. [1] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
-       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.
+       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 
     .. [2] Kull, Meelis, Telmo Silva Filho, and Peter Flach:
        "Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers"
        Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
-       `Get source online <http://proceedings.mlr.press/v54/kull17a/kull17a.pdf>`_
+       `Get source online <http://proceedings.mlr.press/v54/kull17a/kull17a.pdf>`__
 
     .. [3] Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
        "Bayesian Confidence Calibration for Epistemic Uncertainty Modelling."
@@ -194,20 +196,25 @@ def prepare(self, X: np.ndarray) -> torch.Tensor:
 
         # on detection mode, convert confidence to sigmoid and append the remaining features
         data_input = np.concatenate((self._inverse_sigmoid(X[:, 0]).reshape(-1, 1), X[:, 1:]), axis=1)
-        return torch.Tensor(data_input)
+        return torch.from_numpy(data_input)
 
-    def prior(self):
+    def prior(self, dtype: torch.dtype):
         """
         Prior definition of the weights used for log regression. This function has to set the
         variables 'self.weight_prior_dist', 'self.weight_mean_init' and 'self.weight_stddev_init'.
+
+        Parameters
+        ----------
+        dtype: torch.dtype
+            Data type of the input data so that the priors are initialized with the same precision.
         """
 
         # number of weights
         num_weights = 2 * (self.num_features ** 2 + self.num_features)
 
         # prior estimates for decomposed inverse covariance matrices and mean vectors
-        decomposed_inv_cov_prior = torch.diag(torch.ones(self.num_features))
-        mean_mean_prior = torch.ones(self.num_features)
+        decomposed_inv_cov_prior = torch.diag(torch.ones(self.num_features, dtype=dtype))
+        mean_mean_prior = torch.ones(self.num_features, dtype=dtype)
 
         # initial stddev for all weights is always the same
         weights_mean_prior = torch.cat((decomposed_inv_cov_prior.flatten(),
@@ -223,9 +230,9 @@ def prior(self):
             'constraint': constraints.real,
             'init': {
                 'mean': weights_mean_prior,
-                'scale': torch.ones(num_weights)
+                'scale': torch.ones(num_weights, dtype=dtype)
             },
-            'prior': dist.Normal(weights_mean_prior, 10 * torch.ones(num_weights), validate_args=True),
+            'prior': dist.Normal(weights_mean_prior, 10 * torch.ones(num_weights, dtype=dtype), validate_args=True),
         }
 
         # set properties for "bias"
@@ -233,10 +240,10 @@ def prior(self):
             'values': None,
             'constraint': constraints.real,
             'init': {
-                'mean': torch.zeros(1),
-                'scale': torch.ones(1)
+                'mean': torch.zeros(1, dtype=dtype),
+                'scale': torch.ones(1, dtype=dtype)
             },
-            'prior': dist.Normal(torch.zeros(1), 10 * torch.ones(1), validate_args=True),
+            'prior': dist.Normal(torch.zeros(1, dtype=dtype), 10 * torch.ones(1, dtype=dtype), validate_args=True),
         }
 
     def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
@@ -279,28 +286,27 @@ def model(self, X: torch.Tensor = None, y: torch.Tensor = None) -> torch.Tensor:
             # get logits by calculating gaussian ratio between both distributions
             # calculate covariance matrices
             # COV^(-1) = V^(-1) * V^(-1,T)
-            inverse_cov_pos = torch.matmul(decomposed_inv_cov_pos, decomposed_inv_cov_pos.transpose(1, 0))
-            inverse_cov_neg = torch.matmul(decomposed_inv_cov_neg, decomposed_inv_cov_neg.transpose(1, 0))
+            inverse_cov_pos = torch.matmul(decomposed_inv_cov_pos, decomposed_inv_cov_pos.transpose(1, 0))  # (d, d)
+            inverse_cov_neg = torch.matmul(decomposed_inv_cov_neg, decomposed_inv_cov_neg.transpose(1, 0))  # (d, d)
 
             # calculate data without means
             difference_pos = X - mean_pos
             difference_neg = X - mean_neg
 
             # add a new dimensions. This is necessary for torch to distribute dot product
-            difference_pos = torch.unsqueeze(difference_pos, 2)
-            difference_neg = torch.unsqueeze(difference_neg, 2)
-
-            logit = 0.5 * (torch.matmul(difference_neg.transpose(2, 1),
-                                        torch.matmul(inverse_cov_neg, difference_neg)) -
-                           torch.matmul(difference_pos.transpose(2, 1),
-                                        torch.matmul(inverse_cov_pos, difference_pos))
-                           )
+            difference_pos = torch.unsqueeze(difference_pos, 2)  # (n, d, 1)
+            difference_neg = torch.unsqueeze(difference_neg, 2)  # (n, d, 1)
 
-            # remove unnecessary dimensions
-            logit = torch.squeeze(logit)
+            logit = 0.5 * (torch.matmul(
+                difference_neg.transpose(2, 1),
+                torch.matmul(inverse_cov_neg, difference_neg)
+            ) - torch.matmul(
+                difference_pos.transpose(2, 1),
+                torch.matmul(inverse_cov_pos, difference_pos)
+            ))  # (n, 1, 1)
 
             # add bias ratio to logit
-            logit = bias + logit
+            logit = bias + logit[:, 0, 0]
 
             # if MLE, (slow) sampling is not necessary. However, this is needed for 'variational' and 'mcmc'
             if self.method in ['variational', 'mcmc']:
diff --git a/netcal/scaling/TemperatureScaling.py b/netcal/scaling/TemperatureScaling.py
index 3fbd814..a2589e7 100644
--- a/netcal/scaling/TemperatureScaling.py
+++ b/netcal/scaling/TemperatureScaling.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -10,8 +10,10 @@
 
 class TemperatureScaling(LogisticCalibration):
     """
-    On classification or detection, apply the temperature scaling method described in [1]_ to obtain a
-    calibration mapping. For confidence calibration in classification tasks, a
+    On classification or detection, apply the temperature scaling method to obtain a
+    calibration mapping.
+    This method has been proposed by [1]_.
+    For confidence calibration in classification tasks, a
     confidence mapping :math:`g` is applied on top of a miscalibrated scoring classifier :math:`\\hat{p} = h(x)` to
     deliver a calibrated confidence score :math:`\\hat{q} = g(h(x))`.
 
@@ -31,6 +33,7 @@ class TemperatureScaling(LogisticCalibration):
     softmax operator (multiclass classification).
 
     We utilize standard optimization methods to determine the calibration mapping :math:`g(s)`.
+    Capturing epistemic uncertainty of the calibration method is also able with this implementation [2]_.
 
     Parameters
     ----------
@@ -69,13 +72,9 @@ class are treated as independent of each other (sigmoid).
     .. [1] Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
        "On Calibration of Modern Neural Networks."
        Proceedings of the 34th International Conference on Machine Learning-Volume 70. JMLR. org, 2017.
-       `Get source online <https://arxiv.org/abs/1706.04599>`_
+       `Get source online <https://arxiv.org/abs/1706.04599>`__
 
-    .. [2] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
-       "Multivariate Confidence Calibration for Object Detection."
-       The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
-
-    .. [3] Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
+    .. [2] Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
        "Bayesian Confidence Calibration for Epistemic Uncertainty Modelling."
        2021 IEEE Intelligent Vehicles Symposium (IV), 2021
     """
diff --git a/netcal/scaling/__init__.py b/netcal/scaling/__init__.py
index 3f59139..b971847 100644
--- a/netcal/scaling/__init__.py
+++ b/netcal/scaling/__init__.py
@@ -1,14 +1,13 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
 """
-Scaling methods for confidence calibration.
-This package consists of several methods for confidence calibration which use confidence scaling to approximate
-confidence estimates to observed accuracy.
+.. include:: /../../netcal/scaling/README.md
+   :parser: myst_parser.sphinx_
 
 Available classes
 =================

From 992785c51e10eda3531f8e4bdfdd3b37878d3d54 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:46:29 +0200
Subject: [PATCH 06/21] Update copyright in regularization package. Minor
 bugfixes in documentation.

---
 netcal/regularization/ConfidencePenalty.py | 16 +++++++++++-----
 netcal/regularization/DCAPenalty.py        | 10 +++++-----
 netcal/regularization/MMCEPenalty.py       | 12 ++++++------
 netcal/regularization/__init__.py          | 11 +++++------
 4 files changed, 27 insertions(+), 22 deletions(-)

diff --git a/netcal/regularization/ConfidencePenalty.py b/netcal/regularization/ConfidencePenalty.py
index 2fea60e..6769dfc 100644
--- a/netcal/regularization/ConfidencePenalty.py
+++ b/netcal/regularization/ConfidencePenalty.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -39,7 +39,7 @@ def confidence_penalty(X: np.ndarray, weight: float, threshold: float = None, ba
     .. [1] G. Pereyra, G. Tucker, J. Chorowski, Lukasz Kaiser, and G. Hinton:
        “Regularizing neural networks by penalizing confident output distributions.”
        CoRR, 2017.
-       `Get source online <https://arxiv.org/pdf/1701.06548>`_
+       `Get source online <https://arxiv.org/pdf/1701.06548>`__
     """
 
     epsilon = np.finfo(np.float32).eps
@@ -79,7 +79,7 @@ class ConfidencePenalty(_Loss):
     .. [1] G. Pereyra, G. Tucker, J. Chorowski, Lukasz Kaiser, and G. Hinton:
        “Regularizing neural networks by penalizing confident output distributions.”
        CoRR, 2017.
-       `Get source online <https://arxiv.org/pdf/1701.06548>`_
+       `Get source online <https://arxiv.org/pdf/1701.06548>`__
     """
 
     epsilon = 1e-12
@@ -91,7 +91,13 @@ def __init__(self, weight: float = 1.0, threshold: float = -1., reduction='mean'
         self.weight = weight
         self.threshold = threshold
 
-    def forward(self, input: torch.Tensor):
+    @staticmethod
+    def entropy(input: torch.Tensor, calibrated: torch.Tensor) -> torch.Tensor:
+        """ Cross entropy between input tensor and calibrated counter part """
+
+        return -calibrated * torch.log(input)
+
+    def forward(self, input: torch.Tensor, *ig_args, **ig_kwargs):
         """ Forward call. Additional arguments and keyword-arguments are ignored. """
 
         probs = torch.clamp(torch.softmax(input, dim=1), self.epsilon, 1.-self.epsilon)
diff --git a/netcal/regularization/DCAPenalty.py b/netcal/regularization/DCAPenalty.py
index 52aecb1..e510407 100644
--- a/netcal/regularization/DCAPenalty.py
+++ b/netcal/regularization/DCAPenalty.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -11,8 +11,8 @@
 
 class DCAPenalty(_Loss):
     """
-    Difference between Confidence and Accuracy (DCA) [1]_. This regularization returns a single scalar indicating
-    the difference between mean confidence and accuracy within a single batch.
+    Difference between Confidence and Accuracy (DCA). This regularization has been proposed by [1]_ and
+    returns a single scalar indicating the difference between mean confidence and accuracy within a single batch.
 
     Parameters
     ----------
@@ -32,7 +32,7 @@ def __init__(self, weight: float = 1.0):
         super().__init__()
         self.weight = weight
 
-    def forward(self, input: torch.Tensor, target: torch.Tensor):
+    def forward(self, input: torch.Tensor, target: torch.Tensor, **ig_kwargs):
         """ Forward call of module. Providing the target scores is mandatory. """
 
         # assume logits as input
diff --git a/netcal/regularization/MMCEPenalty.py b/netcal/regularization/MMCEPenalty.py
index 4b382e5..f0a1d85 100644
--- a/netcal/regularization/MMCEPenalty.py
+++ b/netcal/regularization/MMCEPenalty.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -10,8 +10,8 @@
 
 class MMCEPenalty(_Loss):
     """
-    Maximum mean calibration error (MMCE) [1]_. This term can be used for online confidence calibration directly
-    during model training.
+    Maximum mean calibration error (MMCE). This technique has been proposed by [1]_ and can be used for online
+    confidence calibration directly during model training.
 
     Parameters
     ----------
@@ -23,7 +23,7 @@ class MMCEPenalty(_Loss):
     .. [1] Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain:
        "Trainable calibration measures for neural networks from kernel mean embeddings."
        International Conference on Machine Learning. PMLR, 2018.
-       `Get source online: <http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf>`_
+       `Get source online: <http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf>`__
     """
 
     epsilon = 1e-12
@@ -40,7 +40,7 @@ def kernel(self, c1: torch.Tensor, c2: torch.Tensor) -> torch.Tensor:
         diff = c1[:, None] - c2
         return torch.exp(-2.5 * torch.abs(diff))
 
-    def forward(self, input: torch.Tensor, target: torch.Tensor):
+    def forward(self, input: torch.Tensor, target: torch.Tensor, **ig_kwargs):
         """ Forward call of module. Returns a single scalar indicating the MMCE for the current batch. """
 
         # assume logits as input
diff --git a/netcal/regularization/__init__.py b/netcal/regularization/__init__.py
index 59dcccc..6fa628b 100644
--- a/netcal/regularization/__init__.py
+++ b/netcal/regularization/__init__.py
@@ -1,15 +1,13 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
 """
-Regularization methods which are applied during model training. These methods should achieve a
-confidence calibration during model training. For example, the Confidence Penalty
-penalizes confident predictions and prohibits over-confident estimates.
-Use the functions to obtain the regularization and callback instances with prebuild parameters.
+.. include:: /../../netcal/regularization/README.md
+   :parser: myst_parser.sphinx_
 
 Available functions
 ===================
@@ -26,5 +24,6 @@
 
 from .ConfidencePenalty import confidence_penalty
 from .ConfidencePenalty import ConfidencePenalty
+from .ECEPenalty import ECEPenalty
 from .MMCEPenalty import MMCEPenalty
 from .DCAPenalty import DCAPenalty

From 26ed6328ba424df78eb16c17d1bbfd6ea4904676 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:47:36 +0200
Subject: [PATCH 07/21] Restructured metrics package into confidence and
 regression part. Add the following new metrics for regression calibration
 evaluation: - Expected Normalized Calibration Error (ENCE) - Uncertainty
 Calibration Error (UCE) - Quantile Calibration Error (QCE) - Negative Log
 Likelihood (NLL) - Prediction Interval Coverage Probability (PICP) (formerly
 in the confidence package)

---
 netcal/metrics/Miscalibration.py          | 173 +++++++----
 netcal/metrics/PICP.py                    | 221 --------------
 netcal/metrics/__init__.py                |  44 ++-
 netcal/metrics/{ => confidence}/ACE.py    |  49 +--
 netcal/metrics/{ => confidence}/ECE.py    |  54 ++--
 netcal/metrics/{ => confidence}/MCE.py    |  47 +--
 netcal/metrics/{ => confidence}/MMCE.py   |  35 ++-
 netcal/metrics/confidence/README.md       |  13 +
 netcal/metrics/confidence/__init__.py     |  28 ++
 netcal/metrics/regression/ENCE.py         | 164 ++++++++++
 netcal/metrics/regression/NLL.py          | 182 +++++++++++
 netcal/metrics/regression/PICP.py         | 163 ++++++++++
 netcal/metrics/regression/QCE.py          | 356 ++++++++++++++++++++++
 netcal/metrics/regression/QuantileLoss.py | 119 ++++++++
 netcal/metrics/regression/README.md       |  17 ++
 netcal/metrics/regression/UCE.py          | 155 ++++++++++
 netcal/metrics/regression/__init__.py     |  34 +++
 17 files changed, 1490 insertions(+), 364 deletions(-)
 delete mode 100644 netcal/metrics/PICP.py
 rename netcal/metrics/{ => confidence}/ACE.py (80%)
 rename netcal/metrics/{ => confidence}/ECE.py (78%)
 rename netcal/metrics/{ => confidence}/MCE.py (81%)
 rename netcal/metrics/{ => confidence}/MMCE.py (85%)
 create mode 100644 netcal/metrics/confidence/README.md
 create mode 100644 netcal/metrics/confidence/__init__.py
 create mode 100644 netcal/metrics/regression/ENCE.py
 create mode 100644 netcal/metrics/regression/NLL.py
 create mode 100644 netcal/metrics/regression/PICP.py
 create mode 100644 netcal/metrics/regression/QCE.py
 create mode 100644 netcal/metrics/regression/QuantileLoss.py
 create mode 100644 netcal/metrics/regression/README.md
 create mode 100644 netcal/metrics/regression/UCE.py
 create mode 100644 netcal/metrics/regression/__init__.py

diff --git a/netcal/metrics/Miscalibration.py b/netcal/metrics/Miscalibration.py
index 1d7263a..e6ead11 100644
--- a/netcal/metrics/Miscalibration.py
+++ b/netcal/metrics/Miscalibration.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -9,19 +9,17 @@
 
 import numpy as np
 from scipy.stats import binned_statistic_dd
-from netcal import accepts, hpdi
+from netcal import accepts, hpdi, squeeze_generic
 
 
 class _Miscalibration(object):
     """
-    Generic base class to calculate Average/Expected/Maximum Calibration Error.
-    ACE [1]_, ECE [2]_ and MCE [2]_ are used for measuring miscalibration on classification.
-    The according variants D-ACE/D-ECE/D-MCE are used for object detection [3]_.
+    Generic base class for binning-based miscalibration metrics.
 
     Parameters
     ----------
     bins : int or iterable, default: 10
-        Number of bins used by the Histogram Binning.
+        Number of bins used for the internal binning.
         On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = ... = bins).
         If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
     equal_intervals : bool, optional, default: True
@@ -40,24 +38,29 @@ class _Miscalibration(object):
     .. [1] Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
        "Obtaining well calibrated probabilities using bayesian binning."
        Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
-       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`_
+       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`__
 
     .. [2] Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi:
        "Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection."
        Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.
-       `Get source online <https://openreview.net/pdf?id=S1lG7aTnqQ>`_
+       `Get source online <https://openreview.net/pdf?id=S1lG7aTnqQ>`__
 
     .. [3] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
        The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
-       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`_
+       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`__
     """
 
     epsilon = np.finfo(np.float).eps
 
     @accepts((int, tuple, list), bool, bool, int)
-    def __init__(self, bins: Union[int, Iterable[int]] = 10, equal_intervals: bool = True,
-                 detection: bool = False, sample_threshold: int = 1):
+    def __init__(
+            self,
+            bins: Union[int, Iterable[int]] = 10,
+            equal_intervals: bool = True,
+            detection: bool = False,
+            sample_threshold: int = 1
+    ):
         """ Constructor. For parameter doc see class doc. """
 
         self.bins = bins
@@ -65,18 +68,36 @@ def __init__(self, bins: Union[int, Iterable[int]] = 10, equal_intervals: bool =
         self.sample_threshold = sample_threshold
         self.equal_intervals = equal_intervals
 
-    @classmethod
-    def squeeze_generic(cls, a: np.ndarray, axes_to_keep: Union[Iterable[int], int]) -> np.ndarray:
-        """ Squeeze input array a but keep axes defined by parameter
-        'axes_to_keep' even if the dimension is of size 1. """
+    def frequency(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            batched: bool = False,
+            uncertainty: str = 'mean'
+    ) -> Tuple[List[np.ndarray], List[np.ndarray], List[np.ndarray], List[np.ndarray], List, int]:
+        """ Measure the frequency of each point by binning. """
 
-        # if type is int, convert to iterable
-        if type(axes_to_keep) == int:
-            axes_to_keep = (axes_to_keep,)
+        # prepare data - first, use "mean" to obtain the mean prediction of the posterior predictive
+        # use flattened confidence estimates in order to get a better evaluation of the accuracy within each bin
+        X_mean, _, sample_uncertainty, bin_bounds, num_features = self.prepare(X, y, batched, uncertainty=uncertainty)
 
-        # iterate over all axes in a and check if dimension is in 'axes_to_keep' or of size 1
-        out_s = [s for i, s in enumerate(a.shape) if i in axes_to_keep or s != 1]
-        return a.reshape(out_s)
+        # convert mean variance to mean std deviation
+        uncertainty = [np.sqrt(var) for var in sample_uncertainty]
+        sample_frequency, num_samples = [], []
+
+        # for batch in zip(X_mean, X_flatten, matched_flatten, bin_bounds):
+        for batch_X_mean, bounds in zip(X_mean, bin_bounds):
+
+            # perform binning
+            # acc_hist, _, _ = self.binning(bounds, batch_X_flatten, batch_matched_flatten)
+            (freq_hist, ), num_samples_hist, _, idx_mean = self.binning(bounds, batch_X_mean, batch_X_mean[:, 0], nan=np.nan)
+
+            # use accuracy histogram from flattened estimates
+            # and assign to "mean" values
+            sample_frequency.append(freq_hist[idx_mean])
+            num_samples.append(num_samples_hist)
+
+        return X_mean, sample_frequency, uncertainty, num_samples, bin_bounds, num_features
 
     def reduce(self, histogram: np.ndarray, distribution: np.ndarray, axis: int, reduce_result: Tuple = None):
         """
@@ -106,10 +127,11 @@ def reduce(self, histogram: np.ndarray, distribution: np.ndarray, axis: int, red
 
             # get the relative amount of samples according to a certain bin combination over all confidence bins
             # leave out empty bin combinations
-            rel_samples_hist_reduced_conf = np.divide(distribution,
-                                                      extended_hist,
-                                                      out=np.zeros_like(distribution),
-                                                      where=extended_hist != 0)
+            rel_samples_hist_reduced_conf = np.divide(
+                distribution, extended_hist,
+                out=np.zeros_like(distribution),
+                where=extended_hist != 0
+            )
         else:
             # reuse reduced data distribution from a previous call
             rel_samples_hist_reduced_conf = reduce_result[1]
@@ -119,8 +141,13 @@ def reduce(self, histogram: np.ndarray, distribution: np.ndarray, axis: int, red
 
         return weighted_mean, rel_samples_hist_reduced_conf
 
-    def prepare(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray],
-                batched: bool = False, uncertainty: str = None) -> Tuple[List[np.ndarray], List[np.ndarray], List[np.ndarray], List, int]:
+    def prepare(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            batched: bool = False,
+            uncertainty: str = None
+    ) -> Tuple[List[np.ndarray], List[np.ndarray], List[np.ndarray], List, int]:
         """ Check input data. For detailed documentation of the input parameters, check "_measure" method. """
 
         # batched: interpret X and y as multiple predictions
@@ -225,8 +252,7 @@ def binning(self, bin_bounds: List, samples: np.ndarray, *values: Iterable, nan:
 
             binning_schemes.append(hist)
 
-        binning_schemes.append(num_samples_hist)
-        _, _, idx = binning_result
+        _, edges, idx = binning_result
 
         # first step: expand bin numbers
         # correct bin number afterwards as this variable has offset of 1
@@ -235,16 +261,17 @@ def binning(self, bin_bounds: List, samples: np.ndarray, *values: Iterable, nan:
 
         # convert to tuple as this can be used for array indexing
         idx = tuple([dim for dim in idx])
-        binning_schemes.append(idx)
 
-        return tuple(binning_schemes)
+        return tuple(binning_schemes), num_samples_hist, edges, idx
 
-    def process(self,
-                metric: str,
-                acc_hist: np.ndarray,
-                conf_hist: np.ndarray,
-                variance_hist: np.ndarray,
-                num_samples_hist: np.ndarray) -> Tuple[float, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
+    def process(
+            self,
+            metric: str,
+            acc_hist: np.ndarray,
+            conf_hist: np.ndarray,
+            variance_hist: np.ndarray,
+            num_samples_hist: np.ndarray
+    ) -> Tuple[float, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
         """
         Determine miscalibration based on passed histograms.
 
@@ -291,8 +318,11 @@ def process(self,
             non_empty_bins = np.count_nonzero(num_samples_hist, axis=0)
 
             # divide by leaving out empty bins (those are initialized to 0)
-            bin_map = np.divide(reduced_deviation_map, non_empty_bins,
-                                out=np.zeros_like(reduced_deviation_map), where=non_empty_bins != 0)
+            bin_map = np.divide(
+                reduced_deviation_map, non_empty_bins,
+                out=np.zeros_like(reduced_deviation_map),
+                where=non_empty_bins != 0
+            )
 
             miscalibration = np.sum(bin_map / np.count_nonzero(np.sum(num_samples_hist, axis=0)))
 
@@ -316,7 +346,13 @@ def process(self,
 
         return miscalibration, bin_map, acc_hist, conf_hist, variance_hist, samples_map
     
-    def _prepare_bins(self, X: List[np.ndarray], num_features: int) -> List[List[np.ndarray]]:
+    def _prepare_bins(
+            self,
+            X: List[np.ndarray],
+            num_features: int,
+            min_: Union[float, List[float]] = 0.0,
+            max_: Union[float, List[float]] = 1.0
+    ) -> List[List[np.ndarray]]:
         """ Prepare number of bins for binning scheme. """
 
         # check bins parameter
@@ -333,8 +369,16 @@ def _prepare_bins(self, X: List[np.ndarray], num_features: int) -> List[List[np.
         else:
             raise AttributeError("Unknown type of parameter \'bins\'.")
 
+        # distribute min_ to all dims
+        if isinstance(min_, (int, float, np.floating, np.integer)):
+            min_ = [min_, ] * num_features
+
+        # distribute min_ to all dims
+        if isinstance(max_, (int, float, np.floating, np.integer)):
+            max_ = [max_, ] * num_features
+
         # create an own set of bin boundaries for each batch in X
-        bin_bounds = [[np.linspace(0.0, 1.0, bins + 1) for bins in bins] for _ in X]
+        bin_bounds = [[np.linspace(min_[dim], max_[dim], b + 1) for dim, b in enumerate(bins)] for _ in X]
 
         # on equal_intervals=True, simply use linspace
         # if the goal is to equalize the amount of samples in each bin, use np.quantile
@@ -349,12 +393,34 @@ def _prepare_bins(self, X: List[np.ndarray], num_features: int) -> List[List[np.
                     bin_bounds[i][dim] = quantile
 
         return bin_bounds
+
+    def _prepare_bins_regression(self, var: np.ndarray, n_dims: int, range_: Union[List[Tuple[float, float]], None]):
+        """ Prepare the bin boundaries for regression tasks where explicit bin boundaries can be passed through. """
+
+        # extract range parameter if given
+        if range_ is not None:
+            assert len(range_) == n_dims, "Parameter \'range_\' must have the same length as number of dimensions."
+            assert all([isinstance(x, (tuple, list)) for x in range_]), "Binning range_ must be passed as tuple/list of length 2."
+
+            min_ = [x[0] for x in range_]
+            max_ = [x[1] for x in range_]
+
+        # if not explicitly given, use min_ and max_ scores in variance
+        else:
+            min_ = np.min(var, axis=0)  # (d,)
+            max_ = np.max(var, axis=0)  # (d,)
+
+        # use the _prepare_bins function to initialize the binning scheme
+        # the function is designed to handle a batch of data - thus, we only need to access the first element
+        bin_bounds = self._prepare_bins([var], num_features=n_dims, min_=min_, max_=max_)[0]
+
+        return bin_bounds
     
     def _prepare_input(self, X: np.ndarray, y: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
         """ Prepare structure of input data (number of dimensions, etc.) """
 
         # remove unnecessary dims if given
-        y = self.squeeze_generic(y, axes_to_keep=0)
+        y = squeeze_generic(y, axes_to_keep=0)
 
         # after processing uncertainty, we expect batch_X to be only 2-D afterwards (but probably with more samples)
         # if we had no uncertainty, we expect that anyway
@@ -514,11 +580,17 @@ def _mode(self, X: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
 
         return np.stack(ret, axis=1), np.var(X, axis=0)
 
-    def _measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray],
-                 metric: str, batched: bool = False, uncertainty: str = None,
-                 return_map: bool = False,
-                 return_num_samples: bool = False,
-                 return_uncertainty_map: bool = False) -> Union[float, Tuple]:
+    def _measure(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            metric: str,
+            batched: bool = False,
+            uncertainty: str = None,
+            return_map: bool = False,
+            return_num_samples: bool = False,
+            return_uncertainty_map: bool = False
+    ) -> Union[float, Tuple]:
         """
         Measure calibration by given predictions with confidence and the according ground truth.
         Assume binary predictions with y=1.
@@ -585,10 +657,9 @@ def _measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable
         for batch_X, batch_matched, batch_uncertainty, bounds in zip(X, matched, sample_uncertainty, bin_bounds):
 
             # perform binning on input arrays and drop last outcome (idx bin indices are not needed here)
-            histograms = self.binning(bounds, batch_X, batch_matched, batch_X[:, 0], batch_uncertainty[:, 0])
-            histograms = histograms[:-1]
+            histograms, num_samples_hist, _, _ = self.binning(bounds, batch_X, batch_matched, batch_X[:, 0], batch_uncertainty[:, 0])
 
-            result = self.process(metric, *histograms)
+            result = self.process(metric, *histograms, num_samples_hist=num_samples_hist)
             results.append(result)
 
         # finally, average over all batches
diff --git a/netcal/metrics/PICP.py b/netcal/metrics/PICP.py
deleted file mode 100644
index 33b0eb9..0000000
--- a/netcal/metrics/PICP.py
+++ /dev/null
@@ -1,221 +0,0 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
-#
-# This Source Code Form is subject to the terms of the Apache License 2.0
-# If a copy of the APL2 was not distributed with this
-# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
-
-from typing import Iterable, NamedTuple, Tuple, List
-from collections import namedtuple
-import numpy as np
-from scipy.stats import norm
-from typing import Union
-
-from netcal import hpdi
-from netcal.metrics import _Miscalibration
-
-
-class PICP(_Miscalibration):
-    """
-    Compute Prediction Interval Coverage Probability (PICP) [1]_,[2]_ and Mean Prediction Interval Width (MPIW) [2]_.
-    This metric is used for Bayesian models to determine the quality of the uncertainty estimates.
-    In Bayesian mode, an uncertainty estimate is attached to each sample. The PICP measures the probability, that
-    the true (observed) accuracy falls into the p% prediction interval. The uncertainty is well-calibrated, if
-    the PICP is equal to p%. Simultaneously, the MPIW measures the mean width of all prediction intervals to evaluate
-    the sharpness of the uncertainty estimates.
-
-    Parameters
-    ----------
-    bins : int or iterable, default: 10
-        Number of bins used by the Histogram Binning.
-        On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = ... = bins).
-        If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
-    equal_intervals : bool, optional, default: True
-        If True, the bins have the same width. If False, the bins are splitted to equalize
-        the number of samples in each bin.
-    detection : bool, default: False
-        If False, the input array 'X' is treated as multi-class confidence input (softmax)
-        with shape (n_samples, [n_classes]).
-        If True, the input array 'X' is treated as a box predictions with several box features (at least
-        box confidence must be present) with shape (n_samples, [n_box_features]).
-    sample_threshold : int, optional, default: 1
-        Bins with an amount of samples below this threshold are not included into the process metrics.
-
-    References
-    ----------
-    .. [1] Kuleshov, V.; Fenner, N. & Ermon, S.:
-       "Accurate Uncertainties for Deep Learning Using Calibrated Regression."
-       International Conference on Machine Learning (ICML), 2018
-       `Get source online <http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf>`_
-
-    .. [2] Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez:
-       "Quality of Uncertainty Quantification for Bayesian Neural Network Inference."
-       Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019
-       `Get source online <https://arxiv.org/pdf/1906.09686.pdf>`_
-    """
-
-    def accuracy(self, X: Union[Iterable[np.ndarray], np.ndarray],
-                 y: Union[Iterable[np.ndarray], np.ndarray],
-                 batched: bool = False,
-                 uncertainty: str = 'mean') -> Tuple[List[np.ndarray], List[np.ndarray], List[np.ndarray], List[np.ndarray], List, int]:
-        """ Measure the accuracy of each point by binning. """
-
-        # prepare data - first, use "mean" to obtain the mean prediction of the posterior predictive
-        # use flattened confidence estimates in order to get a better evaluation of the accuracy within each bin
-        X_mean, _, sample_uncertainty, bin_bounds, num_features = self.prepare(X, y, batched, uncertainty=uncertainty)
-
-        # convert mean variance to mean std deviation
-        uncertainty = [np.sqrt(var) for var in sample_uncertainty]
-        sample_accuracy, num_samples = [], []
-
-        # for batch in zip(X_mean, X_flatten, matched_flatten, bin_bounds):
-        for batch_X_mean, bounds in zip(X_mean, bin_bounds):
-
-            # perform binning
-            # acc_hist, _, _ = self.binning(bounds, batch_X_flatten, batch_matched_flatten)
-            acc_hist, num_samples_hist, idx_mean = self.binning(bounds, batch_X_mean, batch_X_mean[:, 0], nan=np.nan)
-
-            # use accuracy histogram from flattened estimates
-            # and assign to "mean" values
-            sample_accuracy.append(acc_hist[idx_mean])
-            num_samples.append(num_samples_hist)
-
-        return X_mean, sample_accuracy, uncertainty, num_samples, bin_bounds, num_features
-
-    def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray], p: float = 0.05,
-                use_hpd: bool = True, batched: bool = False, uncertainty: str = 'mean',
-                return_map: bool = False) -> NamedTuple:
-        """
-        Measure calibration by given predictions with confidence and the according ground truth.
-        Assume binary predictions with y=1.
-
-        Parameters
-        ----------
-        X : iterable of np.ndarray, or np.ndarray of shape=([n_bayes], n_samples, [n_classes/n_box_features])
-            NumPy array with confidence values for each prediction on classification with shapes
-            1-D for binary classification, 2-D for multi class (softmax).
-            If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-            for a single sample (e.g. variational inference or MC dropout samples).
-            If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
-            interpret this parameter as multiple predictions that should be averaged.
-            On detection, this array must have 2 dimensions with number of additional box features in last dim.
-        y : iterable of np.ndarray with same length as X or np.ndarray of shape=([n_bayes], n_samples, [n_classes])
-            NumPy array with ground truth labels.
-            Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
-            If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-            for a single sample (e.g. variational inference or MC dropout samples).
-            If iterable over multiple instances of np.ndarray and parameter batched=True,
-            interpret this parameter as multiple predictions that should be averaged.
-        p : float, optional, default: 0.05
-            Confidence level.
-        use_hpd : bool, optional, default: True
-            If True, use highest posterior density (HPD) interval to determine the prediction interval width.
-            Use variance with Gaussian assumption otherwise.
-        batched : bool, optional, default: False
-            Multiple predictions can be evaluated at once (e.g. cross-validation examinations) using batched-mode.
-            All predictions given by X and y are separately evaluated and their results are averaged afterwards
-            for visualization.
-        uncertainty : str, optional, default: "mean"
-            Mode to measure mean estimate and uncertainty of the samples in Bayesian mode. Must be one
-            of "mean" (mean of all samples), "mode" (mode of all samples), "median" (median of all samples) or
-            "flatten" (no uncertainty will be computed, all samples are seen as independent predictions).
-        return_map: bool, optional, default: False
-            If True, return map with PICP and MPIW metric separated into all remaining dimension bins.
-
-        Returns
-        -------
-        Namedtuple PICPResult with fields "picp" and "mpiw", where each field either holds the PICP/MPIW score
-        or a tuple of (float, np.ndarray)
-            Always returns a named tuple with PICP (prediction interval coverage probability) and MPIW
-            (mean prediction interval width).
-            If 'return_map' is True, each field holds a tuple for the metric itself and the PICP/MPIW distribution
-            over all bins.
-        """
-
-        # PICP returns a namedtuple - init
-        picpresult = namedtuple('PICPResult', ['picp', 'mpiw'])
-
-        # 'prediction interval coverage probability' and 'mean prediction interval width'
-        picp, picp_map = [], []
-        mpiw, mpiw_map = [], []
-
-        result = self.accuracy(X=X, y=y, batched=batched, uncertainty=uncertainty)
-
-        # TODO: check different cases
-        if not batched and isinstance(X, np.ndarray):
-            X = [X]
-
-        it = (X,) + tuple(result[:-1])
-
-        # iterate over batches and get mean estimates
-        for batch_X, batch_X_mean, batch_acc, batch_uncertainty, batch_num_samples, bounds, in zip(*it):
-
-            batch_uncertainty = batch_uncertainty[:, 0]
-
-            # if uncertainty is 0 everywhere (that is the case if no Bayesian method is evaluated)
-            # return NaN
-            if np.count_nonzero(batch_uncertainty) == 0:
-                return picpresult(np.nan, np.nan)
-
-            # TODO: do that more dynamically
-            elif len(batch_X.shape) == 2:
-                batch_X = np.expand_dims(batch_X, axis=-1)
-
-            # remove all entries that are NaN
-            nans = np.isnan(batch_acc)
-            batch_X_mean, batch_acc, batch_uncertainty = batch_X_mean[~nans], batch_acc[~nans], batch_uncertainty[~nans]
-
-            # since the output distributions might be skewed, using highed posterior density for interval
-            # calculation should be preferred
-            if use_hpd:
-
-                # use confidence only for HPD
-                interval_bounds = hpdi(batch_X[..., 0], 1.-p)
-                lb_ci = interval_bounds[0, :][~nans]
-                ub_ci = interval_bounds[1, :][~nans]
-
-            else:
-
-                # calculate prediction interval assuming a normal distribution
-                # calculate credible interval
-                z_score = norm.ppf(1. - (p / 2))
-                batch_uncertainty = z_score * batch_uncertainty
-                lb_ci = batch_X_mean[:, 0] - batch_uncertainty
-                ub_ci = batch_X_mean[:, 0] + batch_uncertainty
-
-            # use accuracy histogram from flattened estimates
-            # and assign to "mean" values
-            within_interval = np.where((batch_acc >= lb_ci) & (batch_acc <= ub_ci),
-                                       np.ones_like(batch_acc), np.zeros_like(batch_acc))
-            width = ub_ci - lb_ci
-
-            # mean prediction interval width
-            mpiw.append(np.mean(width))
-            picp.append(np.mean(within_interval))
-
-            # if a map along the "feature" bins is requested, use the binning routines of _Miscalibration class
-            if return_map:
-                # TODO: not that pretty
-                threshold = int(self.sample_threshold)
-                self.sample_threshold = 1
-                batch_picp_map, batch_mpiw_map, _ = self.binning(bounds, batch_X_mean, within_interval, width)
-                self.sample_threshold = threshold
-
-                # after binning, reduce first dimension
-                result = self.reduce(batch_picp_map, batch_num_samples, axis=0)
-                batch_mpiw_map, _ = self.reduce(batch_mpiw_map, batch_num_samples, axis=0, reduce_result=result)
-
-                mpiw_map.append(batch_mpiw_map)
-                picp_map.append(result[0])
-
-        picp = np.mean(picp)
-        mpiw = np.mean(mpiw)
-
-        if return_map:
-            picp_map = np.mean(picp_map, axis=0)
-            mpiw_map = np.mean(mpiw_map, axis=0)
-            result = picpresult((picp, picp_map), (mpiw, mpiw_map))
-        else:
-            result = picpresult(picp, mpiw)
-
-        return result
diff --git a/netcal/metrics/__init__.py b/netcal/metrics/__init__.py
index 5a45d71..98d6914 100644
--- a/netcal/metrics/__init__.py
+++ b/netcal/metrics/__init__.py
@@ -1,16 +1,13 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
 """
-Methods for measuring miscalibration. The common methods are given with the
-'Average Calibration Error (ACE)', 'Expected Calibration Error (ECE)' and 'Maximum Calibration Error (MCE)'.
-Each methods bins the samples by their confidence and measures the accuracy in each bin. The ECE gives the
-mean gap between confidence and observed accuracy in each bin weighted by the number of samples.
-The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights each bin equally.
+.. include:: /../../netcal/metrics/README.md
+   :parser: myst_parser.sphinx_
 
 Available classes
 =================
@@ -23,12 +20,33 @@
    ECE
    MCE
    MMCE
+   QuantileLoss
+   PinballLoss
+   ENCE
+   UCE
    PICP
+   QCE
+   NLL
+
+Packages
+========
+
+.. autosummary::
+   :toctree: _autosummary_metric_submodules
+
+   confidence
+   regression
 """
 
-from .ACE import ACE
-from .ECE import ECE
-from .MCE import MCE
-from .Miscalibration import _Miscalibration
-from .PICP import PICP
-from .MMCE import MMCE
+from .confidence.ACE import ACE
+from .confidence.ECE import ECE
+from .confidence.MCE import MCE
+from .confidence.MMCE import MMCE
+
+from .regression.QuantileLoss import QuantileLoss
+from .regression.QuantileLoss import PinballLoss
+from .regression.ENCE import ENCE
+from .regression.UCE import UCE
+from .regression.PICP import PICP
+from .regression.QCE import QCE
+from .regression.NLL import NLL
diff --git a/netcal/metrics/ACE.py b/netcal/metrics/confidence/ACE.py
similarity index 80%
rename from netcal/metrics/ACE.py
rename to netcal/metrics/confidence/ACE.py
index 5fd6b1d..6a4381d 100644
--- a/netcal/metrics/ACE.py
+++ b/netcal/metrics/confidence/ACE.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -7,27 +7,28 @@
 
 import numpy as np
 from typing import Union, Iterable, Tuple
-from .Miscalibration import _Miscalibration
+from netcal.metrics.Miscalibration import _Miscalibration
 
 
 class ACE(_Miscalibration):
     """
-    Average Calibration Error (ACE).
+    Average Calibration Error (ACE) for classification and Detection Average Calibration Error (D-ACE) for
+    object detection or segmentation.
     This metric is used on classification [1]_ or as Detection Average Calibration Error (D-ACE)
     [2]_ on object detection tasks. This metrics measures the average difference between accuracy and confidence by
-    grouping all samples into :math:`K` bins and calculating
+    grouping all samples into :math:`B` bins and calculating
 
     .. math::
 
-       ACE = \\frac{1}{K} \\sum_{i=1}^K |\\text{acc}_i - \\text{conf}_i| ,
+       ACE = \\frac{1}{B} \\sum_{b=1}^B |\\text{acc}(b) - \\text{conf}(b)| ,
 
-    where :math:`\\text{acc}_i` and :math:`\\text{conf}_i` denote the accuracy and average confidence in the i-th bin.
-    The main difference to :class:`ECE` is that each bin is weighted equally.
+    where :math:`\\text{acc}(b)` and :math:`\\text{conf}(b)` denote the accuracy and average confidence in the b-th bin.
+    The main difference to :class:`netcal.regression.confidence.ECE` is that each bin is weighted equally.
 
     Parameters
     ----------
     bins : int or iterable, default: 10
-        Number of bins used by the Histogram Binning.
+        Number of bins used by the ACE.
         On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = ... = bins).
         If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
     equal_intervals : bool, optional, default: True
@@ -46,18 +47,23 @@ class ACE(_Miscalibration):
     .. [1] Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi:
        "Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection."
        Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.
-       `Get source online <https://openreview.net/pdf?id=S1lG7aTnqQ>`_
+       `Get source online <https://openreview.net/pdf?id=S1lG7aTnqQ>`__
     .. [2] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
        The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
-       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`_
+       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`__
     """
 
-    def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray],
-                batched: bool = False, uncertainty: str = None,
-                return_map: bool = False,
-                return_num_samples: bool = False,
-                return_uncertainty_map: bool = False) -> Union[float, Tuple]:
+    def measure(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            batched: bool = False,
+            uncertainty: str = None,
+            return_map: bool = False,
+            return_num_samples: bool = False,
+            return_uncertainty_map: bool = False
+    ) -> Union[float, Tuple]:
         """
         Measure calibration by given predictions with confidence and the according ground truth.
         Assume binary predictions with y=1.
@@ -106,8 +112,9 @@ def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[
             If 'return_uncertainty' is True, return tuple and append the average standard deviation of confidence within each bin (excluding confidence dimension).
         """
 
-        return self._measure(X=X, y=y, metric='ace',
-                             batched=batched, uncertainty=uncertainty,
-                             return_map=return_map,
-                             return_num_samples=return_num_samples,
-                             return_uncertainty_map=return_uncertainty_map)
+        return self._measure(
+            X=X, y=y, metric='ace', batched=batched, uncertainty=uncertainty,
+            return_map=return_map,
+            return_num_samples=return_num_samples,
+            return_uncertainty_map=return_uncertainty_map
+        )
diff --git a/netcal/metrics/ECE.py b/netcal/metrics/confidence/ECE.py
similarity index 78%
rename from netcal/metrics/ECE.py
rename to netcal/metrics/confidence/ECE.py
index bfc9ac6..574d8e0 100644
--- a/netcal/metrics/ECE.py
+++ b/netcal/metrics/confidence/ECE.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -7,28 +7,28 @@
 
 import numpy as np
 from typing import Union, Iterable, Tuple
-from .Miscalibration import _Miscalibration
+from netcal.metrics.Miscalibration import _Miscalibration
 
 
 class ECE(_Miscalibration):
     """
-    Expected Calibration Error (ECE).
-    This metric is used on classification [1]_ or as Detection Expected Calibration Error on object
-    detection tasks [2]_. This metrics measures the expected difference between accuracy and confidence by grouping
-    all samples (size :math:`N`) into :math:`K` bins
-    and calculating
+    Expected Calibration Error (ECE) for classification and Detection Expected Calibration Error (D-ECE) for
+    object detection or segmentation.
+    This metric is used on classification [1]_ or as Detection Expected Calibration Error (D-ECE) on object
+    detection tasks [2]_. This metrics measures the expected difference between accuracy/precision and confidence
+    by grouping all samples (size :math:`N`) into :math:`B` bins, so that the ECE is computed by
 
     .. math::
 
-       ECE = \\sum_{i=1}^K \\frac{|B_i|}{N} |\\text{acc}_i - \\text{conf}_i| ,
+       ECE = \\sum_{b=1}^B \\frac{N_b}{N} |\\text{acc}(b) - \\text{conf}(b)| ,
 
-    where :math:`\\text{acc}_i` and :math:`\\text{conf}_i` denote the accuracy and average confidence in the i-th bin
-    and :math:`|B_i|` denote the number of samples in bin :math:`B_i`.
+    where :math:`\\text{acc}(b)` and :math:`\\text{conf}(b)` denote the accuracy and average confidence in the i-th bin
+    and :math:`N_b` denote the number of samples in bin :math:`b`.
 
     Parameters
     ----------
     bins : int or iterable, default: 10
-        Number of bins used by the Histogram Binning.
+        Number of bins used by the Expected Calibration Error.
         On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = ... = bins).
         If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
     equal_intervals : bool, optional, default: True
@@ -47,18 +47,23 @@ class ECE(_Miscalibration):
     .. [1] Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
        "Obtaining well calibrated probabilities using bayesian binning."
        Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
-       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`_
+       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`__
     .. [2] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
        The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
-       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`_.
+       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`__.
     """
 
-    def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray],
-                batched: bool = False, uncertainty: str = None,
-                return_map: bool = False,
-                return_num_samples: bool = False,
-                return_uncertainty_map: bool = False) -> Union[float, Tuple]:
+    def measure(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            batched: bool = False,
+            uncertainty: str = None,
+            return_map: bool = False,
+            return_num_samples: bool = False,
+            return_uncertainty_map: bool = False
+    ) -> Union[float, Tuple]:
         """
         Measure calibration by given predictions with confidence and the according ground truth.
         Assume binary predictions with y=1.
@@ -107,8 +112,9 @@ def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[
             If 'return_uncertainty' is True, return tuple and append the average standard deviation of confidence within each bin (excluding confidence dimension).
         """
 
-        return self._measure(X=X, y=y, metric='ece',
-                             batched=batched, uncertainty=uncertainty,
-                             return_map=return_map,
-                             return_num_samples=return_num_samples,
-                             return_uncertainty_map=return_uncertainty_map)
+        return self._measure(
+            X=X, y=y, metric='ece', batched=batched, uncertainty=uncertainty,
+            return_map=return_map,
+            return_num_samples=return_num_samples,
+            return_uncertainty_map=return_uncertainty_map
+        )
diff --git a/netcal/metrics/MCE.py b/netcal/metrics/confidence/MCE.py
similarity index 81%
rename from netcal/metrics/MCE.py
rename to netcal/metrics/confidence/MCE.py
index e909b58..df70656 100644
--- a/netcal/metrics/MCE.py
+++ b/netcal/metrics/confidence/MCE.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -7,26 +7,27 @@
 
 from typing import Union, Iterable, Tuple
 import numpy as np
-from .Miscalibration import _Miscalibration
+from netcal.metrics.Miscalibration import _Miscalibration
 
 
 class MCE(_Miscalibration):
     """
-    Maximum Calibration Error (MCE).
+    Maximum Calibration Error (MCE) for classification and Detection Maximum Calibration Error (D-MCE) for
+    object detection or segmentation.
     This metric is used on classification [1]_ or as Detection Maximum calibration error (D-MCE) on
     object detection [2]_. This metrics measures the maximum difference between accuracy and confidence over all bins
-    by grouping all samples into :math:`K` bins and calculating
+    by grouping all samples into :math:`B` bins and calculating
 
     .. math::
 
-       MCE = \max_{i \\in \\{1, ..., K\\}} |\\text{acc}_i - \\text{conf}_i| ,
+       MCE = \max_{b \\in \\{1, ..., B\\}} |\\text{acc}(b) - \\text{conf}(b)| ,
 
-    where :math:`\\text{acc}_i` and :math:`\\text{conf}_i` denote the accuracy and average confidence in the i-th bin.
+    where :math:`\\text{acc}(b)` and :math:`\\text{conf}(b)` denote the accuracy and average confidence in the b-th bin.
 
     Parameters
     ----------
     bins : int or iterable, default: 10
-        Number of bins used by the Histogram Binning.
+        Number of bins used by the MCE.
         On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = ... = bins).
         If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
     equal_intervals : bool, optional, default: True
@@ -45,18 +46,23 @@ class MCE(_Miscalibration):
     .. [1] Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
        "Obtaining well calibrated probabilities using bayesian binning."
        Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
-       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`_
+       `Get source online <https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958>`__
     .. [2] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
        The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
-       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`_
+       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`__
     """
 
-    def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray],
-                batched: bool = False, uncertainty: str = None,
-                return_map: bool = False,
-                return_num_samples: bool = False,
-                return_uncertainty_map: bool = False) -> Union[float, Tuple]:
+    def measure(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            batched: bool = False,
+            uncertainty: str = None,
+            return_map: bool = False,
+            return_num_samples: bool = False,
+            return_uncertainty_map: bool = False
+    ) -> Union[float, Tuple]:
         """
         Measure calibration by given predictions with confidence and the according ground truth.
         Assume binary predictions with y=1.
@@ -105,8 +111,9 @@ def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[
             If 'return_uncertainty' is True, return tuple and append the average standard deviation of confidence within each bin (excluding confidence dimension).
         """
 
-        return self._measure(X=X, y=y, metric='mce',
-                             batched=batched, uncertainty=uncertainty,
-                             return_map=return_map,
-                             return_num_samples=return_num_samples,
-                             return_uncertainty_map=return_uncertainty_map)
+        return self._measure(
+            X=X, y=y, metric='mce', batched=batched, uncertainty=uncertainty,
+            return_map=return_map,
+            return_num_samples=return_num_samples,
+            return_uncertainty_map=return_uncertainty_map
+        )
diff --git a/netcal/metrics/MMCE.py b/netcal/metrics/confidence/MMCE.py
similarity index 85%
rename from netcal/metrics/MMCE.py
rename to netcal/metrics/confidence/MMCE.py
index 018db39..2b93308 100644
--- a/netcal/metrics/MMCE.py
+++ b/netcal/metrics/confidence/MMCE.py
@@ -1,12 +1,11 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
 from typing import Iterable
-import logging
 from typing import Union
 import numpy as np
 
@@ -15,13 +14,13 @@
 
 class MMCE(object):
     """
-    Maximum Mean Calibration Error (MMCE) [1]_.
-    A differentiable approximation to the Expected Calibration Error (ECE) using a
+    Maximum Mean Calibration Error (MMCE).
+    The MMCE [1]_ is a differentiable approximation to the Expected Calibration Error (ECE) using a
     reproducing _kernel Hilbert space (RKHS).
-    Using a dataset :math:`\\mathcal{D}` of size :math:`N` consisting of the ground truth labels :math:`\\hat{y} \\in \\{1, ..., K \\}`
-    with input :math:`\\hat{y} \\in \\mathcal{X}`, the MMCE is calculated by using a scoring classifier :math:`\\hat{p}=h(x)`
-    that returns the highest probability for a certain class in conjunction with the predicted label
-    information :math:`y \\in \\{1, ..., K \\}` and is defined by
+    Using a dataset :math:`\\mathcal{D}` of size :math:`N` consisting of the ground truth labels
+    :math:`\\hat{y} \\in \\{1, ..., K \\}` with input :math:`x \\in \\mathcal{X}`, the MMCE is calculated by using
+    a scoring classifier :math:`\\hat{p}=h(x)` that returns the highest probability for a certain class in conjunction
+    with the predicted label information :math:`y \\in \\{1, ..., K \\}` and is defined by
 
     .. math::
 
@@ -46,19 +45,22 @@ class MMCE(object):
     .. [1] Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain:
        "Trainable calibration measures for neural networks from _kernel mean embeddings."
        International Conference on Machine Learning. 2018.
-       `Get source online <http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf>`_.
+       `Get source online <http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf>`__.
     """
 
     @accepts(bool)
     def __init__(self, detection: bool = False):
         """ Constructor. For parameter doc see class doc. """
 
-        self.logger = logging.getLogger('calibration')
-
         assert not detection, "MMCE is currently not supported for object detection."
         self.detection = detection
 
-    def _batched(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray], batched: bool = False):
+    def _batched(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            batched: bool = False
+    ):
         # batched: interpret X and y as multiple predictions
 
         if not batched:
@@ -88,7 +90,12 @@ def _kernel(self, confidence):
         diff = confidence[:, None] - confidence
         return np.exp(-2.5 * np.abs(diff))
 
-    def measure(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray], batched: bool = False):
+    def measure(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            batched: bool = False
+    ):
         """
         Measure calibration by given predictions with confidence and the according ground truth.
 
diff --git a/netcal/metrics/confidence/README.md b/netcal/metrics/confidence/README.md
new file mode 100644
index 0000000..a7487bd
--- /dev/null
+++ b/netcal/metrics/confidence/README.md
@@ -0,0 +1,13 @@
+# Metrics for Confidence Calibration
+
+Methods for measuring miscalibration in the context of confidence calibration.
+
+The common methods for confidence calibration evaluation are given with the
+*netcal.metrics.confidence.ECE* (ECE), *netcal.metrics.confidence.MCE* (MCE), and
+*netcal.metrics.confidence.ACE* (ACE). Each method bins the samples by their confidence and measures the
+accuracy in each bin. The ECE gives the mean gap between confidence and observed accuracy in each bin weighted by the
+number of samples. The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights
+each bin equally.
+
+A further metric is the Maximum Mean Calibration Error (MMCE) which is a differentiable variant of the ECE that
+might also be used as a regularization technique during model training.
\ No newline at end of file
diff --git a/netcal/metrics/confidence/__init__.py b/netcal/metrics/confidence/__init__.py
new file mode 100644
index 0000000..0511554
--- /dev/null
+++ b/netcal/metrics/confidence/__init__.py
@@ -0,0 +1,28 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+"""
+.. include:: /../../netcal/metrics/confidence/README.md
+   :parser: myst_parser.sphinx_
+
+Available classes
+=================
+
+.. autosummary::
+   :toctree: _autosummary_metric
+   :template: custom_class.rst
+
+   ACE
+   ECE
+   MCE
+   MMCE
+"""
+
+from .ACE import ACE
+from .ECE import ECE
+from .MCE import MCE
+from .MMCE import MMCE
diff --git a/netcal/metrics/regression/ENCE.py b/netcal/metrics/regression/ENCE.py
new file mode 100644
index 0000000..8d2123d
--- /dev/null
+++ b/netcal/metrics/regression/ENCE.py
@@ -0,0 +1,164 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+import warnings
+from typing import Iterable, Tuple, List
+from typing import Union
+import numpy as np
+
+from netcal import accepts, meanvar, cumulative_moments
+from netcal.metrics.Miscalibration import _Miscalibration
+
+
+class ENCE(_Miscalibration):
+    """
+    Expected Normalized Calibration Error (ENCE) for a regression calibration evaluation to test for
+    *variance calibration*. A probabilistic regression model takes :math:`X` as input and outputs a
+    mean :math:`\\mu_Y(X)` and a standard deviation :math:`\\sigma_Y(X)` targeting the ground-truth :math:`y`.
+    Similar to the :class:`netcal.metrics.confidence.ECE`, the ENCE applies a binning scheme with :math:`B` bins
+    over the predicted standard deviation :math:`\\sigma_Y(X)` and measures the absolute (normalized) difference
+    between root mean squared error (RMSE) and root mean variance (RMV) [1]_.
+    Thus, the ENCE [1]_ is defined by
+
+    .. math::
+        \\text{ENCE} := \\frac{1}{B} \\sum^B_{b=1} \\frac{|RMSE(b) - RMV(b)|}{RMV(b)} ,
+
+    where :math:`RMSE(b)` and :math:`RMV(b)` are the root mean squared error and the root mean variance within
+    bin :math:`b`, respectively.
+
+    If multiple dimensions are given, the ENCE is measured for each dimension separately.
+
+    Parameters
+    ----------
+    bins : int or iterable, default: 10
+        Number of bins used by the ENCE binning.
+        If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
+    sample_threshold : int, optional, default: 1
+        Bins with an amount of samples below this threshold are not included into the miscalibration metrics.
+
+    References
+    ----------
+    .. [1] Levi, Dan, et al.:
+       "Evaluating and calibrating uncertainty prediction in regression tasks."
+       arXiv preprint arXiv:1905.11659 (2019).
+       `Get source online <https://arxiv.org/pdf/1905.11659.pdf>`__
+    """
+
+    @accepts((int, tuple, list), int)
+    def __init__(
+            self,
+            bins: Union[int, Iterable[int]] = 10,
+            sample_threshold: int = 1
+    ):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        super().__init__(bins=bins, equal_intervals=True, detection=False, sample_threshold=sample_threshold)
+
+    def measure(
+            self,
+            X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            *,
+            kind: str = 'meanstd',
+            range_: List[Tuple[float, float]] = None,
+    ):
+        """
+        Measure the ENCE for given input data either as tuple consisting of mean and stddev estimates or as
+        NumPy array consisting of a sample distribution.
+        If multiple dimensions are given, the ENCE is measured for each dimension separately.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data obtained by a model that performs inference with uncertainty.
+            See parameter "kind" for input format descriptions.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+        range_ : list of length d with tuples (lower_bound: float, upper_bound: float)
+            List of tuples that define the binning range of the standard deviation for each dimension separately.
+            For example, if input data is given with only a few samples having high standard deviations,
+            this might distort the calculations as the binning scheme commonly takes the (min, max) as the range
+            for the binning, yielding a high amount of empty bins.
+
+        Returns
+        -------
+        NumPy array of shape (d,)
+            NumPy array with the ENCE for each input dimension separately.
+        """
+
+        assert kind in ['meanstd', 'cauchy', 'cumulative'], 'Parameter \'kind\' must be either \'meanstd\', or \'cumulative\'.'
+        if kind == "meanstd":
+            (mean, var), y, cov = meanvar(X, y)
+
+            # check if correlated input is given
+            if cov:
+                raise RuntimeError("UCE is not defined for multivariate data with correlation.")
+
+            mean = np.expand_dims(mean, axis=1) if mean.ndim == 1 else mean  # (n, d)
+            var = np.expand_dims(var, axis=1) if var.ndim == 1 else var  # (n, d)
+
+        # Cauchy distribution has no variance - ENCE is not applicable
+        elif kind == "cauchy":
+
+            n_dims = y.shape[1] if y.ndim == 2 else 1
+
+            warnings.warn("ENCE is not applicable for Cauchy distributions.")
+            return np.full(shape=(n_dims,), fill_value=float('nan'))
+
+        else:
+
+            # extract sampling points t and cumulative
+            # get differences of cumulative and intermediate points of t
+            t, cdf = X
+            mean, var = cumulative_moments(t, cdf)  # (n, d) and (n, d)
+
+        y = np.expand_dims(y, axis=1) if y.ndim == 1 else y
+        std = np.sqrt(var)
+        n_samples, n_dims = y.shape
+
+        # squared error
+        error = np.square(mean - y)  # (n, d)
+
+        # prepare binning boundaries for regression
+        bin_bounds = self._prepare_bins_regression(std, n_dims=n_dims, range_=range_)
+
+        ence = []
+        for dim in range(n_dims):
+
+            # perform binning over 1D stddev
+            (mv_hist, mse_hist), n_samples, _, _ = self.binning(
+                [bin_bounds[dim]],
+                std[:, dim],
+                var[:, dim],
+                error[:, dim]
+            )
+
+            rmv_hist = np.sqrt(mv_hist)  # (b,)
+            rmse_hist = np.sqrt(mse_hist)  # (b,)
+
+            # ENCE for current dim is equally weighted (but normalized) mean over all bins
+            ence.append(
+                np.nanmean(
+                    np.divide(
+                        np.abs(rmv_hist - rmse_hist), rmv_hist,
+                        out=np.full_like(rmv_hist, fill_value=float('nan')),
+                        where=rmv_hist != 0
+                    )
+                )
+            )
+
+        ence = np.array(ence).squeeze()
+        return ence
diff --git a/netcal/metrics/regression/NLL.py b/netcal/metrics/regression/NLL.py
new file mode 100644
index 0000000..7355c8b
--- /dev/null
+++ b/netcal/metrics/regression/NLL.py
@@ -0,0 +1,182 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Tuple
+from typing import Union
+import numpy as np
+from scipy.stats import norm, cauchy
+
+import torch
+from torch.distributions import MultivariateNormal
+
+from netcal import meanvar, mv_cauchy_log_density, density_from_cumulative
+
+
+class NLL(object):
+    """
+    Negative log likelihood (NLL) for probabilistic regression models.
+    If a probabilistic forecaster outputs a probability density function (PDF) :math:`f_Y(y)` targeting the ground-truth
+    :math:`y`, the negative log likelihood is defined by
+
+    .. math::
+        \\text{NLL} = -\\sum^N_{n=1} \\log\\big(f_Y(y)\\big) ,
+
+    with :math:`N` as the number of samples within the examined data set.
+
+    **Note:** the input field for the standard deviation might also be given as quadratic NumPy arrays of shape
+    (n, d, d) with d dimensions. In this case, this method asserts covariance matrices as input
+    for each sample and the NLL is calculated for multivariate distributions.
+    """
+
+    def measure(
+            self,
+            X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            *,
+            kind: str = 'meanstd',
+            reduction: str = 'batchmean',
+    ) -> Union[float, np.ndarray]:
+        """
+        Measures the negative log likelihood (NLL) for probabilistic regression models.
+        If the input standard deviation is given with shape (n, d, d), this method asserts covariance matrices as input
+        for each sample. In this case, the NLL is calculated for multivariate distributions.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data obtained by a model that performs inference with uncertainty.
+            See parameter "kind" for input format descriptions.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) and (n, [d, [d]]), this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If the second NumPy array has shape (n, d, d), this method asserts covariance matrices as input
+                       for each sample. In this case, the NLL is calculated for multivariate distributions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+        reduction : str, one of 'none', 'mean', 'batchmean', 'sum' or 'batchsum', default: 'batchmean'
+            Specifies the reduction to apply to the output:
+            - none : no reduction is performed. Return NLL for each sample and for each dim separately.
+            - mean : calculate mean over all samples and all dimensions.
+            - batchmean : calculate mean over all samples but for each dim separately.
+                          If input has covariance matrices, 'batchmean' is the same as 'mean'.
+            - sum : calculate sum over all samples and all dimensions.
+            - batchsum : calculate sum over all samples but for each dim separately.
+                         If input has covariance matrices, 'batchsum' is the same as 'sum'.
+
+        Returns
+        -------
+        float or np.ndarray
+            Negative Log Likelihood for regression input. See parameter 'reduction' for detailed return type.
+        """
+
+        assert kind in ['meanstd', 'cauchy', 'cumulative'], 'Parameter \'kind\' must be either \'meanstd\', or \'cumulative\'.'
+
+        if kind == "cumulative":
+
+            assert isinstance(X, (tuple, list)), "If kind=\'cumulative\', assert input X as tuple of sampling points" \
+                                                 " and the respective cumulative scores."
+            t, cdf = X[0], X[1]  # (t, n, [d])
+
+            # make t, CDF at least 3d, y at least 2d
+            t = np.expand_dims(t, axis=2) if t.ndim == 2 else t  # (t, n, d)
+            cdf = np.expand_dims(cdf, axis=2) if cdf.ndim == 2 else cdf  # (t, n, d)
+            y = np.expand_dims(y, axis=1) if y.ndim == 1 else y  # (n, d)
+
+            # get density using the cumulative
+            pdf = density_from_cumulative(t, cdf)
+
+            # for the moment, use the nearest point of the curve to determine the actual likelihood
+            nearest = np.argmin(
+                np.abs(t - y[None, ...]),  # (t, n, d)
+                axis=0,
+            )  # (n, d)
+
+            # take likelihood om PDF and compute negative log of likelihood
+            likelihood = np.squeeze(
+                np.take_along_axis(pdf, nearest[None, ...], axis=0),  # (1, n, d)
+                axis=0
+            )  # (n, d)
+
+            # clip likelihood to avoid 0
+            likelihood = np.clip(likelihood, a_min=1e-6, a_max=None)
+
+            nll = -np.log(likelihood)  # (n, d)
+
+        # use Cauchy distribution to measure NLL
+        elif kind == "cauchy":
+
+            mode, scale = X[0], X[1]  # (n, [d])
+
+            mode = np.expand_dims(mode, axis=1) if mode.ndim == 1 else mode  # (n, d)
+            scale = np.expand_dims(scale, axis=1) if scale.ndim == 1 else scale  # (n, d)
+            y = np.expand_dims(y, axis=1) if y.ndim == 1 else y  # (n, d)
+
+            # scale is multivariate?
+            if scale.ndim == 3:
+                with torch.no_grad():
+                    nll = -mv_cauchy_log_density(
+                        torch.from_numpy(y),
+                        torch.from_numpy(mode),
+                        torch.from_numpy(scale)
+                    ).numpy()  # (n,)
+
+            else:
+                nll = -cauchy.logpdf(y, loc=mode, scale=scale)
+
+        # otherwise, use parametric Gaussian expression
+        else:
+            (mean, var), y, correlations = meanvar(X, y)
+
+            # make mean, var and y at least 2d, for covariances 3d
+            mean = np.expand_dims(mean, axis=1) if mean.ndim == 1 else mean  # (n, d)
+            y = np.expand_dims(y, axis=1) if y.ndim == 1 else y  # (n, d)
+
+            # in the multivariate case, use a multivariate normal distribution and get logpdf
+            if correlations:
+                var = np.reshape(var, (-1, 1, 1)) if var.ndim == 1 else var  # (n, d, d)
+
+                # torch's MVN is capable of batched computation in contrast to SciPy's variant
+                mvn = MultivariateNormal(loc=torch.from_numpy(mean), covariance_matrix=torch.from_numpy(var))
+                nll = -mvn.log_prob(torch.from_numpy(y)).numpy()  # (n,)
+
+            # in the independent case, use a standard normal distribution and get logpdf
+            else:
+                var = np.expand_dims(var, axis=1) if var.ndim == 1 else var  # (n, d)
+                std = np.sqrt(var)
+                nll = -norm.logpdf(y, loc=mean, scale=std)
+
+        # perform reduction of (n, d) to single float if requested
+        if reduction is None or reduction == 'none':
+            return nll
+
+        # 'mean' is mean over all samples and all dimensions
+        elif reduction == "mean":
+            return float(np.mean(nll))
+
+        # 'batchmean' is mean over all samples but for each dim separately.
+        # If correlations == True, 'batchmean' is the same as 'mean'.
+        elif reduction == "batchmean":
+            return np.mean(nll, axis=0)  # (d,) or scalar
+
+        # 'sum' is sum over all samples and all dimensions
+        elif reduction == "sum":
+            return float(np.sum(nll))
+
+        # 'batchsum' is sum over all samples but for each dim separately.
+        # If correlations == True, 'batchsum' is the same as 'sum'.
+        elif reduction == "batchsum":
+            return np.sum(nll, axis=0)  # (d,) or scalar
+
+        # unknown reduction method
+        else:
+            raise RuntimeError("Unknown reduction: \'%s\'" % reduction)
diff --git a/netcal/metrics/regression/PICP.py b/netcal/metrics/regression/PICP.py
new file mode 100644
index 0000000..ad1d00a
--- /dev/null
+++ b/netcal/metrics/regression/PICP.py
@@ -0,0 +1,163 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Iterable, NamedTuple
+from collections import namedtuple
+import numpy as np
+from typing import Union
+
+from netcal import is_in_quantile
+from netcal.metrics.Miscalibration import _Miscalibration
+
+
+class PICP(_Miscalibration):
+    """
+    Compute Prediction Interval Coverage Probability (PICP) and Mean Prediction Interval Width (MPIW).
+    These metrics have been proposed by [1]_, [2]_.
+    This metric is used for Bayesian models to determine the quality of the uncertainty estimates.
+    In Bayesian mode, an uncertainty estimate is attached to each sample. The PICP measures the probability, that
+    the true (observed) accuracy falls into the p% prediction interval. The uncertainty is well-calibrated, if
+    the PICP is equal to p%. Simultaneously, the MPIW measures the mean width of all prediction intervals to evaluate
+    the sharpness of the uncertainty estimates.
+
+    Parameters
+    ----------
+    bins : int or iterable, default: 10
+        Number of bins used by the PICP.
+        On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = ... = bins).
+        If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
+    equal_intervals : bool, optional, default: True
+        If True, the bins have the same width. If False, the bins are splitted to equalize
+        the number of samples in each bin.
+    detection : bool, default: False
+        If False, the input array 'X' is treated as multi-class confidence input (softmax)
+        with shape (n_samples, [n_classes]).
+        If True, the input array 'X' is treated as a box predictions with several box features (at least
+        box confidence must be present) with shape (n_samples, [n_box_features]).
+    sample_threshold : int, optional, default: 1
+        Bins with an amount of samples below this threshold are not included into the process metrics.
+
+    References
+    ----------
+    .. [1] Kuleshov, V.; Fenner, N. & Ermon, S.:
+       "Accurate Uncertainties for Deep Learning Using Calibrated Regression."
+       International Conference on Machine Learning (ICML), 2018
+       `Get source online <http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf>`__
+
+    .. [2] Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez:
+       "Quality of Uncertainty Quantification for Bayesian Neural Network Inference."
+       Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019
+       `Get source online <https://arxiv.org/pdf/1906.09686.pdf>`__
+    """
+
+    def measure(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            q: Union[float, Iterable[float], np.ndarray],
+            *,
+            kind: str = 'meanstd',
+            reduction: str = 'batchmean',
+    ) -> NamedTuple:
+        """
+        Measure calibration by given predictions with confidence and the according ground truth.
+        Assume binary predictions with y=1.
+
+        Parameters
+        ----------
+        X : iterable of np.ndarray, or np.ndarray of shape=([n_bayes], n_samples, [n_classes/n_box_features])
+            NumPy array with confidence values for each prediction on classification with shapes
+            1-D for binary classification, 2-D for multi class (softmax).
+            If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
+            for a single sample (e.g. variational inference or MC dropout samples).
+            If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
+            interpret this parameter as multiple predictions that should be averaged.
+            On detection, this array must have 2 dimensions with number of additional box features in last dim.
+        y : iterable of np.ndarray with same length as X or np.ndarray of shape=([n_bayes], n_samples, [n_classes])
+            NumPy array with ground truth labels.
+            Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
+            If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
+            for a single sample (e.g. variational inference or MC dropout samples).
+            If iterable over multiple instances of np.ndarray and parameter batched=True,
+            interpret this parameter as multiple predictions that should be averaged.
+        q : np.ndarray of shape (q,)
+            Quantile scores in [0, 1] of size q to compute the x-valued quantile boundaries for.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) and (n, [d, [d]]), this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If the second NumPy array has shape (n, d, d), this method asserts covariance matrices as input
+                       for each sample. In this case, the NLL is calculated for multivariate distributions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+            - confidence: asserts X as a single NumPy array of shape (t, n, [1]) with t stochastic forward passes with
+                          scores in [0, 1] that represent confidence scores obtained e.g. by Monte-Carlo sampling.
+                          Furthermore, this mode asserts the ground-truth labels 'y' in the {0, 1} set and converts
+                          them to continuous [0, 1] scores by binning. Thus, it is possible to evaluate the
+                          confidence uncertainty with binned labels.
+        reduction : str, one of 'none', 'mean' or 'batchmean', default: 'batchmean'
+            Specifies the reduction to apply to the output:
+            - none : no reduction is performed. Return QCE for each sample and for each dim separately.
+            - mean : calculate mean over all quantiles and all dimensions.
+            - batchmean : calculate mean over all quantiles but for each dim separately.
+                          If input has covariance matrices, 'batchmean' is the same as 'mean'.
+
+        Returns
+        -------
+        Namedtuple PICPResult with fields "picp" and "mpiw", where each field either holds the PICP/MPIW score
+        or a tuple of (float, np.ndarray)
+            Always returns a named tuple with PICP (prediction interval coverage probability) and MPIW
+            (mean prediction interval width).
+        """
+
+        # PICP returns a namedtuple - init
+        picpresult = namedtuple('PICPResult', ['picp', 'mpiw'])
+
+        # kind 'confidence' induces a different treatment - the target scores given by 'y' are assumed
+        # to be in the {0, 1} set and are converted to continuous [0, 1] scores by binning the samples.
+        # Thus, it is possible to evaluate the confidence uncertainty
+        if kind == "confidence":
+            result = self.frequency(X=X, y=y, batched=False, uncertainty="mean")
+
+            # frequency is 2nd entry in return tuple and within first batch
+            X = X[..., :1]  # (t, n, 1)
+            y = np.reshape(result[1][0], (-1, 1))  # (n, 1)
+
+            # kind 'meanstd' will result in a HPDI computation if sample distribution is given
+            kind = "meanstd"
+
+        in_quantile, _, (qbounds_min, qbounds_max), _, _ = is_in_quantile(X, y, q, kind)  # (q, n, [d]), (q, n, d), (q, n, d),
+
+        picp = np.mean(in_quantile, axis=1)  # (q, d)
+        mpiw = np.mean(np.abs(qbounds_max - qbounds_min), axis=1)  # (q, d)
+
+        # no reduction is applied
+        if reduction is None or reduction == 'none':
+            pass
+
+        # 'mean' is mean over all quantiles and all dimensions
+        elif reduction == "mean":
+            picp = np.mean(picp)
+            mpiw = np.mean(mpiw)
+
+        # 'batchmean' is mean over all quantiles but for each dim separately.
+        # If input has covariance matrices, 'batchmean' is the same as 'mean'.
+        elif reduction == "batchmean":
+            picp = np.mean(picp, axis=0)  # (d,)
+            mpiw = np.mean(mpiw, axis=0)  # (d,)
+
+        # unknown reduction method
+        else:
+            raise RuntimeError("Unknown reduction: \'%s\'" % reduction)
+
+        # pack to namedtuple result
+        result = picpresult(picp, mpiw)
+
+        return result
diff --git a/netcal/metrics/regression/QCE.py b/netcal/metrics/regression/QCE.py
new file mode 100644
index 0000000..038531f
--- /dev/null
+++ b/netcal/metrics/regression/QCE.py
@@ -0,0 +1,356 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Iterable, Tuple, List
+from typing import Union
+import numpy as np
+
+from netcal import is_in_quantile
+from netcal.metrics.Miscalibration import _Miscalibration
+
+
+# annotation hint
+QCE_METRIC = Union[float, np.ndarray]
+QCE_MAP = Union[List[np.ndarray], None]
+
+
+class QCE(_Miscalibration):
+    """
+    Marginal Quantile Calibration Error (M-QCE) and Conditional Quantile Calibration Error (C-QCE) which both measure
+    the gap between predicted quantiles and observed quantile coverage also for multivariate distributions.
+    The M-QCE and C-QCE have originally been proposed by [1]_.
+    The derivation of both metrics are based on
+    the Normalized Estimation Error Squared (NEES) known from object tracking [2]_.
+    The derivation of both metrics is shown in the following.
+
+    **Definition of standard NEES:**
+    Given mean prediction :math:`\\hat{\\boldsymbol{y}} \\in \\mathbb{R}^M`, ground-truth
+    :math:`\\boldsymbol{y} \\in \\mathbb{R}^M`, and
+    estimated covariance matrix :math:`\\hat{\\boldsymbol{\\Sigma}} \\in \\mathbb{R}^{M \\times M}` using
+    :math:`M` dimensions, the NEES is defined as
+
+    .. math::
+        \\epsilon = (\\boldsymbol{y} - \\hat{\\boldsymbol{y}})^\\top \\hat{\\boldsymbol{\\Sigma}}^{-1}
+        (\\boldsymbol{y} - \\hat{\\boldsymbol{y}}) .
+
+    The average NEES is defined as the mean error over :math:`N` trials in a Monte-Carlo simulation for
+    Kalman-Filter testing, so that
+
+    .. math::
+        \\bar{\\epsilon} = \\frac{1}{N} \\sum^N_{i=1} \\epsilon_i .
+
+    Under the condition, that :math:`\\mathbb{E}[\\boldsymbol{y} - \\hat{\\boldsymbol{y}}] = \\boldsymbol{0}` (zero mean),
+    a :math:`\\chi^2`-test is performed to evaluate the estimated uncertainty. This test is accepted, if
+
+    .. math::
+        \\bar{\\epsilon} \\leq \\chi^2_M(\\tau),
+
+    where :math:`\\chi^2_M(\\tau)` is the PPF score obtained by a :math:`\\chi^2` distribution
+    with :math:`M` degrees of freedom, for a certain quantile level :math:`\\tau \\in [0, 1]`.
+
+    **Marginal Quantile Calibration Error (M-QCE):**
+    In the case of regression calibration testing, we are interested in the gap between predicted quantile levels and
+    observed quantile coverage probability for a certain set of quantile levels. We assert :math:`N` observations of our
+    test set that are used to estimate the NEES, so that we can compute the expected deviation between predicted
+    quantile level and observed quantile coverage by
+
+    .. math::
+        \\text{M-QCE}(\\tau) := \\mathbb{E} \\Big[ \\big| \\mathbb{P} \\big( \\epsilon \\leq \\chi^2_M(\\tau) \\big) - \\tau \\big| \\Big] ,
+
+    which is the definition of the Marginal Quantile Calibration Error (M-QCE) [1]_.
+    The M-QCE is calculated by
+
+    .. math::
+        \\text{M-QCE}(\\tau) = \\Bigg| \\frac{1}{N} \\sum^N_{n=1} \\mathbb{1} \\big( \\epsilon_n \\leq \\chi^2_M(\\tau) \\big) - \\tau \\Bigg|
+
+    **Conditional Quantile Calibration Error (C-QCE):**
+    The M-QCE measures the marginal calibration error which is more suitable to test for *quantile calibration*.
+    However, similar to :class:`netcal.metrics.regression.UCE` and :class:`netcal.metrics.regression.ENCE`,
+    we want to induce a dependency on the estimated covariance, since we require
+    that
+
+    .. math::
+        &\\mathbb{E}[(\\boldsymbol{y} - \\hat{\\boldsymbol{y}})(\\boldsymbol{y} - \\hat{\\boldsymbol{y}})^\\top |
+        \\hat{\\boldsymbol{\\Sigma}} = \\boldsymbol{\\Sigma}] = \\boldsymbol{\\Sigma},
+
+        &\\forall \\boldsymbol{\\Sigma} \\in \\mathbb{R}^{M \\times M}, \\boldsymbol{\\Sigma} \\succcurlyeq 0,
+        \\boldsymbol{\\Sigma}^\\top = \\boldsymbol{\\Sigma} .
+
+    To estimate the a *covariance* dependent QCE, we apply a binning scheme (similar to the
+    :class:`netcal.metrics.confidence.ECE`) over the square root of the *standardized generalized variance* (SGV) [3]_,
+    that is defined as
+
+    .. math::
+        \\sigma_G = \\sqrt{\\text{det}(\\hat{\\boldsymbol{\\Sigma}})^{\\frac{1}{M}}} .
+
+    Using the generalized standard deviation, it is possible to get a summarized statistic across different
+    combinations of correlations to denote the distribution's dispersion. Thus, the Conditional Quantile Calibration
+    Error (C-QCE) [1]_ is defined by
+
+    .. math::
+        \\text{C-QCE}(\\tau) := \\mathbb{E}_{\\sigma_G, X}\\Big[\\Big|\\mathbb{P}\\big(\\epsilon \\leq \\chi^2_M(\\tau) | \\sigma_G\\big) - \\tau \\Big|\\Big] ,
+
+    To approximate the expectation over the generalized standard deviation, we use a binning scheme with :math:`B` bins
+    (similar to the ECE) and :math:`N_b` samples per bin to compute the weighted sum across all bins, so that
+
+    .. math::
+        \\text{C-QCE}(\\tau) \\approx \\sum^B_{b=1} \\frac{N_b}{N} | \\text{freq}(b) - \\tau |
+
+    where :math:`\\text{freq}(b)` is the coverage frequency within bin :math:`b` and given by
+
+    .. math::
+        \\text{freq}(b) = \\frac{1}{N_b} \\sum_{n \\in \\mathcal{M}_b} \\mathbb{1}\\big(\\epsilon_i \\leq \\chi^2_M(\\tau)\\big) ,
+
+    with :math:`\\mathcal{M}_b` as the set of indices within bin :math:`b`.
+
+    Parameters
+    ----------
+    bins : int or iterable, default: 10
+        Number of bins used for the internal binning.
+        If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
+    marginal : bool, optional, default: False
+        If True, compute the M-QCE. This is the marginal probability over all samples falling into the desired
+        quantiles. If False, use the C-QCE.
+        The C-QCE uses a binning scheme by the gerneralized standard deviation to measure the conditional probability
+        over all samples falling into the desired quantiles w.r.t. the generalized standard deviation.
+    sample_threshold : int, optional, default: 1
+        Bins with an amount of samples below this threshold are not included into the miscalibration metrics.
+
+    References
+    ----------
+    .. [1] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+       "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+       European Conference on Computer Vision (ECCV) Workshops, 2022.
+       `Get source online <https://arxiv.org/pdf/2207.01242.pdf>`__
+
+    .. [2] Y. Bar-Shalom, X. R. Li, and T. Kirubarajan:
+       "Estimation with applications to tracking and navigation."
+       Theory algorithms and software. John Wiley & Sons, 2004.
+
+    .. [3] A. SenGupta:
+       “Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions.”
+       Journal of Multivariate Analysis, vol. 23, no. 2, pp. 209–219, 1987.
+       `Get source online <https://pdf.sciencedirectassets.com/272481/1-s2.0-S0047259X87X8001X/1-s2.0-0047259X87901539/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEB0aCXVzLWVhc3QtMSJHMEUCIAo6pl1vIu8%2F8ZEnEt6OKsA92ajSFy8%2BgjC8Tt9Tr360AiEAiVljbWcKBWAkrSpyT3LCCiX1Wug9gDf9WqxygiF%2B1G8q0gQIRhAEGgwwNTkwMDM1NDY4NjUiDLFU4Fzvuej7%2FpkSSCqvBNybwrdLhAP1yVFKRn0AQPK3G5t2wOY5ssTpqbS1HQzoz1EvOo%2BvWNeXPrWTo%2FhUvw8knQEWp9wA7a5wGdsbnmaBmCAWUFStKxSib9htTLAX1Ij5NCh%2ByA%2BiJwvPk4SXcRAJx4zQfJ8N%2FM2jcA3Lji7VPDYR8jNu7FfMd54veXYuqzUDoIdhVWIF4Czx0fwqngck9errYuNVSQCGSaW28m3%2BCr3%2FiePEQrXJcX0K7Q3z5D0%2FHGJvMsw%2FDqugg9gjWAFCquBO6EL9ircGBmzVsYnx8pKPZfa84aHZgGJPwvJp01o6qvUEdBZXbC5pmvDNAwIkguMahAHfNM3ffVDfyIVzRq1WrZIAKLYfgqFiGpNd3kGEUX5dGbSggAvxNXP7JX%2BifNsde9cIhzhqpjS0Z8BoOW8AGbXq9n15qEK%2F6xKJttpIhouxiadU6DtW%2BSDDFXDgdMVs1xU%2FE6dnWtl%2BQeA5VX4ITvTQMAjHOqu22lXEmOpHOmZ8fGKG5QTmz4iShixLGsgxpUMp2Wz%2F2OlCwt64m0sbI7zXr3YkUpyR019fs6IHJ28EVbeHsvp9xLrc5qltKHN3aoBmK4ZK0SFi%2FqHLhuz1HmWzCRQ0%2FkShcOXz80ttPlaHuX54VdVptvSy%2F1obsurjYuaR2HG9rO3lIneMgwKwwodZcKlu%2Fyo4WUCIk%2FhfKZrOWqVfAqqFPjWomg4CX787OIoqP%2FTz8H6sueGWk7HoeJKgSIW4yEISjNkwpdH7lQY6qQHS3GFk4XwFQEzwimYc%2B59DxQowARFI3PgPN%2F4FzUV5OHhm5G8455Dzm4T6R6E1%2F%2B86lSLdpH9JCkbDXBPJndiHTqXwBUej4wSWPASAvqQ6neC1lcJAqimCB7zn17je6g1dCi80xg1rZ6qU0c5BGtRqsCAB2NZlNn8jul1%2BM%2BiBF8SLE4xoNnT5kwEI%2FnnY81jvJw1kf4DspI9S8sAI2Z3efRca%2FBTIwgVw&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20220701T132912Z&X-Amz-SignedHeaders=host&X-Amz-Expires=300&X-Amz-Credential=ASIAQ3PHCVTYZE6GY4EQ%2F20220701%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Signature=416cca57ae51cdc7c137e60fa5eba2ba651152e29e6b3485feeeb45f66aaeebb&hash=f03a242d7d2e0652dfaa7c5e3fb713736b321247242986106eaa5412f136af12&host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&pii=0047259X87901539&tid=spdf-4216aa85-a41c-4358-8d5e-3e877785fe29&sid=4e9c65da63ee0949f79bfc42fc03dd438d5egxrqb&type=client&ua=4d545d0256065c055303&rr=723f7d3c3edc2199>`__
+    """
+
+    def __init__(
+            self,
+            bins: int = 10,
+            *,
+            marginal: bool = True,
+            sample_threshold: int = 1
+    ):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        super().__init__(bins=bins, equal_intervals=True, detection=False, sample_threshold=sample_threshold)
+        self.marginal = marginal
+
+        # these fields only act as a buffer to reuse within QCE presentation
+        self._bin_edges = []
+        self._is_cov = False
+
+    def measure(
+            self,
+            X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            q: Union[float, Iterable[float], np.ndarray],
+            *,
+            kind: str = 'meanstd',
+            reduction: str = 'batchmean',
+            range_: List[Tuple[float, float]] = None,
+            return_map: bool = False,
+            return_num_samples: bool = False,
+    ) -> Union[QCE_METRIC, Tuple[QCE_METRIC, QCE_MAP], Tuple[QCE_METRIC, QCE_MAP, QCE_MAP]]:
+        """
+        Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as
+        NumPy array consisting of a sample distribution. The loss is computed for several quantiles
+        given by parameter q.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data obtained by a model that performs inference with uncertainty.
+            See parameter "kind" for input format descriptions.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        q : np.ndarray of shape (q,)
+            Quantile scores in [0, 1] of size q to compute the x-valued quantile boundaries for.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) and (n, [d, [d]]), this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If the second NumPy array has shape (n, d, d), this method asserts covariance matrices as input
+                       for each sample. In this case, the NLL is calculated for multivariate distributions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+            - confidence: asserts X as a single NumPy array of shape (t, n, [1]) with t stochastic forward passes with
+                          scores in [0, 1] that represent confidence scores obtained e.g. by Monte-Carlo sampling.
+                          Furthermore, this mode asserts the ground-truth labels 'y' in the {0, 1} set and converts
+                          them to continuous [0, 1] scores by binning. Thus, it is possible to evaluate the
+                          confidence uncertainty with binned labels.
+        reduction : str, one of 'none', 'mean' or 'batchmean', default: 'batchmean'
+            Specifies the reduction to apply to the output:
+            - none : no reduction is performed. Return QCE for each sample and for each dim separately.
+            - mean : calculate mean over all quantiles and all dimensions.
+            - batchmean : calculate mean over all quantiles but for each dim separately.
+                          If input has covariance matrices, 'batchmean' is the same as 'mean'.
+        range_ : list of length d with tuples (lower_bound: float, upper_bound: float)
+            List of tuples that define the binning range of the standard deviation for each dimension separately.
+            For example, if input data is given with only a few samples having high standard deviations,
+            this might distort the calculations as the binning scheme commonly takes the (min, max) as the range
+            for the binning, yielding a high amount of empty bins.
+        return_map: bool, optional, default: False
+            If True, return miscalibration score for each quantile and each bin separately. Otherwise, compute mean
+            over all quantiles and all bins.
+        return_num_samples : bool, optional, default: False
+            If True, also return the number of samples in each bin.
+
+        Returns
+        -------
+        float or np.ndarray or tuple of (float, List[np.ndarray], [List[np.ndarray]])
+            Always returns miscalibration metric. See parameter "reduction" for a detailed description.
+            If 'return_map' is True, return tuple and append miscalibration map over all bins.
+            If 'return_num_samples' is True, return tuple and append the number of samples in each bin (excluding confidence dimension).
+        """
+
+        # clear bin_edges buffer list and is_cov buffer
+        self._bin_edges = []
+        self._is_cov = False
+
+        # kind 'confidence' induces a different treatment - the target scores given by 'y' are assumed
+        # to be in the {0, 1} set and are converted to continuous [0, 1] scores by binning the samples.
+        # Thus, it is possible to evaluate the confidence uncertainty
+        if kind == "confidence":
+            result = self.frequency(X=X, y=y, batched=False, uncertainty="mean")
+
+            # frequency is 2nd entry in return tuple and within first batch
+            X = X[..., :1]  # (t, n, 1)
+            y = np.reshape(result[1][0], (-1, 1))  # (n, 1)
+
+            # kind 'meanstd' will result in a HPDI computation if sample distribution is given
+            kind = "meanstd"
+
+        in_quantile, _, _, mean, var = is_in_quantile(X, y, q, kind)  # (q, n, [d]), (q, n, d), (n, d), (n, d, [d])
+        n_samples, n_dims = mean.shape
+
+        # if marginal, do not use a binning scheme but rather compute the marginal
+        # probabilities for each quantile level
+        if self.marginal:
+            frequency = np.mean(in_quantile, axis=1)  # (q, [d])
+
+            # expand q if frequency ndim = 2
+            q = np.expand_dims(q, axis=1) if frequency.ndim == 2 else q
+
+            # QCE is difference between expected quantile level and actual frequency
+            qce = np.abs(frequency - q)  # (q, [d])
+
+            qce_map = None
+            num_samples_hist = None
+
+        # if conditional, apply a binning scheme
+        else:
+
+            # independent variables: compute histogram edges for each dimensions independently
+            if var.ndim == 2:
+
+                self._is_cov = False
+                qce, qce_map, num_samples_hist = [], [], []
+                std = np.sqrt(var)
+
+                # prepare binning boundaries for regression
+                bin_bounds = self._prepare_bins_regression(std, n_dims=n_dims, range_=range_)
+
+                for dim in range(n_dims):
+
+                    # split up arrays for each quantile
+                    splitted = [x[:, dim] for x in in_quantile]  # [(n,), (n,), ...] of length q
+
+                    # perform binning over 1D variance
+                    freq_hist, n_samples_hist, bounds, _ = self.binning([bin_bounds[dim]], std[:, dim], *splitted)
+                    freq_hist, n_samples_hist = np.array(freq_hist), np.array(n_samples_hist)  # (q, b) , (b,)
+
+                    # calculate the difference between the expected quantile level and the observed frequency
+                    # compute the weighted sum
+                    qce_map_dim = np.abs(freq_hist - q[:, None])  # (q, b)
+                    qce_dim = np.average(qce_map_dim, axis=1, weights=n_samples_hist / n_samples)  # (q,)
+
+                    # add dimension results to overal result lists
+                    qce.append(qce_dim)
+                    qce_map.append(qce_map_dim)
+                    num_samples_hist.append(n_samples_hist)
+                    self._bin_edges.extend(bounds)
+
+                qce = np.stack(qce, axis=1)  # (q, d)
+
+            # multivariate (dependent case) - compute joint histogram bounds
+            # based on standardized generalized variance
+            else:
+
+                self._is_cov = True
+
+                # matrix determinant raise an exception - catch this to output a more meaningful error
+                try:
+                    determinant = np.linalg.det(var)  # (n,)
+                except np.linalg.LinAlgError:
+                    raise RuntimeError("QCE: found invalid input covariance matrices.")
+
+                # calculate standardized generalized variance
+                sgv = np.power(determinant, 1. / (n_dims))  # (n,)
+                sg_std = np.sqrt(sgv)
+
+                # prepare binning boundaries for regression
+                bin_bounds = self._prepare_bins_regression(sg_std, n_dims=1, range_=range_)
+
+                # split up arrays for each quantile
+                splitted = [x for x in in_quantile]  # [(n,), (n,), ...] of length q
+
+                # perform binning over SGV
+                frequency_hist, num_samples_hist, edges, _ = self.binning(bin_bounds, sg_std, *splitted)
+                frequency_hist, num_samples_hist = np.array(frequency_hist), np.array(num_samples_hist)  # (q, b) , (b,)
+
+                # calculate the difference between the expected quantile level and the observed frequency
+                # compute the weighted sum
+                qce_map = np.abs(frequency_hist - q[:, None])  # (q, b)
+                qce = np.average(qce_map, axis=1, weights=num_samples_hist / n_samples)  # (q,)
+
+                qce_map = [qce_map]
+                num_samples_hist = [num_samples_hist]
+
+                self._bin_edges.extend(edges)
+
+        # no reduction is applied
+        if reduction is None or reduction == 'none':
+            metric = qce
+
+        # 'mean' is mean over all quantiles and all dimensions
+        elif reduction == "mean":
+            metric = float(np.mean(qce))
+
+        # 'batchmean' is mean over all quantiles but for each dim separately.
+        # If input has covariance matrices, 'batchmean' is the same as 'mean'.
+        elif reduction == "batchmean":
+            metric = np.mean(qce, axis=0)  # (d,)
+
+        # unknown reduction method
+        else:
+            raise RuntimeError("Unknown reduction: \'%s\'" % reduction)
+
+        # build output structure w.r.t. user input
+        if not return_map and not return_num_samples:
+            return metric
+
+        return_value = (metric,)
+        if return_map and not self.marginal:
+            return_value = return_value + (qce_map,)
+
+        if return_num_samples and not self.marginal:
+            return_value = return_value + (num_samples_hist,)
+
+        return return_value
diff --git a/netcal/metrics/regression/QuantileLoss.py b/netcal/metrics/regression/QuantileLoss.py
new file mode 100644
index 0000000..9228de9
--- /dev/null
+++ b/netcal/metrics/regression/QuantileLoss.py
@@ -0,0 +1,119 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Iterable, Tuple
+from typing import Union
+import numpy as np
+from netcal import accepts, squeeze_generic, is_in_quantile
+
+
+class QuantileLoss(object):
+    """
+    Pinball aka quantile loss within regression calibration to test for *quantile calibration* of a probabilistic
+    regression model. The Pinball loss is an asymmetric loss that measures the quality of the predicted
+    quantiles. Given a probabilistic regression model that outputs a probability density function (PDF) :math:`f_Y(y)`
+    targeting the ground-truth :math:`y`, we further denote the cumulative as :math:`F_Y(y)` and the (inverse)
+    percent point function (PPF) as :math:`F_Y^{-1}(\\tau)` for a certain quantile level :math:`\\tau \\in [0, 1]`.
+
+    The Pinball loss is given by
+
+    .. math::
+       L_{\\text{Pin}}(\\tau) =
+       \\begin{cases}
+            \\big( y-F_Y^{-1}(\\tau) \\big)\\tau \\quad &\\text{if } y \\geq F_Y^{-1}(\\tau)\\\\
+            \\big( F_Y^{-1}(\\tau)-y \\big)(1-\\tau) \\quad &\\text{if } y < F_Y^{-1}(\\tau)
+       \\end{cases} .
+    """
+
+    def measure(
+            self, X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            q: Union[float, Iterable[float], np.ndarray],
+            *,
+            kind: str = 'meanstd',
+            reduction: str = 'mean',
+    ):
+        """
+        Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as
+        NumPy array consisting of a sample distribution. The loss is computed for several quantiles
+        given by parameter q.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data obtained by a model that performs inference with uncertainty.
+            See parameter "kind" for input format descriptions.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        q : np.ndarray of shape (q,)
+            Quantile scores in [0, 1] of size q to compute the x-valued quantile boundaries for.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+        reduction : str, one of 'none', 'mean' or 'sum' default: 'mean'
+            Specifies the reduction to apply to the output:
+            - none : no reduction is performed. Return quantile loss for each sample, each
+                     quantile and for each dim separately.
+            - mean : calculate mean over all quantiles, all samples and all dimensions.
+            - sum : calculate sum over all quantiles, all samples and all dimensions
+
+        Returns
+        -------
+        np.ndarray of shape (q, d)
+            Quantile loss for quantile q in dimension d over all samples in input X.
+            See parameter "reduction" for a detailed description of the return type.
+        """
+
+        # get quantile boundaries
+        in_quantile, qbounds, _, _, _ = is_in_quantile(X, y, q, kind)  # (q, n, [d]), (q, n, d)
+
+        # qbounds is None if input is given with covariance matrices
+        if qbounds is None:
+            raise RuntimeError("QuantileLoss is currently not defined for multivariate data with correlation.")
+
+        # make y at least 2d
+        y = np.expand_dims(y, axis=1) if y.ndim == 1 else y  # (n, d)
+
+        # broadcast q array to all dimensions
+        n_samples, n_dims = y.shape
+
+        # standard case: use L1 (absolute) distance between ground-truth and quantile boundary
+        q = np.broadcast_to(q[:, None, None], (q.shape[0], n_samples, n_dims))  # (q, n, d)
+        distance = np.abs(y[None, :] - qbounds)  # (q, n, d)
+
+        # compute weights for pinball loss
+        weights = np.where(in_quantile, 1.-q, q)  # (q, n, [d])
+
+        # finally, compute loss
+        loss = distance * weights  # (q, n, [d])
+
+        # no reduction is applied
+        if reduction is None or reduction == 'none':
+            return loss
+
+        # 'mean' is mean over all quantiles and all dimensions
+        elif reduction == "mean":
+            return float(np.mean(loss))
+
+        # 'sum' is sum over all quantiles and all dimensions
+        elif reduction == "sum":
+            return float(np.sum(loss))
+
+        # unknown reduction method
+        else:
+            raise RuntimeError("Unknown reduction: \'%s\'" % reduction)
+
+
+class PinballLoss(QuantileLoss):
+    """ Synonym for Quantile loss. For documentation, see :class:`netcal.metrics.regression.QuantileLoss`. """
+    pass
diff --git a/netcal/metrics/regression/README.md b/netcal/metrics/regression/README.md
new file mode 100644
index 0000000..e0d1532
--- /dev/null
+++ b/netcal/metrics/regression/README.md
@@ -0,0 +1,17 @@
+# Metrics for Regression Uncertainty Calibration
+
+Methods for measuring miscalibration in the context of regression uncertainty calibration for probabilistic
+regression models.
+
+The common methods for regression uncertainty evaluation are *netcal.metrics.regression.PinballLoss* (Pinball
+loss), the *netcal.metrics.regression.NLL* (NLL), and the *netcal.metrics.regression.QCE* (M-QCE and
+C-QCE). The Pinball loss as well as the Marginal/Conditional Quantile Calibration Error (M-QCE and C-QCE) evaluate
+the quality of the estimated quantiles compared to the observed ground-truth quantile coverage. The NLL is a proper
+scoring rule to measure the overall quality of the predicted probability distributions.
+
+Further metrics are the *netcal.metrics.regression.UCE* (UCE) and the *netcal.metrics.regression.ENCE*
+(ENCE) which both apply a binning scheme over the predicted standard deviation/variance and test for *variance
+calibration*.
+
+For a detailed description of the available metrics within regression calibration, see the module doc of
+*netcal.regression*.
\ No newline at end of file
diff --git a/netcal/metrics/regression/UCE.py b/netcal/metrics/regression/UCE.py
new file mode 100644
index 0000000..43c0c39
--- /dev/null
+++ b/netcal/metrics/regression/UCE.py
@@ -0,0 +1,155 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+import warnings
+from typing import Iterable, Tuple, List
+from typing import Union
+import numpy as np
+
+from netcal import accepts, meanvar, cumulative_moments
+from netcal.metrics.Miscalibration import _Miscalibration
+
+
+class UCE(_Miscalibration):
+    """
+    Uncertainty Calibration Error (UCE) for a regression calibration evaluation to test for
+    *variance calibration*. A probabilistic regression model takes :math:`X` as input and outputs a
+    mean :math:`\\mu_Y(X)` and a variance :math:`\\sigma_Y^2(X)` targeting the ground-truth :math:`y`.
+    Similar to the :class:`netcal.metrics.confidence.ECE`, the UCE applies a binning scheme with :math:`B` bins
+    over the predicted variance :math:`\\sigma_Y^2(X)` and measures the absolute difference
+    between mean squared error (MSE) and mean variance (RMV) [1]_.
+    Thus, the UCE [1]_ is defined by
+
+    .. math::
+        \\text{UCE} := \\sum^B_{b=1} \\frac{N_b}{N} |MSE(b) - MV(b)| ,
+
+    where :math:`MSE(b)` and :math:`MV(b)` are the mean squared error and the mean variance within
+    bin :math:`b`, respectively, and :math:`N_b` is the number of samples within bin :math:`b`.
+
+    If multiple dimensions are given, the UCE is measured for each dimension separately.
+
+    Parameters
+    ----------
+    bins : int or iterable, default: 10
+        Number of bins used by the UCE binning.
+        If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
+    sample_threshold : int, optional, default: 1
+        Bins with an amount of samples below this threshold are not included into the miscalibration metrics.
+
+    References
+    ----------
+    .. [1] Laves, Max-Heinrich, et al.:
+       "Well-calibrated regression uncertainty in medical imaging with deep learning."
+       Medical Imaging with Deep Learning. PMLR, 2020.
+       `Get source online <http://proceedings.mlr.press/v121/laves20a/laves20a.pdf>`__
+    """
+
+    @accepts((int, tuple, list), int)
+    def __init__(
+            self,
+            bins: Union[int, Iterable[int]] = 10,
+            sample_threshold: int = 1
+    ):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        super().__init__(bins=bins, equal_intervals=True, detection=False, sample_threshold=sample_threshold)
+
+    def measure(
+            self,
+            X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            *,
+            kind: str = 'meanstd',
+            range_: List[Tuple[float, float]] = None
+    ):
+        """
+        Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as
+        NumPy array consisting of a sample distribution. The loss is computed for several quantiles
+        given by parameter q.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data obtained by a model that performs inference with uncertainty.
+            See parameter "kind" for input format descriptions.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+        range_ : list of length d with tuples (lower_bound: float, upper_bound: float)
+            List of tuples that define the binning range of the variance for each dimension separately.
+            For example, if input data is given with only a few samples having high variance,
+            this might distort the calculations as the binning scheme commonly takes the (min, max) as the range
+            for the binning, yielding a high amount of empty bins.
+
+        Returns
+        -------
+        NumPy array of shape (d,)
+            NumPy array with the UCE for each input dimension separately.
+        """
+
+        assert kind in ['meanstd', 'cauchy', 'cumulative'], 'Parameter \'kind\' must be either \'meanstd\', or \'cumulative\'.'
+        if kind == "meanstd":
+            (mean, var), y, cov = meanvar(X, y)
+
+            # check if correlated input is given
+            if cov:
+                raise RuntimeError("UCE is not defined for multivariate data with correlation.")
+
+            mean = np.expand_dims(mean, axis=1) if mean.ndim == 1 else mean  # (n, d)
+            var = np.expand_dims(var, axis=1) if var.ndim == 1 else var  # (n, d)
+
+        # Cauchy distribution has no variance - ENCE is not applicable
+        elif kind == "cauchy":
+
+            n_dims = y.shape[1] if y.ndim == 2 else 1
+
+            warnings.warn("UCE is not applicable for Cauchy distributions.")
+            return np.full(shape=(n_dims,), fill_value=float('nan'))
+
+        else:
+
+            # extract sampling points t and cumulative
+            # get differences of cumulative and intermediate points of t
+            t, cdf = X
+            mean, var = cumulative_moments(t, cdf)  # (n, d) and (n, d)
+
+        y = np.expand_dims(y, axis=1) if y.ndim == 1 else y
+        n_samples, n_dims = y.shape
+
+        # squared error
+        error = np.square(mean - y)  # (n, d)
+
+        # prepare binning boundaries for regression
+        bin_bounds = self._prepare_bins_regression(var, n_dims=n_dims, range_=range_)
+
+        uce = []
+        for dim in range(n_dims):
+
+            # perform binning over 1D variance
+            (mv_hist, mse_hist), n_samples_hist, bounds, _ = self.binning(
+                [bin_bounds[dim]],
+                var[:, dim],
+                var[:, dim],
+                error[:, dim]
+            )
+            n_samples_hist = n_samples_hist / n_samples
+
+            # UCE for current dim is weighted sum over all bins
+            uce.append(
+                np.sum(np.abs(mse_hist-mv_hist) * n_samples_hist)
+            )
+
+        uce = np.array(uce).squeeze()
+        return uce
diff --git a/netcal/metrics/regression/__init__.py b/netcal/metrics/regression/__init__.py
new file mode 100644
index 0000000..844ee01
--- /dev/null
+++ b/netcal/metrics/regression/__init__.py
@@ -0,0 +1,34 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+"""
+.. include:: /../../netcal/metrics/regression/README.md
+   :parser: myst_parser.sphinx_
+
+Available classes
+=================
+
+.. autosummary::
+   :toctree: _autosummary_metric
+   :template: custom_class.rst
+
+   QuantileLoss
+   PinballLoss
+   ENCE
+   UCE
+   PICP
+   QCE
+   NLL
+"""
+
+from .QuantileLoss import QuantileLoss
+from .QuantileLoss import PinballLoss
+from .ENCE import ENCE
+from .UCE import UCE
+from .PICP import PICP
+from .QCE import QCE
+from .NLL import NLL

From ca5c7f08a95e923f540b58c15fa659e6ac4316d7 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:53:20 +0200
Subject: [PATCH 08/21] Update presentation package. Update code style of
 ReliabilityDiagram class. New methods: - ReliabilityRegression: visualize
 expected quantile vs. observerd quantile coverage - ReliabilityQCE: visualize
 quantile calibration error (QCE) over the estimated stddevs

---
 netcal/presentation/ReliabilityDiagram.py    | 132 +++++++++----
 netcal/presentation/ReliabilityQCE.py        | 188 +++++++++++++++++++
 netcal/presentation/ReliabilityRegression.py | 185 ++++++++++++++++++
 netcal/presentation/__init__.py              |  14 +-
 4 files changed, 475 insertions(+), 44 deletions(-)
 create mode 100644 netcal/presentation/ReliabilityQCE.py
 create mode 100644 netcal/presentation/ReliabilityRegression.py

diff --git a/netcal/presentation/ReliabilityDiagram.py b/netcal/presentation/ReliabilityDiagram.py
index 186c9b0..f1dc24f 100644
--- a/netcal/presentation/ReliabilityDiagram.py
+++ b/netcal/presentation/ReliabilityDiagram.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -13,12 +13,13 @@
 import matplotlib.pyplot as plt
 import tikzplotlib
 
-from netcal.metrics import _Miscalibration
+from netcal.metrics.Miscalibration import _Miscalibration
 
 
 class ReliabilityDiagram(object):
     """
-    Plot Confidence Histogram and Reliability Diagram to visualize miscalibration.
+    Plot Confidence Histogram and Reliability Diagram to visualize miscalibration in the context of
+    confidence calibration.
     On classification, plot the gaps between average confidence and observed accuracy bin-wise over the confidence
     space [1]_, [2]_.
     On detection, plot the miscalibration w.r.t. the additional regression information provided (1-D or 2-D) [3]_.
@@ -49,23 +50,31 @@ class ReliabilityDiagram(object):
     .. [1] Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
        "On Calibration of Modern Neural Networks."
        Proceedings of the 34th International Conference on Machine Learning-Volume 70. JMLR. org, 2017.
-       `Get source online <https://arxiv.org/abs/1706.04599>`_
+       `Get source online <https://arxiv.org/abs/1706.04599>`__
 
     .. [2] A. Niculescu-Mizil and R. Caruana:
        “Predicting good probabilities with supervised learning.”
        Proceedings of the 22nd International Conference on Machine Learning, 2005, pp. 625–632.
-       `Get source online <https://www.cs.cornell.edu/~alexn/papers/calibration.icml05.crc.rev3.pdf>`_
+       `Get source online <https://www.cs.cornell.edu/~alexn/papers/calibration.icml05.crc.rev3.pdf>`__
 
     .. [3] Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
        "Multivariate Confidence Calibration for Object Detection."
        The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
-       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`_
+       `Get source online <https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf>`__
     """
 
-    def __init__(self, bins: Union[int, Iterable[int]] = 10, equal_intervals: bool = True,
-                 detection: bool = False, sample_threshold: int = 1,
-                 fmin: float = None, fmax: float = None,
-                 metric: str = 'ECE', **kwargs):
+    def __init__(
+            self,
+            bins: Union[int, Iterable[int]] = 10,
+            *,
+            equal_intervals: bool = True,
+            detection: bool = False,
+            sample_threshold: int = 1,
+            fmin: float = None,
+            fmax: float = None,
+            metric: str = 'ECE',
+            **kwargs
+    ):
         """ Constructor. For detailed parameter documentation view classdocs. """
 
         self.bins = bins
@@ -81,12 +90,24 @@ def __init__(self, bins: Union[int, Iterable[int]] = 10, equal_intervals: bool =
         if 'title_suffix' in kwargs:
             self.title_suffix = kwargs['title_suffix']
 
-        self._miscalibration = _Miscalibration(bins=bins, equal_intervals=equal_intervals,
-                                               detection=detection, sample_threshold=sample_threshold)
-
-    def plot(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.ndarray], np.ndarray],
-             batched: bool = False, uncertainty: str = None, filename: str = None, tikz: bool = False,
-             title_suffix: str = None, feature_names: List[str] = None, **save_args) -> Union[plt.Figure, str]:
+        self._miscalibration = _Miscalibration(
+            bins=bins, equal_intervals=equal_intervals,
+            detection=detection, sample_threshold=sample_threshold
+        )
+
+    def plot(
+            self,
+            X: Union[Iterable[np.ndarray], np.ndarray],
+            y: Union[Iterable[np.ndarray], np.ndarray],
+            *,
+            batched: bool = False,
+            uncertainty: str = None,
+            filename: str = None,
+            tikz: bool = False,
+            title_suffix: str = None,
+            feature_names: List[str] = None,
+            **save_args
+    ) -> Union[plt.Figure, str]:
         """
         Reliability diagram to visualize miscalibration. This could be either in classical way for confidences only
         or w.r.t. additional properties (like x/y-coordinates of detection boxes, width, height, etc.). The additional
@@ -136,6 +157,7 @@ def plot(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.
         Returns
         -------
         matplotlib.pyplot.Figure if 'tikz' is False else str with tikz code.
+            Visualization of the reliability diagrams either as Matplotlib figure or as string with tikz code.
 
         Raises
         ------
@@ -170,21 +192,31 @@ def plot(self, X: Union[Iterable[np.ndarray], np.ndarray], y: Union[Iterable[np.
             raise AttributeError("Diagram is not defined for more than 2 additional feature dimensions.")
 
         histograms = []
+        num_samples_hist = []
         for batch_X, batch_matched, batch_uncertainty, bounds in zip(X, matched, sample_uncertainty, bin_bounds):
-            batch_histograms = self._miscalibration.binning(bounds, batch_X, batch_matched, batch_X[:, 0], batch_uncertainty[:, 0])
-            histograms.append(batch_histograms[:-1])
+
+            batch_histograms, batch_num_samples, _, _ = self._miscalibration.binning(
+                bounds,
+                batch_X,
+                batch_matched,
+                batch_X[:, 0],
+                batch_uncertainty[:, 0]
+            )
+
+            histograms.append(batch_histograms)
+            num_samples_hist.append(batch_num_samples)
 
         # no additional dimensions? compute standard reliability diagram
         if num_features == 1:
-            fig = self.__plot_confidence_histogram(X, matched, histograms, bin_bounds, title_suffix)
+            fig = self.__plot_confidence_histogram(X, matched, histograms, num_samples_hist, bin_bounds, title_suffix)
 
         # one additional feature? compute 1D-plot
         elif num_features == 2:
-            fig = self.__plot_1d(histograms, bin_bounds, title_suffix, feature_names)
+            fig = self.__plot_1d(histograms, num_samples_hist, bin_bounds, title_suffix, feature_names)
 
         # two additional features? compute 2D plot
         elif num_features == 3:
-            fig = self.__plot_2d(histograms, bin_bounds, title_suffix, feature_names)
+            fig = self.__plot_2d(histograms, num_samples_hist, bin_bounds, title_suffix, feature_names)
 
         # number of dimensions exceeds 3? quit
         else:
@@ -223,8 +255,15 @@ def __interpolate_grid(cls, metric_map: np.ndarray) -> np.ndarray:
         metric_map[nans] = griddata(x(~nans), metric_map[~nans], x(nans), method='cubic', fill_value=mean)
         return metric_map
 
-    def __plot_confidence_histogram(self, X: List[np.ndarray], matched: List[np.ndarray], histograms: List[np.ndarray],
-                                    bin_bounds: List, title_suffix: str = None) -> plt.Figure:
+    def __plot_confidence_histogram(
+            self,
+            X: List[np.ndarray],
+            matched: List[np.ndarray],
+            histograms: List[np.ndarray],
+            num_samples_hist: List[np.ndarray],
+            bin_bounds: List,
+            title_suffix: str = None
+    ) -> plt.Figure:
         """ Plot confidence histogram and reliability diagram to visualize miscalibration for condidences only. """
 
         # get number of bins (self.bins has not been processed yet)
@@ -232,9 +271,12 @@ def __plot_confidence_histogram(self, X: List[np.ndarray], matched: List[np.ndar
 
         median_confidence = [(bounds[0][1:] + bounds[0][:-1]) * 0.5 for bounds in bin_bounds]
         mean_acc, mean_conf = [], []
-        for batch_X, batch_matched, batch_hist, batch_median in zip(X, matched, histograms, median_confidence):
-            acc_hist, conf_hist, _, num_samples_hist = batch_hist
-            empty_bins, = np.nonzero(num_samples_hist == 0)
+        for batch_X, batch_matched, batch_hist, batch_num_samples, batch_median in zip(
+                X, matched, histograms, num_samples_hist, median_confidence
+        ):
+
+            acc_hist, conf_hist, _ = batch_hist
+            empty_bins, = np.nonzero(batch_num_samples == 0)
 
             # calculate overall mean accuracy and confidence
             mean_acc.append(np.mean(batch_matched))
@@ -245,13 +287,13 @@ def __plot_confidence_histogram(self, X: List[np.ndarray], matched: List[np.ndar
             conf_hist[empty_bins] = batch_median[empty_bins]
 
             # convert num_samples to relative afterwards (inplace denoted by [:])
-            num_samples_hist[:] = num_samples_hist / np.sum(num_samples_hist)
+            batch_num_samples[:] = batch_num_samples / np.sum(batch_num_samples)
 
         # get mean histograms and values over all batches
         acc = np.mean([hist[0] for hist in histograms], axis=0)
         conf = np.mean([hist[1] for hist in histograms], axis=0)
         uncertainty = np.sqrt(np.mean([hist[2] for hist in histograms], axis=0))
-        num_samples = np.mean([hist[3] for hist in histograms], axis=0)
+        num_samples = np.mean([x for x in num_samples_hist], axis=0)
         mean_acc = np.mean(mean_acc)
         mean_conf = np.mean(mean_conf)
         median_confidence = np.mean(median_confidence, axis=0)
@@ -318,11 +360,17 @@ def __plot_confidence_histogram(self, X: List[np.ndarray], matched: List[np.ndar
         ax.set_ylabel('Accuracy')
         ax.legend(['Perfect Calibration', 'Output', 'Gap'])
 
-        plt.tight_layout()
+        fig.tight_layout()
         return fig
 
-    def __plot_1d(self, histograms: List[np.ndarray], bin_bounds: List,
-                  title_suffix: str = None, feature_names: List[str] = None) -> plt.Figure:
+    def __plot_1d(
+            self,
+            histograms: List[np.ndarray],
+            num_samples_hist: List[np.ndarray],
+            bin_bounds: List,
+            title_suffix: str = None,
+            feature_names: List[str] = None
+    ) -> plt.Figure:
         """ Plot 1-D miscalibration w.r.t. one additional feature. """
 
         # z score for credible interval (if uncertainty is given)
@@ -330,8 +378,9 @@ def __plot_1d(self, histograms: List[np.ndarray], bin_bounds: List,
         z_score = norm.ppf(1. - (p / 2))
 
         results = []
-        for batch_hist, bounds in zip(histograms, bin_bounds):
-            result = self._miscalibration.process(self.metric, *batch_hist)
+        for batch_hist, batch_num_samples, bounds in zip(histograms, num_samples_hist, bin_bounds):
+
+            result = self._miscalibration.process(self.metric, *batch_hist, num_samples_hist=batch_num_samples)
             bin_median = (bounds[-1][:-1] + bounds[-1][1:]) * 0.5
 
             # interpolate missing values
@@ -406,13 +455,20 @@ def __plot_1d(self, histograms: List[np.ndarray], bin_bounds: List,
         fig.tight_layout()
         return fig
 
-    def __plot_2d(self, histograms: List[np.ndarray], bin_bounds: List[np.ndarray],
-                  title_suffix: str = None, feature_names: List[str] = None) -> plt.Figure:
+    def __plot_2d(
+            self,
+            histograms: List[np.ndarray],
+            num_samples_hist: List[np.ndarray],
+            bin_bounds: List[np.ndarray],
+            title_suffix: str = None,
+            feature_names: List[str] = None
+    ) -> plt.Figure:
         """ Plot 2D miscalibration reliability diagram heatmap. """
 
         results = []
-        for batch_hist in histograms:
-            result = self._miscalibration.process(self.metric, *batch_hist)
+        for batch_hist, batch_num_samples in zip(histograms, num_samples_hist):
+
+            result = self._miscalibration.process(self.metric, *batch_hist, num_samples_hist=batch_num_samples)
 
             # interpolate 2D data inplace to avoid "empty" bins
             batch_samples = result[-1]
diff --git a/netcal/presentation/ReliabilityQCE.py b/netcal/presentation/ReliabilityQCE.py
new file mode 100644
index 0000000..c5c2aee
--- /dev/null
+++ b/netcal/presentation/ReliabilityQCE.py
@@ -0,0 +1,188 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Union, Iterable, Tuple, List
+import numpy as np
+from matplotlib import pyplot as plt
+import tikzplotlib
+
+from netcal.metrics.regression import QCE
+
+
+class ReliabilityQCE(object):
+    """
+    Visualizes the Conditional Quantile Calibration Error (C-QCE) in the scope of regression calibration as a bar chart
+    for probabilistic regression models.
+    See :class:`netcal.metrics.regression.QCE` for a detailed documentation of the C-QCE [1]_.
+    This method is able to visualize the C-QCE in terms of multiple univariate distributions if the input is given
+    as multiple independent Gaussians.
+    This method is also able to visualize the multivariate C-QCE for a multivariate Gaussian if the input is given
+    with covariance matrices.
+
+    Parameters
+    ----------
+    bins : int or iterable, default: 10
+        Number of bins used by the C-QCE binning.
+        If iterable, use different amount of bins for each dimension (nx1, nx2, ... = bins).
+
+    References
+    ----------
+    .. [1] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+       "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+       European Conference on Computer Vision (ECCV) Workshops, 2022.
+       `Get source online <https://arxiv.org/pdf/2207.01242.pdf>`__
+    """
+
+    eps = np.finfo(np.float32).eps
+
+    def __init__(self, bins: Union[int, Iterable[float], np.ndarray] = 10):
+        """ Constructor. For detailed parameter documentation view classdocs. """
+
+        self.qce = QCE(bins=bins, marginal=False)
+
+    def plot(
+            self,
+            X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            q: Union[float, Iterable[float], np.ndarray],
+            *,
+            kind: str = 'meanstd',
+            range_: List[Tuple[float, float]] = None,
+            filename: str = None,
+            tikz: bool = False,
+            title_suffix: str = None,
+            **save_args
+    ) -> Union[plt.Figure, str]:
+        """
+        Visualizes the C-QCE as a bar chart either for multiple univariate data (if standard deviations are given as
+        input) or for a joint multivariate distribution (if covariance matrices are given as input).
+        See parameter "kind" for a detailed description of the input format.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data obtained by a model that performs inference with uncertainty.
+            See parameter "kind" for input format descriptions.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        q : np.ndarray of shape (q,)
+            Quantile scores in [0, 1] of size q to compute the x-valued quantile boundaries for.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) and (n, [d, [d]]), this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If the second NumPy array has shape (n, d, d), this method asserts covariance matrices as input
+                       for each sample. In this case, the NLL is calculated for multivariate distributions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+        range_ : list of length d with tuples (lower_bound: float, upper_bound: float)
+            List of tuples that define the binning range of the standard deviation for each dimension separately.
+            For example, if input data is given with only a few samples having high standard deviations,
+            this might distort the calculations as the binning scheme commonly takes the (min, max) as the range
+            for the binning, yielding a high amount of empty bins.
+        filename : str, optional, default: None
+            Optional filename to save the plotted figure.
+        tikz : bool, optional, default: False
+            If True, use 'tikzplotlib' package to return tikz-code for Latex rather than a Matplotlib figure.
+        title_suffix : str, optional, default: None
+            Suffix for plot title.
+        **save_args : args
+            Additional arguments passed to 'matplotlib.pyplot.Figure.savefig' function if 'tikz' is False.
+            If 'tikz' is True, the argument are passed to 'tikzplotlib.get_tikz_code' function.
+
+        Returns
+        -------
+        matplotlib.pyplot.Figure if 'tikz' is False else str with tikz code.
+            Visualization of the C-QCE either as Matplotlib figure or as string with tikz code.
+        """
+
+        # measure QCE and return a miscalibration map
+        _, qce_map, num_samples_hist = self.qce.measure(
+            X=X,
+            y=y,
+            q=q,
+            kind=kind,
+            reduction="none",
+            range_=range_,
+            return_map=True,
+            return_num_samples=True
+        )  # (q, b)
+
+        # get number of dimensions
+        ndims = len(qce_map)
+
+        # catch if bin_edges is None
+        assert len(self.qce._bin_edges) != 0, "Fatal error: could not compute bin_edges for ReliabilityQCE."
+
+        # initialize plot and create an own chart for each dimension
+        fig, axes = plt.subplots(nrows=2, ncols=ndims, figsize=(7 * ndims, 6), squeeze=False)
+        for dim in range(ndims):
+
+            # convert absolute number of samples to relative amount
+            n_samples_hist = np.divide(num_samples_hist[dim], np.sum(num_samples_hist[dim]))
+
+            # compute mean over all quantiles as well as mean over all bins separately
+            mean_over_quantiles = np.mean(qce_map[dim], axis=0)  # (b,)
+
+            # get binning boundaries for actual dimension
+            bounds = self.qce._bin_edges[dim]  # (b+1)
+
+            for ax, metric, title, ylabel in zip(
+                [axes[0][dim], axes[1][dim]],
+                [n_samples_hist, mean_over_quantiles],
+                ["Sample Histogram", "QCE mean over quantiles"],
+                ["% of Samples", "Quantile Calibration Error (QCE)"],
+            ):
+
+                # draw bar chart with given edges and metrics
+                ax.bar(bounds[:-1], height=metric, width=np.diff(bounds), align='edge', edgecolor='black')
+
+                # set axes edges
+                ax.set_xlim((bounds[0], bounds[-1]))
+                ax.set_ylim((0., 1.))
+
+                # labels and grid
+                if self.qce._is_cov:
+                    title = title + ' - multivariate'
+                    ax.set_xlabel("sqrt( Standardized Generalized Variance (SGV) )")
+                else:
+                    title = title + ' - dim %02d' % dim
+                    ax.set_xlabel("Standard Deviation")
+
+                ax.set_ylabel(ylabel)
+                ax.grid(True)
+
+                # set axis title
+                if title_suffix is not None:
+                    title = title + ' - ' + title_suffix
+
+                ax.set_title(title)
+
+        fig.tight_layout()
+
+        # if tikz is true, create tikz code from matplotlib figure
+        if tikz:
+
+            # get tikz code for our specific figure and also pass filename to store possible bitmaps
+            tikz_fig = tikzplotlib.get_tikz_code(fig, filepath=filename, **save_args)
+
+            # close matplotlib figure when tikz figure is requested to save memory
+            plt.close(fig)
+            fig = tikz_fig
+
+        # save figure either as matplotlib PNG or as tikz output file
+        if filename is not None:
+            if tikz:
+                with open(filename, "w") as open_file:
+                    open_file.write(fig)
+            else:
+                fig.savefig(filename, **save_args)
+
+        return fig
diff --git a/netcal/presentation/ReliabilityRegression.py b/netcal/presentation/ReliabilityRegression.py
new file mode 100644
index 0000000..1ca2a58
--- /dev/null
+++ b/netcal/presentation/ReliabilityRegression.py
@@ -0,0 +1,185 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Union, Iterable, Tuple, List
+import numpy as np
+from matplotlib import pyplot as plt
+import tikzplotlib
+
+from netcal import is_in_quantile
+
+
+class ReliabilityRegression(object):
+    """
+    Reliability diagram in the scope of regression calibration for probabilistic regression models.
+    This diagram visualizes the quantile coverage frequency for several quantile levels and plots these observed
+    coverage scores above the desired quantile levels.
+    In this way, it is possible to compare the predicted and the observed quantile levels with each other.
+
+    This method is able to visualize the quantile coverage in terms of multiple univariate distributions if the input
+    is given as multiple independent Gaussians.
+    This method is also able to visualize the multivariate quantile coverage for a joint multivariate Gaussian if the
+    input is given with covariance matrices.
+
+    Parameters
+    ----------
+    quantiles : int or iterable, default: 11
+        Quantile levels that are used for the visualization of the regression reliability diagram.
+        If int, use NumPy's linspace method to get the quantile levels.
+        If iterable, use the specified quantiles for visualization.
+    """
+
+    eps = np.finfo(np.float32).eps
+
+    def __init__(self, quantiles: Union[int, Iterable[float], np.ndarray] = 11):
+        """ Constructor. For detailed parameter documentation view classdocs. """
+
+        # init list of quantiles if input type is int
+        if isinstance(quantiles, int):
+            self.quantiles = np.clip(np.linspace(0., 1., quantiles), self.eps, 1.-self.eps)
+
+        # use input list or array as quantile list
+        elif isinstance(quantiles, (list, np.ndarray)):
+
+            # at this point, allow for 0 and 1 quantile to be aligned on the miscalibration curve
+            assert (quantiles >= 0).all(), "Found quantiles <= 0."
+            assert (quantiles <= 1).all(), "Found quantiles >= 1."
+            self.quantiles = np.clip(np.array(quantiles), self.eps, 1.-self.eps)
+
+        else:
+            raise AttributeError("Unknown type \'%s\' for param \'quantiles\'." % type(quantiles))
+
+    def plot(
+            self,
+            X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            *,
+            kind: str = 'meanstd',
+            filename: str = None,
+            tikz: bool = False,
+            title_suffix: str = None,
+            feature_names: List[str] = None,
+            **save_args
+    ) -> Union[plt.Figure, str]:
+        """
+        Reliability diagram for regression calibration to visualize the predicted quantile levels vs. the actually
+        observed quantile coverage probability.
+        This method is able to visualize the reliability diagram in terms of multiple univariate distributions if the
+        input is given as multiple independent Gaussians.
+        This method is also able to visualize the joint multivariate quantile calibration for a multivariate Gaussian
+        if the input is given with covariance matrices (see parameter "kind" for a detailed description of the input
+        format).
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or (t, n, [d]), or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data obtained by a model that performs inference with uncertainty.
+            See parameter "kind" for input format descriptions.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        kind : str, either "meanstd" or "cumulative"
+            Specify the kind of the input data. Might be one of:
+            - meanstd: if X is tuple of two NumPy arrays with shape (n, [d]) and (n, [d, [d]]), this method asserts the
+                       first array as mean and the second one as the according stddev predictions for d dimensions.
+                       If the second NumPy array has shape (n, d, d), this method asserts covariance matrices as input
+                       for each sample. In this case, the NLL is calculated for multivariate distributions.
+                       If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+                       inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+                       case, the mean and stddev is computed automatically.
+            - cumulative: assert X as tuple of two NumPy arrays of shape (t, n, [d]) with t points on the cumulative
+                          for sample n (and optionally d dimensions).
+        filename : str, optional, default: None
+            Optional filename to save the plotted figure.
+        tikz : bool, optional, default: False
+            If True, use 'tikzplotlib' package to return tikz-code for Latex rather than a Matplotlib figure.
+        title_suffix : str, optional, default: None
+            Suffix for plot title.
+        feature_names : list, optional, default: None
+            Names of the additional features that are attached to the axes of a reliability diagram.
+        **save_args : args
+            Additional arguments passed to 'matplotlib.pyplot.Figure.savefig' function if 'tikz' is False.
+            If 'tikz' is True, the argument are passed to 'tikzplotlib.get_tikz_code' function.
+
+        Returns
+        -------
+        matplotlib.pyplot.Figure if 'tikz' is False else str with tikz code.
+            Visualization of the quantile calibration either as Matplotlib figure or as string with tikz code.
+        """
+
+        assert kind in ['meanstd', 'cauchy', 'cumulative'], 'Parameter \'kind\' must be either \'meanstd\', or \'cumulative\'.'
+
+        # get quantile coverage of input
+        in_quantile, _, _, _, _ = is_in_quantile(X, y, self.quantiles, kind)  # (q, n, [d]), (q, n, d), (n, d), (n, d, [d])
+
+        # get the frequency of which y is within the quantile bounds
+        frequency = np.mean(in_quantile, axis=1)  # (q, [d])
+
+        # make frequency array at least 2d
+        if frequency.ndim == 1:
+            frequency = np.expand_dims(frequency, axis=1)  # (q, d) or (q, 1)
+
+        n_dims = frequency.shape[-1]
+
+        # check feature names parameter
+        if feature_names is not None:
+            assert isinstance(feature_names, (list, tuple)), "Parameter \'feature_names\' must be tuple or list."
+            assert len(feature_names) == n_dims, "Length of parameter \'feature_names\' must be equal to the amount " \
+                                                 "of dimensions. Input with full covariance matrices is interpreted " \
+                                                 "as n_features=1."
+
+        # initialize plot and create an own chart for each dimension
+        fig, axes = plt.subplots(nrows=n_dims, figsize=(7, 3 * n_dims), squeeze=False)
+        for dim, ax in enumerate(axes):
+
+            # ax object also has an extra dim for columns
+            ax = ax[0]
+
+            ax.plot(self.quantiles, frequency[:, dim], "o-")
+
+            # draw diagonal as perfect calibration line
+            ax.plot([0, 1], [0, 1], color='red', linestyle='--')
+            ax.set_xlim((0.0, 1.0))
+            ax.set_ylim((0.0, 1.0))
+
+            # labels and legend of second plot
+            ax.set_xlabel('Expected quantile')
+            ax.set_ylabel('Observed frequency')
+            ax.legend(['Output', 'Perfect Calibration'])
+            ax.grid(True)
+
+            # set axis title
+            title = 'Reliability Regression Diagram'
+            if title_suffix is not None:
+                title = title + ' - ' + title_suffix
+            if feature_names is not None:
+                title = title + ' - ' + feature_names[dim]
+            else:
+                title = title + ' - dim %02d' % dim
+
+            ax.set_title(title)
+
+        fig.tight_layout()
+
+        # if tikz is true, create tikz code from matplotlib figure
+        if tikz:
+
+            # get tikz code for our specific figure and also pass filename to store possible bitmaps
+            tikz_fig = tikzplotlib.get_tikz_code(fig, filepath=filename, **save_args)
+
+            # close matplotlib figure when tikz figure is requested to save memory
+            plt.close(fig)
+            fig = tikz_fig
+
+        # save figure either as matplotlib PNG or as tikz output file
+        if filename is not None:
+            if tikz:
+                with open(filename, "w") as open_file:
+                    open_file.write(fig)
+            else:
+                fig.savefig(filename, **save_args)
+
+        return fig
diff --git a/netcal/presentation/__init__.py b/netcal/presentation/__init__.py
index 83c2ba1..2f41b86 100644
--- a/netcal/presentation/__init__.py
+++ b/netcal/presentation/__init__.py
@@ -1,14 +1,13 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
 """
-Methods for the visualization of miscalibration. This package consists of a Reliability Diagram method.
-This method bins similar to the ACE or ECE the samples in equally sized bins by their confidence and
-displays the gap between confidence and observed accuracy in each bin.
+.. include:: /../../netcal/presentation/README.md
+   :parser: myst_parser.sphinx_
 
 Available classes
 =================
@@ -18,8 +17,11 @@
    :template: custom_class.rst
 
    ReliabilityDiagram
+   ReliabilityRegression
+   ReliabilityQCE
 """
 
 
 from .ReliabilityDiagram import ReliabilityDiagram
-
+from .ReliabilityRegression import ReliabilityRegression
+from .ReliabilityQCE import ReliabilityQCE

From 8e7220b879d366334a35b9cb869e5e3d35c43c9a Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:55:29 +0200
Subject: [PATCH 09/21] Add new package: regression.

This package partially uses Gaussian process
for recalibration and therefore has a subpackage
named gp. The following methods have been implemented:
- Isotonic Regression
- Variance Scaling
- GP-Beta
- GP-Normal
- GP-Cauchy
---
 netcal/regression/IsotonicRegression.py       | 291 +++++++
 netcal/regression/VarianceScaling.py          | 188 ++++
 netcal/regression/__init__.py                 |  39 +
 netcal/regression/gp/AbstractGP.py            | 816 ++++++++++++++++++
 netcal/regression/gp/GPBeta.py                | 281 ++++++
 netcal/regression/gp/GPCauchy.py              | 205 +++++
 netcal/regression/gp/GPNormal.py              | 240 ++++++
 netcal/regression/gp/README.md                |  28 +
 netcal/regression/gp/__init__.py              |  37 +
 .../regression/gp/kernel/GaussianRBFKernel.py | 141 +++
 netcal/regression/gp/kernel/README.md         |   3 +
 netcal/regression/gp/kernel/__init__.py       |  22 +
 .../gp/likelihood/BetaLikelihood.py           | 420 +++++++++
 .../gp/likelihood/CauchyLikelihood.py         |  64 ++
 netcal/regression/gp/likelihood/README.md     |   4 +
 .../ScaledMultivariateNormalLikelihood.py     | 172 ++++
 .../gp/likelihood/ScaledNormalLikelihood.py   |  62 ++
 netcal/regression/gp/likelihood/__init__.py   |  28 +
 18 files changed, 3041 insertions(+)
 create mode 100644 netcal/regression/IsotonicRegression.py
 create mode 100644 netcal/regression/VarianceScaling.py
 create mode 100644 netcal/regression/__init__.py
 create mode 100644 netcal/regression/gp/AbstractGP.py
 create mode 100644 netcal/regression/gp/GPBeta.py
 create mode 100644 netcal/regression/gp/GPCauchy.py
 create mode 100644 netcal/regression/gp/GPNormal.py
 create mode 100644 netcal/regression/gp/README.md
 create mode 100644 netcal/regression/gp/__init__.py
 create mode 100644 netcal/regression/gp/kernel/GaussianRBFKernel.py
 create mode 100644 netcal/regression/gp/kernel/README.md
 create mode 100644 netcal/regression/gp/kernel/__init__.py
 create mode 100644 netcal/regression/gp/likelihood/BetaLikelihood.py
 create mode 100644 netcal/regression/gp/likelihood/CauchyLikelihood.py
 create mode 100644 netcal/regression/gp/likelihood/README.md
 create mode 100644 netcal/regression/gp/likelihood/ScaledMultivariateNormalLikelihood.py
 create mode 100644 netcal/regression/gp/likelihood/ScaledNormalLikelihood.py
 create mode 100644 netcal/regression/gp/likelihood/__init__.py

diff --git a/netcal/regression/IsotonicRegression.py b/netcal/regression/IsotonicRegression.py
new file mode 100644
index 0000000..402a7cd
--- /dev/null
+++ b/netcal/regression/IsotonicRegression.py
@@ -0,0 +1,291 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Mozilla Public
+# License, v. 2.0. If a copy of the MPL was not distributed with this
+# file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+from typing import Union, List, Tuple, Optional
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+from sklearn.isotonic import IsotonicRegression as sklearn_iso
+from scipy.stats import norm
+from matplotlib import pyplot as plt
+
+from netcal import AbstractCalibration, cumulative, meanvar, density_from_cumulative
+
+
+class IsotonicRegression(AbstractCalibration):
+    """
+    Isotonic regression calibration for probabilistic regression models with multiple independent
+    output dimensions (optionally).
+    Isotonic regression is a piecewise constant, monotonically increasing mapping function used to recalibrate
+    the estimated cumulative density function (CDF) of a probabilistic forecaster [1]_. The goal of regression
+    calibration using Isotonic regression is to achieve quantile calibration.
+
+    On the one hand, this method accepts as input X either a tuple X = (mean, stddev) using two NumPy arrays of
+    shape N with N number of samples that express the estimated mean and standard deviation of a probabilistic
+    forecaster. On the other hand, a NumPy array of shape (R, N) is also accepted where R denotes the number of
+    probabilistic forecasts. For example, if probabilistic outputs are obtained by Monte-Carlo sampling using N samples
+    and R stochastic forward passes, it is possible to pass all outputs to the calibration function in a single
+    NumPy array.
+
+    This method is capable of multiple independent data dimensions where separate calibration models are fitted for
+    each data dimension. This method outputs a tuple consisting of three NumPy arrays:
+
+    - 1st array: T points where the density/cumulative distribution functions are defined, shape: (T, N, D)
+    - 2nd array: calibrated probability density function, shape: (T, N, D)
+    - 3rd array: calibrated cumulative density function, shape: (T, N, D)
+
+    **Mathematical background:** In [1]_, regression calibration is defined in terms of *quantile calibration*.
+    A probabilistic forecaster :math:`h(X)` outputs for any input :math:`X \\in \\mathbb{R}` a probability density
+    distribution :math:`f_Y(y)` for the target domain :math:`Y \\in \\mathcal{Y} = \\mathbb{R}`. The according
+    cumulative density function (CDF) is denoted as :math:`F_Y(y)`, the respective (inverse) quantile function
+    :math:`F^{-1}_Y(\\tau)` for a certain confidence level :math:`\\tau \\in [0, 1]`. The quantile function denotes
+    the quantile boundaries in :math:`\\mathcal{Y}` given a certain confidence level :math:`\\tau`.
+    Using this notation, *quantile calibration* [1]_ is defined as
+
+    .. math::
+        \\mathbb{P}(Y \\leq F^{-1}_Y(\\tau)) = \\tau, \\quad \\forall \\tau \\in [0, 1] ,
+
+    which is equivalent to
+
+    .. math::
+        \\mathbb{P}(F^{-1}_Y(\\tau_1) \\leq Y \\leq F^{-1}_Y(\\tau_2)) = \\tau_2 - \\tau_1,
+        \\quad \\forall \\tau_1, \\tau_2 \\in [0, 1] .
+
+    In other words, the estimated quantiles should match the observed quantiles. For example, if we inspect the 90%
+    quantiles of a forecaster over multiple samples, we would expect that 90% of all ground-truth estimates fall into
+    these quantiles.
+
+    The Isotonic Regression consumes the input cumulative distribution function (CDF) and compares it with the
+    empirical data CDF. With this comparison, it is possible to map the uncalibrated CDF estimates to calibrated
+    ones using a monotonically increasing step function.
+
+    References
+    ----------
+    .. [1] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+       "Accurate uncertainties for deep learning using calibrated regression."
+       International Conference on Machine Learning. PMLR, 2018.
+       `Get source online <http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf>`__
+    """
+
+    def __init__(self):
+        """ Constructor. """
+
+        super().__init__(detection=False, independent_probabilities=False)
+        self._iso = None
+
+    def clear(self):
+        """ Clear model parameters. """
+
+        self._iso = None
+
+    def fit(
+            self,
+            X: Union[List[np.ndarray], Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            tensorboard: Optional[SummaryWriter] = None
+    ) -> 'IsotonicRegression':
+        """
+        Fit a isotonic regression calibration method to the provided data. If multiple dimensions are provided,
+        multiple independent regression models are fitted for each dimension.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        tensorboard: torch.utils.tensorboard.SummaryWriter, optional, default: None
+            Instance of type "SummaryWriter" to log training statistics.
+
+        Returns
+        -------
+        IsotonicRegression
+            Instance of class :class:`netcal.regression.IsotonicRegression`.
+        """
+
+        # add a preceeding (sample) dimension to y as "cumulative" expects multiple points on the
+        # cumulative in the first dimension
+        y = np.expand_dims(y, axis=0)  # (1, n, [d])
+        cdf_predicted, y = cumulative(X, y)  # (1, n, d)
+
+        # squeeze out the first data dim
+        cdf_predicted = np.squeeze(cdf_predicted, axis=0)  # (n, d)
+        n_samples, n_dims = cdf_predicted.shape
+
+        # fit the isotonic regression for each dimension independently
+        self._iso = []
+        for dim in range(n_dims):
+            iso = sklearn_iso(out_of_bounds='clip')
+
+            # get the empirical cumulative for the current dim
+            # use sort algorithm to determine how many samples are less or equal given a certain sample
+            # simply use linspace to give the fraction of the relative amount of less or equal
+            # samples in a sorted array
+            cdf = np.sort(cdf_predicted[:, dim])  # (n,)
+            cdf_empirical = np.linspace(1./n_samples, 1., n_samples)  # (n,)
+
+            # this method might introduce a small error when consecutive samples have the same value
+            # in this case, identify equal samples and reassign the new cumulative score in reversed order
+            equal, = np.where(cdf[:-1] == cdf[1:])  # (n-1, )
+            for idx in reversed(equal):
+                cdf_empirical[idx] = cdf_empirical[idx+1]
+
+            iso.fit(cdf, cdf_empirical)
+            self._iso.append(iso)
+
+            # draw calibration curve for current dimension and add to SummaryWriter
+            if tensorboard is not None:
+
+                # draw matplotlib figure
+                fig, ax = plt.subplots()
+                ax.plot(iso.X_thresholds_, iso.y_thresholds_)
+                ax.grid(True)
+                ax.set_xlim([0., 1.])
+                ax.set_ylim([0., 1.])
+                ax.set_title("Isotonic recalibration curve dim %02d" % dim)
+
+                # add matplotlib figure to SummaryWriter
+                tensorboard.add_figure("isotonic/train/curve/dim%02d" % dim, fig, close=True)
+
+        # add number of training samples to tensorboard
+        if tensorboard is not None:
+            tensorboard.add_scalar("isotonic/train/n_samples", n_samples)
+
+        return self
+
+    def transform(
+            self,
+            X: Union[List[np.ndarray], Tuple[np.ndarray, np.ndarray], np.ndarray],
+            t: Union[int, np.ndarray] = 512
+    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+        """
+        Transform uncalibrated distributional estimates (mean and stddev or stochastic samples) to calibrated ones
+        by applying isotonic regression calibration of quantiles. Use the parameter "t" to control the base points
+        for the returned density/cumulative functions.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+        t : int or np.ndarray of shape (t, [n, [d]])
+            Parameter to control the output sample distribution. If integer, the given amount of
+            sample points for each input X is created. If np.ndarray, use this as distribution values for each
+            sample and each dim in X at location t (either for all samples equally with shape (t,) or for each sample
+            individually with shape (t, n, [d])).
+
+        Returns
+        -------
+        tuple of 3 np.ndarray, each of shape (t, n, d)
+            First array holds the points where the density and cumulative functions are defined, shape: (t, n ,d).
+            Second array is the recalibrated probability density function (PDF), shape: (t, n, d).
+            Third array is the recalibrated cumulative density function (CDF), shape: (t, n, d).
+            Note that the data dimension d is always present (also for d=1).
+        """
+
+        # check if method has already been trained
+        if self._iso is None:
+            raise RuntimeError("IsotonicRegression: call \'fit()\' method first before transform.")
+
+        # get number of dimension used for training
+        n_dims = len(self._iso)
+        mean, variance, cov = meanvar(X)
+
+        # catch covariance input
+        if cov:
+            raise RuntimeError("IsotonicRegression: covariance input is currently not supported for quantile computation.")
+
+        # make mean and variance at least 2d
+        mean = np.expand_dims(mean, axis=1) if mean.ndim == 1 else mean  # (n, d)
+        variance = np.expand_dims(variance, axis=1) if variance.ndim == 1 else variance  # (n, d)
+
+        # initialize sampling points to define the recalibrated PDF/CDF
+        n_samples = mean.shape[0]
+        if isinstance(t, int):
+
+            target_quantile = 1e-7
+            stddev = np.sqrt(variance)
+
+            # initialize empty boundaries for cumulative x-scores
+            lb_cdf = np.zeros(len(self._iso))  # (d,)
+            ub_cdf = np.zeros(len(self._iso))  # (d,)
+
+            # iterate over all dimensions and examine the according isotonic regression model
+            for dim, iso in enumerate(self._iso):
+
+                # get the indices of the isotonic calibration curve where the desired relevance level is reached
+                lb_idx = np.argmax(iso.y_thresholds_ >= target_quantile)
+                ub_idx = len(iso.y_thresholds_) - np.argmax(np.flip(iso.y_thresholds_) < (1-target_quantile)) - 1
+
+                # get the according x-scores of the (recalibrated) cumulative
+                lb_cdf[dim] = iso.X_thresholds_[lb_idx]
+                ub_cdf[dim] = iso.X_thresholds_[ub_idx]
+
+            # finally, convert these scores back to the uncalibrated cumulative to obtain the sampling points
+            # with boundaries for the uncalibrated cumulative
+            lb = norm.ppf(lb_cdf[None, :], loc=mean, scale=stddev)  # (n, d)
+            ub = norm.ppf(ub_cdf[None, :], loc=mean, scale=stddev)  # (n, d)
+
+            sampling_points = np.linspace(lb, ub, t, axis=0)  # (t, n, d)
+
+        # if t is np.ndarray, use this points as the base for the calibrated
+        # output distribution
+        elif isinstance(t, np.ndarray):
+
+            # distribute 1d/2d array
+            if t.ndim == 1:
+                sampling_points = np.reshape(t, (-1, 1, 1))  # (t, 1, 1)
+                sampling_points = np.broadcast_to(sampling_points, (t.shape[0], n_samples, n_dims))  # (t, n, d)
+
+            elif t.ndim == 2:
+                sampling_points = np.expand_dims(t, axis=2)  # (t, n, 1)
+                sampling_points = np.broadcast_to(sampling_points, (t.shape[0], n_samples, n_dims))  # (t, n, d)
+
+            elif t.ndim == 3:
+                sampling_points = t  # (t, n, d)
+
+            else:
+                raise RuntimeError("Invalid shape for parameter \'t\'.")
+
+            # guarantee monotonically increasing sampling points (required for PDF diff)
+            sampling_points = np.sort(sampling_points, axis=0)  # (t, n, d)
+        else:
+            raise AttributeError("Parameter \'t\' must be either of type int or np.ndarray.")
+
+        t = sampling_points.shape[0]
+        cdf, _ = cumulative(X, sampling_points)  # (t, n, d)
+
+        # iterate over dimensions and perform recalibration of the cumulative
+        for dim in range(n_dims):
+            cdf[..., dim] = np.clip(
+                self._iso[dim].transform(cdf[..., dim].flatten()),  # (t*n,)
+                np.finfo(np.float32).eps,
+                1.-np.finfo(np.float32).eps
+            ).reshape((t, n_samples))  # (t, n)
+
+        # get density function using the cumulative
+        pdf = density_from_cumulative(sampling_points, cdf)
+
+        return sampling_points, pdf, cdf
+
+    def __repr__(self):
+        """ Returns a string representation of the calibration method with the most important parameters. """
+
+        if self._iso is None:
+            return "IsotonicRegression(fitted=False)"
+        else:
+            return "IsotonicRegression(fitted=True)"
diff --git a/netcal/regression/VarianceScaling.py b/netcal/regression/VarianceScaling.py
new file mode 100644
index 0000000..9e4047e
--- /dev/null
+++ b/netcal/regression/VarianceScaling.py
@@ -0,0 +1,188 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Mozilla Public
+# License, v. 2.0. If a copy of the MPL was not distributed with this
+# file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+from typing import Union, List, Tuple, Optional
+from torch.utils.tensorboard import SummaryWriter
+import numpy as np
+
+from netcal import AbstractCalibration, meanvar
+
+
+class VarianceScaling(AbstractCalibration):
+    """
+    Variance recalibration using maximum likelihood estimation for multiple independent dimensions (optionally).
+    Rescales the input standard deviation by a scalar parameter to achieve *variance calibration* [1]_, [2]_.
+    This method uses the negative log likelihood as the loss function to optimize the scalar scaling parameter.
+    The distributional mean is fixed during optimization.
+
+    On the one hand, this method accepts as input X either a tuple X = (mean, stddev) using two NumPy arrays of
+    shape N with N number of samples that express the estimated mean and standard deviation of a probabilistic
+    forecaster. On the other hand, a NumPy array of shape (R, N) is also accepted where R denotes the number of
+    probabilistic forecasts. For example, if probabilistic outputs are obtained by Monte-Carlo sampling using N samples
+    and R stochastic forward passes, it is possible to pass all outputs to the calibration function in a single
+    NumPy array.
+
+    This method is capable of multiple independent data dimensions where separate calibration models are fitted for
+    each data dimension. This method outputs the recalibrated standard deviation (stddev) for each dimension D.
+
+    **Mathematical background:** In [1]_ and [2]_, regression calibration is defined in terms of *variance calibration*.
+    A probabilistic forecaster :math:`h(X)` outputs for any input :math:`X \\in \\mathbb{R}` a mean :math:`\\mu_Y(X)`
+    and a variance :math:`\\sigma_Y^2(X)` for the target domain :math:`Y \\in \\mathcal{Y} = \\mathbb{R}`.
+    Using this notation, *variance calibration* [1]_, [2]_ is defined as
+
+    .. math::
+        \\mathbb{E}_{X,Y}\\Big[(\\mu_Y(X) - Y)^2 | \\sigma^2_Y(X) = \\sigma \\Big] = \\sigma^2,
+        \\quad \\forall \\sigma \\in \\mathbb{R}_{>0},
+
+    In other words, the estimated variance should match the observed variance given a certain variance level.
+    For example, if a forecaster outputs 100 predictions with a variance of :math:`\\sigma^2=2`, we would also expect
+    a variance (mean squared error) of 2.
+    Further definitions for regression calibration are *quantile calibration* and *distribution calibration*.
+
+    To achieve *variance calibration*, the Variance Scaling methods applies a temperature scaling on the
+    input variance by a single scalar parameter :math:`\\theta`. The methods uses the negative log likelihood as the
+    loss for the scalar. Since we are working with Gaussians, the loss is given by
+
+    .. math::
+        \\mathcal{L}(\\theta) &= -\\sum^N_{n=1} \\frac{1}{\\sqrt{2\\pi} \\theta \\cdot \\sigma_Y(x_n)}
+        \\exp\\Bigg( \\frac{y_n - \\mu_Y(x_n)}{2 (\\theta \\cdot \\sigma_Y(x_n))^2} \\Bigg) \\\\
+        &\\propto -N \\log(\\theta) - \\frac{1}{2\\theta^2} \\sum^N_{n=1} \\sigma_Y^{-2}(x_n) ,
+        \\big(y_n - \\mu_Y(x_n)\\big)^2
+
+    which is to be minimized.
+    Thus, we seek to get the minimum of the optimization objective which can be analytically determined in this case,
+    setting its first derivative to 0 by
+
+    .. math::
+        &\\frac{\\partial \\mathcal{L}(\\theta)}{\\partial \\theta} = 0\\\\
+        \\leftrightarrow \\quad & -N \\theta^2 \\sum^N_{n=1} \\sigma_Y^{-2}(x_n) \\big(y_n - \\mu_Y(x_n) \\big)^2 \\\\
+        \\leftrightarrow \\quad & \\theta \\pm \\sqrt{\\frac{1}{N} \\sum^N_{n=1} \\sigma_Y^{-2}(x_n) \\big(y_n - \\mu_Y(x_n) \\big)^2} .
+
+
+    References
+    ----------
+    .. [1] Levi, Dan, et al.:
+       "Evaluating and calibrating uncertainty prediction in regression tasks."
+       arXiv preprint arXiv:1905.11659 (2019).
+       `Get source online <https://arxiv.org/pdf/1905.11659.pdf>`__
+
+    .. [2] Laves, Max-Heinrich, et al.:
+       "Well-calibrated regression uncertainty in medical imaging with deep learning."
+       Medical Imaging with Deep Learning. PMLR, 2020.
+       `Get source online <http://proceedings.mlr.press/v121/laves20a/laves20a.pdf>`__
+    """
+
+    def __init__(self):
+        """ Constructor. """
+
+        super().__init__(detection=False, independent_probabilities=False)
+        self._weight = None
+
+    def clear(self):
+        """ Clear model parameters. """
+
+        self._weight = None
+
+    def fit(
+            self,
+            X: Union[List[np.ndarray], Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray,
+            tensorboard: Optional[SummaryWriter] = None
+    ) -> 'VarianceScaling':
+        """
+        Fit a variance scaling calibration method to the provided data. If multiple dimensions are provided,
+        multiple independent recalibration models are fitted for each dimension.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        tensorboard: torch.utils.tensorboard.SummaryWriter, optional, default: None
+            Instance of type "SummaryWriter" to log training statistics.
+
+        Returns
+        -------
+        VarianceScaling
+            Instance of class :class:`netcal.regression.VarianceScaling`.
+        """
+
+        (mean, var), y, cov = meanvar(X, y)
+
+        # covariance rescaling is currently not supported
+        if cov:
+            raise RuntimeError("VarianceScaling: covariance rescaling is currently not supported.")
+
+        mean = np.expand_dims(mean, axis=1) if mean.ndim == 1 else mean  # (n, d)
+        var = np.expand_dims(var, axis=1) if var.ndim == 1 else var  # (n, d)
+        y = np.expand_dims(y, axis=1) if y.ndim == 1 else y  # (n, d)
+
+        # used closed-form solution to obtain the optimal rescaling parameter
+        self._weight = np.sqrt(np.mean(np.square(y - mean) / var, axis=0, keepdims=True))  # (1, d)
+
+        # log number of training samples and scalar weight to tensorboard
+        if tensorboard is not None:
+            for dim, weight in enumerate(self._weight[0]):
+                tensorboard.add_scalar("nllvariance/train/scale/dim%02d" % dim, weight)
+
+            tensorboard.add_scalar("nllvariance/train/n_samples", y.shape[0])
+
+        return self
+
+    def transform(self, X: Union[List[np.ndarray], Tuple[np.ndarray, np.ndarray], np.ndarray]) -> np.ndarray:
+        """
+        Transform uncalibrated distributional estimates (mean and stddev or stochastic samples) to calibrated ones
+        by applying variance recalibration. Returns the calibrated standard deviation.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+
+        Returns
+        -------
+        np.ndarray of shape (n, d)
+            Recalibrated standard deviation for each sample in each dimension.
+        """
+
+        # check if method has already been trained
+        if self._weight is None:
+            raise RuntimeError("VarianceScaling: call \'fit()\' method first before transform.")
+
+        # get mean and variance from input
+        mean, var, cov = meanvar(X)
+
+        # covariance rescaling is currently not supported
+        if cov:
+            raise RuntimeError("VarianceScaling: covariance rescaling is currently not supported.")
+
+        # make variance at least 2d and perform rescaling of stddev
+        var = np.expand_dims(var, axis=1) if var.ndim == 1 else var  # (n, d)
+        calibrated_scale = np.sqrt(var) * self._weight  # (n, d)
+
+        return calibrated_scale
+
+    def __repr__(self):
+        """ Returns a string representation of the calibration method with the most important parameters. """
+
+        if self._weight is None:
+            return "VarianceScaling(weight=None)"
+        else:
+            return "VarianceScaling(weight=%.4f)" % self._weight
diff --git a/netcal/regression/__init__.py b/netcal/regression/__init__.py
new file mode 100644
index 0000000..7f3b877
--- /dev/null
+++ b/netcal/regression/__init__.py
@@ -0,0 +1,39 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+"""
+.. include:: /../../netcal/regression/README.md
+   :parser: myst_parser.sphinx_
+
+Available classes
+=================
+
+.. autosummary::
+   :toctree: _autosummary_regression
+   :template: custom_class.rst
+
+   IsotonicRegression
+   VarianceScaling
+   GPBeta
+   GPNormal
+   GPCauchy
+
+Package for Gaussian process optimization
+=========================================
+
+.. autosummary::
+   :toctree: _autosummary_regression_gp
+
+   gp
+"""
+
+from .IsotonicRegression import IsotonicRegression
+from .VarianceScaling import VarianceScaling
+
+from .gp.GPBeta import GPBeta
+from .gp.GPNormal import GPNormal
+from .gp.GPCauchy import GPCauchy
diff --git a/netcal/regression/gp/AbstractGP.py b/netcal/regression/gp/AbstractGP.py
new file mode 100644
index 0000000..c99759e
--- /dev/null
+++ b/netcal/regression/gp/AbstractGP.py
@@ -0,0 +1,816 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from tqdm import tqdm
+from copy import deepcopy
+from typing import Tuple, Iterable, Union, Optional, Dict
+import numpy as np
+from scipy.stats import norm
+from matplotlib import pyplot as plt
+
+import torch
+import torch.nn as nn
+from torch.utils.data import DataLoader, TensorDataset
+from torch.utils.tensorboard import SummaryWriter
+
+import pyro
+import gpytorch
+
+from netcal import AbstractCalibration, meanvar
+from netcal.regression.gp.kernel import GaussianRBFKernel
+
+
+class AbstractGP(AbstractCalibration, gpytorch.models.ApproximateGP):
+    """
+    Distribution recalibration of regression models using a Gaussian process parameter estimation.
+    The goal of regression calibration using a GP scheme is to achieve *distribution calibration*,
+    i.e., to match the predicted moments (mean, variance) to the true observed ones. In contrast to *quantile
+    calibration* [3]_, where only the marginal calibration is of interest, the *distribution calibration* is more
+    restrictive. It requires that the predicted moments should match the observed ones *given a certain probability
+    distribution*. Therefore, the authors in [1]_ propose to use Gaussian process to estimate the recalibration
+    parameters of a Beta calibration function locally (i.e., matching the observed moments of neighboring samples).
+
+    In this framework, we use the base GP scheme to implement the Beta calibration for regression [1]_ as well as
+    to derive a novel parametric recalibration that yields a parametric Gaussian or Cauchy distribution as
+    calibration output [2]_.
+
+    On the one hand, this method accepts as input X either a tuple X = (mean, stddev) using two NumPy arrays of
+    shape N with N number of samples that express the estimated mean and standard deviation of a probabilistic
+    forecaster. On the other hand, a NumPy array of shape (R, N) is also accepted where R denotes the number of
+    probabilistic forecasts. For example, if probabilistic outputs are obtained by Monte-Carlo sampling using N samples
+    and R stochastic forward passes, it is possible to pass all outputs to the calibration function in a single
+    NumPy array.
+
+    This method is capable of multiple independent data dimensions that are jointly optimized using a single Gaussian
+    process. This method outputs a tuple consisting of three NumPy arrays:
+
+    - 1st array: T points where the density/cumulative distribution functions are defined, shape: (T, N, D)
+    - 2nd array: calibrated probability density function, shape: (T, N, D)
+    - 3rd array: calibrated cumulative density function, shape: (T, N, D)
+
+    **Mathematical background:** In [1]_, regression calibration is defined in terms of *distribution calibration*.
+    A probabilistic forecaster :math:`h(X)` outputs for any input :math:`X \\in \\mathbb{R}` a probability density
+    distribution :math:`f_Y(y) \\in \\mathcal{F}_Y` (where :math:`\\mathcal{F}` denotes the set of all possible
+    probability distributions) for the target domain :math:`Y \\in \\mathcal{Y} = \\mathbb{R}`. Furthermore, let
+    :math:`S = h(X)` denote the random variable of model predictions.
+    Using this notation, *distribution calibration* [1]_ is defined as
+
+    .. math::
+        f_Y(Y=y | S = s) = s(y), \\quad \\forall s \\in \\mathcal{F}_Y, \\forall y \\in \\mathcal{Y} .
+
+    In other words, "*this definition implies that if a calibrated model predicts a distribution with some mean*
+    :math:`\\mu` *and variance* :math:`\\sigma^2` *, then it means that on average over all cases with the same
+    prediction the mean of the target is* :math:`\\mu` *and variance is* :math:`\\sigma^2`" (cf. [1]_, p. 4 ll. 25-28).
+
+    For uncertainty recalibration, a standard calibration function can be used, e. g., Variance Scaling.
+    In contrast to the standard methods, we can use a Gaussian process to estimate the rescaling parameter of the
+    scaling method. This offers more flexibility and a more "local" or focused recalibration of a single sample.
+
+    Since not all calibration methods yield an analytically tractable likelihood (e.g., the GP-Beta uses a non-standard
+    likelihood), the current GP scheme is a sampling based variational one.
+    Furthermore, as the amount of training data might grow very large, we use an approximate GP with so called
+    inducing points that are learnt from the data and used during inference to obtain the calibration parameters.
+    Therefore, we the computational complexity keeps fixed during inference.
+    For a detailed derivation of the GP scheme, cf. [1]_.
+    For a detailed description of the kernel function, cf. :class:`netcal.regression.gp.kernel.GaussianRBFKernel`.
+
+    Parameters
+    ----------
+    n_inducing_points: int
+        Number of inducing points used to approximate the input space. These inducing points are also optimized.
+    n_random_samples: int
+        Number of random samples used to sample from the parameter distribution during optimization and inference.
+    n_parameters: int
+        Number of parameters that are required for a dedicated implementation of the GP method (mainly used internally).
+    correlations: bool, default: False
+        If True, perform covariance estimation or covariance recalibration on multivariate input data.
+        Only works for GPNormal.
+    n_epochs: int, default: 200
+        Number of optimization epochs.
+    batch_size: int, default: 256
+        Size of batches during optimization.
+    num_workers : int, optional, default: 0
+        Number of workers used for the dataloader.
+    lr: float, optional, default: 1e-2
+        Learning rate used for the Adam optimizer.
+    use_cuda: str or bool, optional, default: False
+        The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+        You can also pass a string "cuda:0", "cuda:1", etc. to specify the CUDA device.
+        If False, use CPU for optimization and inference.
+    jitter: float, optional, default: 1e-5
+        Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+        Gaussian process optimization.
+    name_prefix: str, optional, default: "abstractgp"
+        Name prefix internally used in Pyro to distinguish between parameter stores.
+
+    References
+    ----------
+    .. [1] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+           "Distribution calibration for regression."
+           International Conference on Machine Learning (pp. 5897-5906), 2019.
+           `Get source online <http://proceedings.mlr.press/v97/song19a/song19a.pdf>`__
+    .. [2] Song, L., Zhang, X., Smola, A., Gretton, A., & Schölkopf, B.:
+           "Tailoring density estimation via reproducing kernel moment matching."
+           In Proceedings of the 25th international conference on Machine learning (pp. 992-999), July 2008.
+           `Get source online <https://www.cs.uic.edu/~zhangx/pubDoc/xinhua_icml08.pdf>`__
+    """
+
+    precision = torch.float64
+    precision_np = np.float64
+
+    def __init__(
+            self,
+            n_inducing_points: int,
+            n_random_samples: int,
+            *,
+            n_parameters: int,
+            correlations: bool = False,
+            n_epochs: int = 200,
+            batch_size: int = 256,
+            num_workers : int = 0,
+            lr: float = 1e-2,
+            use_cuda: Union[str, bool] = False,
+            jitter: float = 1e-5,
+            name_prefix="abstractgp"
+    ):
+
+        if isinstance(use_cuda, str):
+            # this line will throw an exception if the cuda device does not exist
+            device = torch.device(use_cuda)
+            torch.cuda.get_device_name(use_cuda)
+
+        else:
+            device = torch.device('cuda') if use_cuda and torch.cuda.is_available() else torch.device('cpu')
+
+        # optimization hyperparameters
+        self.n_inducing_points = n_inducing_points
+        self.n_random_samples = n_random_samples
+        self.n_parameters = n_parameters
+        self.n_epochs = n_epochs
+        self.batch_size = batch_size
+        self.num_workers = num_workers
+        self.lr = lr
+        self.device = device
+        self.correlations = correlations
+        self.jitter = jitter
+        self.name_prefix = name_prefix
+
+        self.marginal_correlations = None
+        self.variational_strategy = None
+        self.mean_module = None
+        self.covar_module = None
+        self.inv_gamma = None
+        self.delta = None
+        self.pyro_scope = {'params': {}, 'constraints': {}}
+
+        # Standard initializtation
+        AbstractCalibration.__init__(self, detection=False, independent_probabilities=False)
+        gpytorch.models.ApproximateGP.__init__(self, None)
+
+    def clear(self):
+        """ Clear module parameters. """
+
+        for layer in self.children():
+            if hasattr(layer, 'reset_parameters'):
+                layer.reset_parameters()
+
+        self.marginal_correlations = None
+        self.variational_strategy = None
+        self.mean_module = None
+        self.covar_module = None
+        self.inv_gamma = None
+        self.delta = None
+        self.pyro_scope = {'params': {}, 'constraints': {}}
+
+    def get_params(self, deep=True) -> Dict:
+        """
+        Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC
+        coefficients, etc.
+        """
+
+        parameters = {
+            "get_params": super().get_params(deep=deep),
+            "n_dims": self.ndim,
+            "state_dict": self.state_dict(),
+        }
+
+        return parameters
+
+    def load_model(self, filename, use_cuda: Union[str, bool, None] = None) -> 'AbstractGP':
+        """
+        Overwrite base method's load_model function as the parameters for the GP methods are stored differently
+        compared to the remaining methods.
+
+        Parameters
+        ----------
+        filename : str
+            String with filename.
+        use_cuda : str or bool, optional, default: None
+            Specify if CUDA should be used. If str, you can also specify the device
+            number like 'cuda:0', etc. If unset, use the device id that has been stored on disk.
+
+        Returns
+        -------
+        AbstractGP
+            Instance of a child class of `AbstractGP`.
+        """
+
+        with open(filename, 'rb') as read_object:
+            loaded_params = torch.load(read_object, map_location=torch.device('cpu'))
+
+        # in a first step, recover all base parameters
+        params = loaded_params["get_params"]
+        n_dims = loaded_params["n_dims"]
+        self.set_params(**params)
+
+        # ---------------------------------------
+        # overwrite default computing device
+        # if not set, leave self.device untouched
+        if use_cuda is None:
+            pass
+
+        # otherwise, overwrite default device
+        else:
+            if isinstance(use_cuda, str):
+                # this line will throw an exception if the cuda device does not exist
+                device = torch.device(use_cuda)
+                torch.cuda.get_device_name(use_cuda)
+
+            else:
+                device = torch.device('cuda') if use_cuda and torch.cuda.is_available() else torch.device('cpu')
+
+            self.device = device
+
+        # ---------------------------------------
+
+        # initialize (empty) mean/covar module, LMC variational strategy and inducing points
+        mean, var = torch.zeros(1, n_dims, dtype=self.precision), torch.ones(1, n_dims, dtype=self.precision)
+        if self.correlations:
+            var = torch.diag_embed(var)
+            tril_idx = torch.tril_indices(row=n_dims, col=n_dims)
+            var = var[:, tril_idx[0], tril_idx[1]]
+
+        # using the "empty" initialization, we can recover the learnt parameter by the passed state dict
+        self._init_gp_model(mean, var)
+        self.load_state_dict(loaded_params["state_dict"])
+
+        return self
+
+    @property
+    def inducing_points(self) -> Tuple[np.ndarray, np.ndarray]:
+        """ Return inducing points mean and variance/covariance as tuple. """
+
+        if self.variational_strategy is None:
+            raise RuntimeError("AbstractGP: could not return inducing points: call fit() first.")
+
+        # get raw inducing points
+        inducing_points = self.variational_strategy.base_variational_strategy.inducing_points.detach()  # (m, d) or (m, d + (d^2+d)//2))
+
+        # if covariance estimation, recover cov from decomposed lower triangular
+        if self.correlations:
+            n_dims = int((np.sqrt(8 * inducing_points.shape[-1] + 9) - 3) // 2)
+
+            # get lower triangular indices and recover cov
+            tril_idx = torch.tril_indices(row=n_dims, col=n_dims)
+            var = torch.zeros(self.n_inducing_points, n_dims, n_dims, dtype=inducing_points.dtype, device=inducing_points.device)
+            var[:, tril_idx[0], tril_idx[1]] = inducing_points[:, n_dims:]
+            var = var @ var.transpose(dim0=2, dim1=1)
+
+        # simply return the (diagonal) variances
+        else:
+            n_dims = int(inducing_points.shape[-1] // 2)
+            var = inducing_points[:, n_dims:]
+
+        # extract the mean and return everything as NumPy arrays
+        mean = inducing_points[:, :n_dims]
+        return mean.numpy(), var.numpy()
+
+    @property
+    def ndim(self):
+        """ Get number of dimensions for which this method was trained for """
+
+        if self.variational_strategy is None:
+            raise RuntimeError("AbstractGP: could not return ndim: call fit() first.")
+
+        # get raw inducing points
+        inducing_points = self.variational_strategy.base_variational_strategy.inducing_points  # (m, d) or (m, d + (d^2+d)//2))
+        if self.correlations:
+            n_dims = int((np.sqrt(8 * inducing_points.shape[-1] + 9) - 3) // 2)
+        else:
+            n_dims = int(inducing_points.shape[-1] // 2)
+
+        return n_dims
+
+    # -------------------------------------------------------------------------
+    # Pyro + GPyTorch functions
+
+    def forward(self, x) -> gpytorch.distributions.MultivariateNormal:
+        """
+        Forward method defines the prior for the GP.
+
+        Parameters
+        ----------
+        x : torch.Tensor of shape (n, 2*d)
+            Set of samples used for kernel computation consisting of mean and variance for each input point.
+
+        Returns
+        -------
+        gpytorch.distributions.MultivariateNormal
+            Multivariate normal distribution holding the GP prior information.
+        """
+
+        mean = self.mean_module(x)
+        covar = self.covar_module(x)
+
+        return gpytorch.distributions.MultivariateNormal(mean, covar)
+
+    def guide(self, x, y):
+        """
+        Pyro guide that defines the variational distribution for the Gaussian process.
+
+        Parameters
+        ----------
+        x : torch.Tensor of shape (n, 2*d)
+            Set of samples used for kernel computation consisting of mean and variance for each input point.
+        y : torch.Tensor of shape (n, d)
+            Ground-truth regression information (not used within the guide).
+        """
+
+        # Get q(f) - variational (guide) distribution of latent function
+        function_dist = self.pyro_guide(x)
+
+        # Use a plate here to mark conditional independencies
+        with pyro.plate(self.name_prefix + ".data_plate", dim=-1):
+            # Sample from latent function distribution
+            pyro.sample(self.name_prefix + ".f(x)", function_dist)
+
+    def model(self, x: torch.Tensor, y: torch.Tensor):
+        """
+        Model function that defines the computation graph. Get the variational
+        distribution for the Gaussian process and sample function parameters for recalibration.
+
+        Parameters
+        ----------
+        x : torch.Tensor of shape (n, 2*d)
+            Set of samples used for kernel computation consisting of mean and variance for each input point.
+        y : torch.Tensor of shape (n, d)
+            Ground-truth regression information used for the ELBO loss.
+
+        Returns
+        -------
+        pyro.sample statement
+            Sample statement using the specified likelihood.
+        """
+
+        # decompose input arguments
+        assert x.ndim == 2, "GP optimization: x must be 2-D with shape (n, 2*d) or (n, d + (d^2+d)//2)."
+
+        # if correlations, x is the mean and decomposed cov
+        if self.correlations:
+            n_dims = int((np.sqrt(8 * x.shape[-1] + 9) - 3) // 2)
+        else:
+            n_dims = x.shape[1] // 2
+
+        x_loc = x[:, :n_dims]  # (n, d)
+        x_var = x[:, n_dims:]  # (n, d) or (n, (d^2 +d) // 2)
+
+        # register module in pyro
+        pyro.module(self.name_prefix + ".gp", self)
+
+        # get p(f) - prior distribution of latent function
+        function_dist = self.pyro_model(x)
+
+        # use a plate here to mark conditional independencies
+        with pyro.plate(self.name_prefix + ".data_plate", dim=-1):
+            # sample from latent function distribution
+            function_samples = pyro.sample(self.name_prefix + ".f(x)", function_dist)  # ([r], n, p*d)
+            function_samples = function_samples * self.inv_gamma + self.delta  # ([r], n, p*d)
+
+            # if we're in the random sampling mode, prepend a distribution dim to data
+            if function_samples.ndim == 3:
+                x_loc = x_loc.unsqueeze(0)  # (1, n, d)
+                x_var = x_var.unsqueeze(0)  # (1, n, d)
+                y = y.unsqueeze(0)  # (1, n, d)
+
+            # sample from observed distribution and use custom likelihood
+            # to_event(1) marks the last dim d as event_dim so that pyro infers a single likelihood over all d
+            # e.g., for independent normals, this is simply the sum of the log_probs
+            likelihood = self.likelihood(x_loc, x_var, parameters=function_samples)
+
+            # if no correlations are modelled across the different dimensions, use independent distributions
+            # by calling "to_event" method
+            if not self.correlations:
+                likelihood = likelihood.to_event(1)
+
+            return pyro.sample(
+                self.name_prefix + ".y",
+                likelihood,
+                obs=y
+            )
+
+    # -------------------------------------------------------------------------
+
+    def _init_gp_model(self, Xmean: torch.Tensor, Xlogvariance: torch.Tensor):
+        """
+        Initialize the GP model. This method prepares the mean and variance to have the right shape.
+        If "correlations=True", the input variance/covariance gets LDL* decomposed.
+        Furthermore, the inducing points are initialized and the variational distribution is set up.
+
+        Parameters
+        ----------
+        Xmean : torch.Tensor of shape (n, d)
+            The mean of the training data (see _get_input output description).
+        Xlogvariance : torch.Tensor of shape (n, d, [d])
+            The log-variance of covariance of the training data (see _get_input output description).
+        """
+
+        # convert log of variance back to variance
+        Xvariance = torch.exp(Xlogvariance)
+
+        # get number of dimensions
+        n_samples, n_dims = Xmean.shape
+
+        # -------------------------------------------------
+        # initialize inducing points based on training data
+        # initialize range for inducing points
+        loc_min, loc_max = torch.min(Xmean, dim=0).values, torch.max(Xmean, dim=0).values
+
+        # initialize inducing points with ones
+        inducing_points_var = torch.ones(self.n_inducing_points, n_dims, dtype=self.precision) * 3 # (n, d)
+
+        # if input is given as cov, we also need inducing points with covariance
+        if self.correlations:
+
+            tril_idx = torch.tril_indices(row=n_dims, col=n_dims)
+            stddev_diagonal = Xvariance[:, tril_idx[0] == tril_idx[1]]  # (n, d)
+            std_max = torch.max(stddev_diagonal, dim=0).values  # (d,)
+
+            # initialize off-diagonal and concatenate to "flat" array
+            inducing_points_var = torch.cat(
+                (inducing_points_var,
+                 torch.ones((self.n_inducing_points, (n_dims ** 2 - n_dims) // 2),
+                            dtype=inducing_points_var.dtype,
+                            device=inducing_points_var.device
+                            ).normal_(std=1e-3)
+                 ),
+                dim=1
+            )  # (m, (d^d + d)//2)
+
+        else:
+            # get maximum standard deviation to init space of inducing points
+            std_max = torch.sqrt(torch.max(Xvariance, dim=0).values)  # (d,)
+
+            # use log of inducing points variance to guarantee positive variances during optimization
+            inducing_points_var = torch.log(inducing_points_var)
+
+        # use NumPy linspace as it supports vectorized start and end points (in contrast to PyTorch)
+        inducing_points_mean = torch.from_numpy(
+            np.linspace(
+                (loc_min - 3 * std_max).numpy(),
+                (loc_max + 3 * std_max).numpy(),
+                self.n_inducing_points
+            )
+        ).to(self.precision)  # (m, d)
+
+        # concatenate mean and var of inducing points to a single pytorch tensor
+        inducing_points = torch.cat((inducing_points_mean, inducing_points_var), dim=1)
+
+        # variational distribution for inducing points
+        variational_distribution = gpytorch.variational.CholeskyVariationalDistribution(
+            num_inducing_points=self.n_inducing_points, batch_shape=torch.Size([1])
+        )
+
+        # convert dtype of variational distribution
+        variational_distribution.variational_mean.data = variational_distribution.variational_mean.data.to(
+            dtype=self.precision)
+        variational_distribution.chol_variational_covar.data = variational_distribution.chol_variational_covar.data.to(
+            dtype=self.precision)
+
+        # scale the number of estimated parameters depending on the correlations parameter
+        # if self.correlations is True, assert variance rescaling using multivariate normal
+        # in this case, the number of output parameters is (n^2 + n)/2
+        if self.correlations:
+            n_outputs = (n_dims + n_dims ** 2) // 2
+        else:
+            n_outputs = n_dims * self.n_parameters
+
+        # initialize variational multitask strategy
+        self.variational_strategy = gpytorch.variational.LMCVariationalStrategy(
+            gpytorch.variational.VariationalStrategy(
+                self, inducing_points, variational_distribution, learn_inducing_locations=True,
+            ), num_tasks=n_outputs, num_latents=1
+        )
+
+        # num_latents is 1 so we have a batch_shape of 1 to approximate an intrinsic model of coregionalization (ICM)
+        # that is used in the original paper. See: https://github.com/cornellius-gp/gpytorch/issues/1035
+        # the linear dependencies are modelled by the 'LMCVariationalStrategy'
+        self.mean_module = gpytorch.means.ConstantMean(batch_shape=torch.Size([1]))
+        self.covar_module = gpytorch.kernels.ScaleKernel(
+            GaussianRBFKernel(cov=self.correlations),
+            batch_shape=torch.Size([1])
+        )
+
+        if self._learn_scale_shift:
+            # scaling parameters for sampled weights
+            self.inv_gamma = nn.Parameter(data=torch.ones(size=(1, n_outputs)), requires_grad=True)
+            self.delta = nn.Parameter(data=torch.zeros(size=(1, n_outputs)), requires_grad=True)
+
+            self.register_parameter('inv_gamma', self.inv_gamma)
+            self.register_parameter('delta', self.delta)
+
+        else:
+            self.inv_gamma = 1.
+            self.delta = 0.
+
+    def _get_input(
+            self,
+            X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray],
+            y: np.ndarray = None
+    ) -> Union[Tuple[torch.Tensor, torch.Tensor], Tuple[Tuple[torch.Tensor, torch.Tensor], torch.Tensor]]:
+        """
+        Perform some input checks on the data and convert to PyTorch.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+
+        Returns
+        -------
+        tuple of size 2
+            If y is given, the first entry in the tuple is a tuple consisting of the
+            transformed input mean and variance. The second entry is the transformed y.
+            If y is None, simply return the transformed input mean and variance.
+        """
+
+        # preprocess inputs to extract mean, variance and according target scores
+        if y is not None:
+            (Xmean, Xvariance), y, input_cov = meanvar(X, y)
+        else:
+            Xmean, Xvariance, input_cov = meanvar(X)
+
+        # perform consistency check
+        if input_cov and not self.correlations:
+            raise RuntimeError("Found input covariance matrices but \'correlations\' is set to False.")
+
+        # if Xmean or Xvariance is 1-D, append a second axis
+        Xmean = np.expand_dims(Xmean, axis=1) if Xmean.ndim == 1 else Xmean  # (n, d)
+        Xvariance = np.expand_dims(Xvariance, axis=1) if Xvariance.ndim == 1 else Xvariance  # (n, d)
+
+        # convert mean, variance and target scores to PyTorch tensors
+        Xmean = torch.from_numpy(Xmean).to(dtype=self.precision)
+        Xvariance = torch.from_numpy(Xvariance).to(dtype=self.precision)
+
+        # if capturing correlations is enabled, prepare the given variance/covariance matrices
+        if self.correlations:
+
+            # if input is given as variance vector, convert it to diagonal covariance matrix first
+            if not input_cov:
+                Xvariance = torch.diag_embed(Xvariance)  # (n, d, d)
+
+                # in the next step, capture the marginal correlation coefficients (correlation between d dimensions
+                # across the whole dataset)
+                # use NumPy function as PyTorch does not serve this functionality
+                if self.marginal_correlations is None:
+                    assert y is not None, "Fatal: building correlation coefficients but y is None. " \
+                                          "You maybe trained a GP model using covariance matrices but try to " \
+                                          "transform using variances only."
+
+                    self.marginal_correlations = torch.from_numpy(
+                        np.corrcoef(y, rowvar=False)
+                    ).unsqueeze(dim=0)  # (1, d, d)
+
+                # use the previously defined correlation coefficients to compute the covariances for each
+                # sample individually
+                Xvariance = torch.sqrt(Xvariance) @ self.marginal_correlations @ torch.sqrt(Xvariance)  # (n, d, d)
+
+            # use cholesky decomposed covariance matrices during optimization
+            # return "flattened" lower triangular
+            n_dims = Xmean.shape[-1]
+            tril_idx = torch.tril_indices(row=n_dims, col=n_dims)
+
+            # catch possible errors in covariance decomposition and turn it into
+            # a more useful error message
+            try:
+                Xvariance = torch.linalg.cholesky(Xvariance)  # (n, d, d)
+            except RuntimeError:
+                raise RuntimeError("Input covariance matrices are not positive semidefinite.")
+
+            # only use the lower decomposed matrix during optimization
+            Xvariance = Xvariance[:, tril_idx[0], tril_idx[1]]  # (n, (d^2+d)//2)
+
+        # in the univariate case, use the log variance to guarantee positive variance estimates for the inducing points
+        else:
+            Xvariance = torch.log(Xvariance)
+
+        if y is not None:
+            y = np.expand_dims(y, axis=1) if y.ndim == 1 else y
+            y = torch.from_numpy(y).to(dtype=self.precision)
+
+            return (Xmean, Xvariance), y
+        else:
+            return Xmean, Xvariance
+
+    def fit(self, X: Union[Tuple[np.ndarray, np.ndarray], np.ndarray], y: np.ndarray,
+            tensorboard: Optional[SummaryWriter] = None) -> 'AbstractGP':
+        """
+        Fit a GP model to the provided data using Gaussian process optimization.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+        y : np.ndarray of shape (n, [d])
+            Target scores for each prediction estimate in X.
+        tensorboard: torch.utils.tensorboard.SummaryWriter, optional, default: None
+            Instance of type "SummaryWriter" to log training statistics.
+
+        Returns
+        -------
+        AbstractGP
+            (Child) instance of class :class:`AbstractGP`.
+        """
+
+        self.clear()
+        with torch.no_grad():
+            (Xmean, Xvariance), y = self._get_input(X, y)
+
+        with pyro.get_param_store().scope() as scope:
+
+            # initialize covariance module, variational distribution and inducing points based on the input data
+            self._init_gp_model(Xmean, Xvariance)
+
+            # concatenate mean and var of training points to a single pytorch tensor
+            X = torch.cat((Xmean, Xvariance), dim=1)  # (n, 2*d) or (n, d + (d^2+d)//2)
+
+            # -------------------------------------------------
+            # initialize training
+
+            # create PyTorch dataset and dataloader for optimization
+            dataset = TensorDataset(X, y)
+            dataloader = DataLoader(dataset, batch_size=self.batch_size, shuffle=True,
+                                    num_workers=self.num_workers, pin_memory=True)
+
+            optimizer = pyro.optim.Adam({"lr": self.lr})
+            elbo = pyro.infer.Trace_ELBO(num_particles=self.n_random_samples, vectorize_particles=True, retain_graph=True)
+            svi = pyro.infer.SVI(self.model, self.guide, optimizer, elbo)
+
+            # log hyperparameters to tensorboard
+            if tensorboard is not None:
+                prefix = "%s/train" % self.name_prefix
+                tensorboard.add_scalar("%s/lr" % prefix, self.lr)
+                tensorboard.add_scalar("%s/batch_size" % prefix, self.batch_size)
+                tensorboard.add_scalar("%s/n_epochs" % prefix, self.n_epochs)
+                tensorboard.add_scalar("%s/n_inducing_points" % prefix, self.n_inducing_points)
+                tensorboard.add_scalar("%s/n_random_samples" % prefix, self.n_random_samples)
+                tensorboard.add_scalar("%s/jitter" % prefix, self.jitter)
+                tensorboard.add_scalar("%s/correlations" % prefix, int(self.correlations))
+
+            self.train()
+            self.to(self.device, dtype=self.precision)
+
+            best_loss, best_parameters = float('inf'), {}
+
+            # enter optimization loop and iterate over epochs and batches
+            with gpytorch.settings.cholesky_jitter(float=self.jitter, double=self.jitter), tqdm(total=self.n_epochs) as pbar:
+                step = 0
+                for epoch in range(self.n_epochs):
+                    train_loss = []
+                    for batch_X, batch_y in dataloader:
+
+                        # set proper device for optimization
+                        batch_X = batch_X.to(self.device)
+                        batch_y = batch_y.to(self.device)
+
+                        self.zero_grad()
+                        batch_loss = svi.step(batch_X, batch_y) / len(batch_X)
+                        train_loss.append(batch_loss)
+
+                        # log batch-wise loss
+                        if tensorboard is not None:
+                            tensorboard.add_scalar("%s/train/loss/batch" % self.name_prefix, batch_loss, step)
+
+                        step += 1
+
+                    # store best weights after each epoch
+                    epoch_loss = np.mean(train_loss)
+                    if epoch_loss < best_loss:
+                        best_loss = epoch_loss
+                        best_parameters = deepcopy(self.state_dict())
+
+                    # log epoch loss - assign "step" as global step to sync to batch loss
+                    if tensorboard is not None:
+                        tensorboard.add_scalar("%s/train/loss/epoch" % self.name_prefix, epoch_loss, step)
+
+                    pbar.set_description("Loss: %.4f" % epoch_loss)
+                    pbar.update(1)
+
+            # restore best weights with lowest loss and set into eval mode
+            self.load_state_dict(best_parameters)
+            self.cpu()
+            self.eval()
+
+            # draw inducing points space
+            if tensorboard is not None:
+
+                # log lengthscale parameter of kernel module
+                tensorboard.add_scalar("%s/train/lengthscale" % self.name_prefix, self.covar_module.outputscale)
+
+                # get learned inducing points
+                inducing_mean, inducing_var = self.inducing_points  # (m, d)
+                n_dims = inducing_mean.shape[-1]
+
+                # only use diagonal if capturing correlations is enabled
+                if self.correlations:
+                    inducing_var = np.diagonal(inducing_var, axis1=1, axis2=2)
+                else:
+                    inducing_var = np.exp(inducing_var)
+
+                x = np.linspace(
+                    np.min(inducing_mean, axis=0) - 3 * np.sqrt(np.max(inducing_var, axis=0)),
+                    np.max(inducing_mean, axis=0) + 3 * np.sqrt(np.max(inducing_var, axis=0)),
+                    1000,
+                )  # (n, d)
+
+                # get Gaussian mixture model
+                inducing_density = norm.pdf(x[:, None, :], loc=inducing_mean[None, ...], scale=np.sqrt(inducing_var)[None, ...])  # (n, m, d)
+                inducing_density = np.sum(inducing_density / n_dims, axis=1)  # (n, d)
+
+                # iterate over dimensions and log stats
+                for dim in range(n_dims):
+
+                    # visualize as Gaussian mixture model
+                    fig, ax = plt.subplots()
+                    ax.plot(x[:, dim], inducing_density[:, dim], "-")
+                    ax.grid(True)
+                    ax.set_title("GP inducing points dim %02d" % dim)
+
+                    # add matplotlib figure to SummaryWriter
+                    tensorboard.add_figure("%s/train/inducing_points/dim%02d" % (self.name_prefix, dim), fig, close=True)
+
+                    # also log gamma and delta parameter (mostly used for gpbeta)
+                    if self._learn_scale_shift:
+                        tensorboard.add_scalar("%s/train/gamma/dim%02d" % (self.name_prefix, dim), 1./self.inv_gamma[0, dim])
+                        tensorboard.add_scalar("%s/train/delta/dim%02d" % (self.name_prefix, dim), self.delta[0, dim])
+
+        # store pyro's scope
+        self.pyro_scope = scope
+        return self
+
+    def transform(self, X: Union[Iterable[np.ndarray], np.ndarray]) -> np.ndarray:
+        """
+        Transform the given stddev to a distribution-calibrated one using the input
+        mean and stddev as priors for the underlying Gaussian process.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+        """
+
+        raise NotImplementedError("AbstractGP.transform must be implemented by child class.")
+
+    def extra_repr(self) -> str:
+        """ Additional information used to print if str(method) is called. """
+
+        content = "n_inducing_points=%d\n" \
+                  "n_random_samples=%d\n" \
+                  "n_epochs=%d\n" \
+                  "batch_size=%d\n" \
+                  "lr=%.2E\n" \
+                  "correlations=%r\n" \
+                  "jitter=%.2E" % \
+                  (
+                      self.n_inducing_points, self.n_random_samples, self.n_epochs,
+                      self.batch_size, self.lr, self.correlations, self.jitter
+                  )
+        return content
+
+    def __repr__(self) -> str:
+        """ Returns a string representation of the calibration method with the most important parameters. """
+
+        return str(nn.Module.__repr__(self))
diff --git a/netcal/regression/gp/GPBeta.py b/netcal/regression/gp/GPBeta.py
new file mode 100644
index 0000000..40b8d65
--- /dev/null
+++ b/netcal/regression/gp/GPBeta.py
@@ -0,0 +1,281 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Iterable, Union, Tuple
+import numpy as np
+
+import torch
+from torch.utils.data import DataLoader, TensorDataset
+import pyro
+
+from netcal.regression.gp import AbstractGP
+from netcal.regression.gp.likelihood import BetaLikelihood
+
+
+class GPBeta(AbstractGP):
+    """
+    GP-Beta recalibration method for regression uncertainty calibration using the well-known Beta calibration method
+    from  classification calibration in combination with a Gaussian process (GP) parameter estimation.
+    The basic idea of GP-Beta [1]_ is to apply recalibration on the uncalibrated cumulative density function (CDF),
+    similar as to the Isotonic Regression method [2]_.
+    Since the CDF is restricted to the :math:`[0, 1]` interval, the authors in [1]_ propose to use the
+    Beta calibration scheme [3]_ known in the scope of confidence calibration.
+    Furthermore, the authors use a GP to obtain the recalibration parameters of the Beta function for each
+    sample individually, so that it should finally achieve *distribution calibration* [1]_.
+
+    **Mathematical background:** Let :math:`f_Y(y)` denote the uncalibrated probability density function (PDF),
+    targeting the probability distribution for :math:`Y`.
+    Let :math:`\\tau_y \\in [0, 1]` denote a certain quantile on the uncalibrated CDF which
+    is denoted by :math:`\\tau_y = F_Y(y)`.
+    Furthermore, let :math:`g_Y(y)` and :math:`G_Y(y)` denote the recalibrated PDF and CDF, respectively.
+    The Beta calibration function :math:`\\mathbf{c}_\\beta(\\tau_y)` known from [3]_ is given by
+
+    .. math::
+        \\mathbf{c}_\\beta(\\tau_y) = \\phi\\big( a \\log(\\tau_y) - b \\log(1-\\tau_y) + c \\big)
+
+    with recalibration parameters :math:`a,b \\in \\mathbb{R}_{>0}` and :math:`c \\in \\mathbb{R}`, and
+    :math:`\\phi(\\cdot)` as the sigmoid function [3]_.
+    This method serves as a mapping from the uncalibrated CDF to the calibrated one, so that
+
+    .. math::
+        G_Y(y) = \\mathbf{c}_\\beta\\big( F_Y(y) \\big)
+
+    holds. The PDF is the derivative of the CDF, so that the calibrated PDF is given by
+
+    .. math::
+        g_Y(y) = \\frac{\\partial \\mathbf{c}_\\beta}{\\partial y}
+        = \\frac{\\partial \\mathbf{c}_\\beta}{\\partial \\tau_y} \\frac{\\partial \\tau_y}{\\partial y}
+        = \\mathbf{r}_\\beta(\\tau_y) f_Y(y) ,
+
+    with :math:`\\mathbf{r}_\\beta(\\tau_y)` as a beta link function [1]_ given by
+
+    .. math::
+        \\mathbf{r}_\\beta(\\tau_y) = \\Bigg(\\frac{a}{\\tau_y} + \\frac{b}{1-\\tau_y} \\Bigg)
+        \\mathbf{c}_\\beta(\\tau_y) \\big(1 - \\mathbf{c}_\\beta(\\tau_y)\\big) .
+
+    Finally, the recalibration parameters :math:`a, b` and :math:`c` are obtained using a Gaussian process scheme.
+    In this way, it is possible to apply non-parametric *distribution calibration* [1]_.
+
+    Parameters
+    ----------
+    n_inducing_points: int
+        Number of inducing points used to approximate the input space. These inducing points are also optimized.
+    n_random_samples: int
+        Number of random samples used to sample from the parameter distribution during optimization and inference.
+    n_epochs: int, default: 200
+        Number of optimization epochs.
+    batch_size: int, default: 256
+        Size of batches during optimization.
+    num_workers : int, optional, default: 0
+        Number of workers used for the dataloader.
+    lr: float, optional, default: 1e-2
+        Learning rate used for the Adam optimizer.
+    use_cuda: str or bool, optional, default: False
+        The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+        You can also pass a string "cuda:0", "cuda:1", etc. to specify the CUDA device.
+        If False, use CPU for optimization and inference.
+    jitter: float, optional, default: 1e-5
+        Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+        Gaussian process optimization.
+    name_prefix: str, optional, default: "gpbeta"
+        Name prefix internally used in Pyro to distinguish between parameter stores.
+
+    References
+    ----------
+    .. [1] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+       "Distribution calibration for regression."
+       International Conference on Machine Learning. PMLR, 2019.
+       `Get source online <http://proceedings.mlr.press/v97/song19a/song19a.pdf>`__
+
+    .. [2] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+       "Accurate uncertainties for deep learning using calibrated regression."
+       International Conference on Machine Learning. PMLR, 2018.
+       `Get source online <http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf>`__
+
+    .. [3] Kull, Meelis, Telmo Silva Filho, and Peter Flach:
+       "Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers"
+       Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
+       `Get source online <http://proceedings.mlr.press/v54/kull17a/kull17a.pdf>`__
+    """
+
+    precision = torch.float64
+
+    def __init__(
+            self,
+            n_inducing_points: int = 12,
+            n_random_samples: int = 128,
+            *,
+            name_prefix: str = "gpbeta",
+            **kwargs
+    ):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        # call super constructor
+        super().__init__(
+            n_inducing_points=n_inducing_points,
+            n_random_samples=n_random_samples,
+            n_parameters=3,
+            correlations=False,
+            name_prefix=name_prefix,
+            **kwargs
+        )
+
+        # set likelihood and number of parameters per dim
+        self.likelihood = BetaLikelihood
+
+        # use inv_gamma and delta to rescale sampled parameters before exponential
+        self._learn_scale_shift = True
+
+    # -------------------------------------------------------------------------
+    # Pyro + GPyTorch functions
+
+    def transform(
+            self, X: Union[Iterable[np.ndarray], np.ndarray],
+            t: Union[int, np.ndarray] = 512
+    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+        """
+        Transform the given stddev to a distribution-calibrated one using the input
+        mean and stddev as priors for the underlying Gaussian process.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+        t : int or np.ndarray of shape (t, [n, [d]])
+            Parameter to control the output sample distribution. If integer, the given amount of
+            sample points for each input X is created. If np.ndarray, use this as distribution values for each
+            sample and each dim in X at location t (either for all samples equally with shape (t,) or for each sample
+            individually with shape (t, n, [d])).
+
+        Returns
+        -------
+        tuple of 3 np.ndarray, each of shape (t, n, d)
+            First array holds the points where the density and cumulative functions are defined, shape: (t, n ,d).
+            Second array is the recalibrated probability density function (PDF), shape: (t, n, d).
+            Third array is the recalibrated cumulative density function (CDF), shape: (t, n, d).
+            Note that the data dimension d is always present (also for d=1).
+        """
+
+        # get mean, variance and stddev of input
+        with torch.no_grad():
+            Xmean, Xvariance = self._get_input(X)
+
+        # concatenate mean and var of training points to a single pytorch tensor
+        n_samples, n_dims = Xmean.shape
+        X = torch.cat((Xmean, Xvariance), dim=1).to(dtype=self.precision)  # (n, 2*d)
+
+        # -------------------------------------------------
+        # check parameter t and prepare sampling points
+
+        # if t is np.ndarray, use this points as the base for the calibrated output distribution
+        if isinstance(t, np.ndarray):
+
+            # distribute 1D array - assert only sampling points dim
+            if t.ndim ==1:
+                sampling_points = torch.from_numpy(t).reshape(t.shape[0], 1, 1)  # (t, 1, 1)
+                sampling_points = sampling_points.expand(t.shape[0], n_samples, n_dims)  # (t, n, d)
+
+            # on 2D, assert sampling points for each sample individually
+            elif t.ndim == 2:
+                sampling_points = torch.from_numpy(t).unsqueeze(dim=2)  # (t, n, 1)
+                sampling_points = sampling_points.expand(t.shape[0], n_samples, n_dims)  # (t, n, d)
+
+            elif t.ndim == 3:
+                sampling_points = torch.from_numpy(t)  # (t, n, d)
+
+            else:
+                raise RuntimeError("Invalid shape for parameter \'t\'.")
+
+            # guarantee monotonically increasing sampling points
+            sampling_points, _ = torch.sort(sampling_points, dim=0)  # (t, n, d)
+
+            # create PyTorch dataset and dataloader for optimization
+            # we need to transpose the sampling points into (n, t, d) order so that TensorDataset
+            # does not throw an error
+            sampling_points = sampling_points.permute(1, 0, 2)
+            sampling_points = sampling_points.to(dtype=self.precision)
+            dataset = TensorDataset(X, sampling_points)
+
+        else:
+            dataset = TensorDataset(X)
+
+        # -------------------------------------------------
+
+        # initialize dataloader
+        dataloader = DataLoader(dataset, batch_size=self.batch_size, shuffle=False,
+                                num_workers=self.num_workers, pin_memory=True)
+
+        # set model in eval mode and use variational distribution for inference
+        self.eval()
+
+        # work in distinct pyro parameter store
+        with pyro.get_param_store().scope(self.pyro_scope):
+
+            # move self and sampling points to the proper precision. Move self to proper device
+            self.to(device=self.device, dtype=self.precision)
+
+            # placeholders for final calibrated density and cumulative
+            sampling_points_list, calibrated_density, calibrated_cumulative = [], [], []
+
+            with torch.no_grad():
+                for batch in dataloader:
+
+                    # let the calibration method itself create the sampling points of the cumulative
+                    # if only the amount of sampling points is given
+                    if len(batch) == 1:
+                        batch_X, batch_t = batch[0], t
+
+                    # otherwise, use the given sampling points to build the recalibrated cumulative
+                    else:
+                        batch_X, batch_t = batch
+
+                        batch_t = batch_t.to(device=self.device).permute(1, 0, 2)  # (t, n, d)
+                        batch_t = batch_t.unsqueeze(dim=1)  # (t, 1, n, d)
+
+                    # move input to GPU
+                    n_batch = len(batch_X)
+                    batch_X = batch_X.to(device=self.device)  # (n, 2*d)
+
+                    # invoke GP model with learnt variational distribution
+                    output = self(batch_X)
+
+                    # sample from the variational distribution
+                    function_samples = output(torch.Size([self.n_random_samples]))  # (r, n, 3*d)
+                    function_samples = function_samples * self.inv_gamma + self.delta
+
+                    # unsqueeze to distribute computation
+                    x_loc = torch.reshape(batch_X[:, :n_dims], (1, 1, n_batch, n_dims))  # (1, 1, n, d)
+                    x_logvar = torch.reshape(batch_X[:, n_dims:], (1, 1, n_batch, n_dims))  # (1, 1, n, d)
+                    function_samples = function_samples.unsqueeze(0)  # (1, r, n, 3*d)
+
+                    # init likelihood of beta link
+                    likelihood = BetaLikelihood(x_loc, x_logvar, function_samples)
+
+                    # get calibrated cumulative distribution
+                    sampling_points_batch, calibrated_cumulative_batch = likelihood.cdf(batch_t)  # (t, 1, n, d), (t, r, n, d)
+                    calibrated_cumulative_batch = torch.mean(calibrated_cumulative_batch, dim=1).to(dtype=torch.float32, device='cpu')  # (t, n, d)
+
+                    # get calibrated density distribution
+                    calibrated_density_batch = likelihood.log_prob(sampling_points_batch)  # (t, r, n, d)
+                    calibrated_density_batch = torch.mean(torch.exp(calibrated_density_batch), dim=1).to(dtype=torch.float32, device='cpu')  # (t, n, d)
+
+                    sampling_points_list.append(torch.squeeze(sampling_points_batch, dim=1).to(dtype=torch.float32, device="cpu"))
+                    calibrated_density.append(calibrated_density_batch)
+                    calibrated_cumulative.append(calibrated_cumulative_batch)
+
+            # concatenate batch tensors to a single tensor
+            sampling_points = torch.cat(sampling_points_list, dim=1)  # (t, n, d)
+            calibrated_density = torch.cat(calibrated_density, dim=1)  # (t, n, d)
+            calibrated_cumulative = torch.cat(calibrated_cumulative, dim=1)  # (t, n, d)
+
+        return sampling_points.numpy(), calibrated_density.numpy(), calibrated_cumulative.numpy()
diff --git a/netcal/regression/gp/GPCauchy.py b/netcal/regression/gp/GPCauchy.py
new file mode 100644
index 0000000..3f94e08
--- /dev/null
+++ b/netcal/regression/gp/GPCauchy.py
@@ -0,0 +1,205 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Iterable, Union
+import numpy as np
+
+import torch
+from torch.utils.data import DataLoader, TensorDataset
+import pyro
+
+from netcal.regression.gp import AbstractGP
+from netcal.regression.gp.likelihood import CauchyLikelihood
+
+
+class GPCauchy(AbstractGP):
+    """
+    GP-Cauchy recalibration method for regression uncertainty calibration that consumes an uncalibrated Gaussian
+    distribution but converts it to a calibrated Cauchy distribution.
+    This method uses a Gaussian process (GP) for a flexible estimation of the recalibration parameter (cf. [1]_).
+    Similar to :class:`netcal.regression.gp.GPNormal`, the GP-Cauchy [2]_ acts as a kind of temperature scaling for
+    the variance of a Gaussian distribution [3]_, [4]_. However, the rescaled variance is interpreted as the
+    scaling parameter of a Cauchy distribution. Furthermore, the rescaling parameter is not globally fixed but obtained
+    by a GP for each sample individually, so that we are able to convert a Gaussian to a Cauchy distribution [2]_.
+    Thus, the GP-Cauchy seeks for **distribution calibration** but for parametric Cauchy distributions.
+    Note that this method does not change the mean but only reinterprets the predicted variance as the Cauchy scaling
+    parameter. The mode of the Cauchy is assumed to be equal to the input mean.
+
+    **Mathematical background:** Let :math:`f_Y(y)` denote the uncalibrated probability density function (PDF),
+    targeting the probability distribution for :math:`Y`. In our case, the uncalibrated PDF is given as a Gaussian, so
+    that :math:`f_Y(y) = \\mathcal{N}\\big(y; \\mu_Y(X), \\sigma^2_Y(X)\\big)` with mean :math:`\\mu_Y(X)` and variance
+    :math:`\\sigma^2_Y(X)` obtained by a probabilistic regression model that depends on the input :math:`X`.
+    The calibrated PDF :math:`g_Y(y)` is a rescaled Cauchy distribution with fixed mode :math:`x_0 \\in \\mathbb{R}`
+    and rescaled scaling parameter :math:`\\lambda \\in \\mathbb{R}_{>0}`, so that
+
+    .. math::
+        g_Y(y) = \\text{Cauchy}\\Big(y; x_0=\\mu_Y(X), \\lambda=\\big(\\theta_y \\cdot \\sigma_Y(X)\\big) \\Big) ,
+
+    where  :math:`\\theta_y` is the adaptive rescaling weight for a certain :math:`y`.
+
+    The GP-Cauchy utilizes a Gaussian process to obtain :math:`\\theta_y`, so that
+
+    .. math::
+        \\theta_y \\sim \\text{gp}(0, k) ,
+
+    where :math:`k` is the kernel function (for a more detailed description of the underlying Gaussian process, see
+    documentation of parent class :class:`netcal.regression.gp.AbstractGP`).
+
+    Parameters
+    ----------
+    n_inducing_points: int
+        Number of inducing points used to approximate the input space. These inducing points are also optimized.
+    n_random_samples: int
+        Number of random samples used to sample from the parameter distribution during optimization and inference.
+    n_epochs: int, default: 200
+        Number of optimization epochs.
+    batch_size: int, default: 256
+        Size of batches during optimization.
+    num_workers : int, optional, default: 0
+        Number of workers used for the dataloader.
+    lr: float, optional, default: 1e-2
+        Learning rate used for the Adam optimizer.
+    use_cuda: str or bool, optional, default: False
+        The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+        You can also pass a string "cuda:0", "cuda:1", etc. to specify the CUDA device.
+        If False, use CPU for optimization and inference.
+    jitter: float, optional, default: 1e-5
+        Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+        Gaussian process optimization.
+    name_prefix: str, optional, default: "gpcauchy"
+        Name prefix internally used in Pyro to distinguish between parameter stores.
+
+    References
+    ----------
+    .. [1] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+       "Distribution calibration for regression."
+       International Conference on Machine Learning. PMLR, 2019.
+       `Get source online <http://proceedings.mlr.press/v97/song19a/song19a.pdf>`__
+
+    .. [2] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+       "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+       European Conference on Computer Vision (ECCV) Workshops, 2022.
+       `Get source online <https://arxiv.org/pdf/2207.01242.pdf>`__
+
+    .. [3] Levi, Dan, et al.:
+       "Evaluating and calibrating uncertainty prediction in regression tasks."
+       arXiv preprint arXiv:1905.11659 (2019).
+       `Get source online <https://arxiv.org/pdf/1905.11659.pdf>`__
+
+    .. [4] Laves, Max-Heinrich, et al.:
+       "Well-calibrated regression uncertainty in medical imaging with deep learning."
+       Medical Imaging with Deep Learning. PMLR, 2020.
+       `Get source online <http://proceedings.mlr.press/v121/laves20a/laves20a.pdf>`__
+    """
+
+    precision = torch.float64
+
+    def __init__(
+            self,
+            n_inducing_points: int = 12,
+            n_random_samples: int = 128,
+            *,
+            name_prefix: str = "gpcauchy",
+            **kwargs
+    ):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        # call super constructor
+        super().__init__(
+            n_inducing_points=n_inducing_points,
+            n_random_samples=n_random_samples,
+            n_parameters=1,
+            correlations=False,
+            name_prefix=name_prefix,
+            **kwargs
+        )
+
+        # set likelihood and number of parameters per dim
+        self.likelihood = CauchyLikelihood
+
+        # do not use inv_gamma and delta to rescale sampled parameters before exponential
+        self._learn_scale_shift = False
+
+    # -------------------------------------------------------------------------
+    # Pyro + GPyTorch functions
+
+    def transform(self, X: Union[Iterable[np.ndarray], np.ndarray]) -> np.ndarray:
+        """
+        Transform the given stddev to a distribution-calibrated one using the input
+        mean and stddev as priors for the underlying Gaussian process. If correlation=True, perform either recalibration
+        of given covariance matrices or learn local correlations between dimensions if only standard deviations
+        are provided as input. In this case, the function returns covariance matrices for each input sample.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+
+        Returns
+        -------
+        np.ndarray of shape (n, d) or (n, d, d)
+            Recalibrated standard deviation for each sample in each dimension. If correlations=True, return
+            estimated/recalibrated covariance matrices for each input sample in n.
+        """
+
+        # get mean, variance and stddev of input
+        with torch.no_grad():
+            Xmean, Xvariance = self._get_input(X)
+
+        # concatenate mean and var of training points to a single pytorch tensor
+        n_dims = Xmean.shape[1]
+        X = torch.cat((Xmean, Xvariance), dim=1).to(dtype=self.precision)  # (n, 2*d)
+
+        # create PyTorch dataset and dataloader for optimization
+        dataset = TensorDataset(X)
+        dataloader = DataLoader(dataset, batch_size=self.batch_size, shuffle=False,
+                                num_workers=self.num_workers, pin_memory=True)
+
+        # set model in eval mode and use variational distribution for inference
+        self.eval()
+
+        # work in distinct pyro parameter store
+        with pyro.get_param_store().scope(self.pyro_scope):
+
+            # move self to the proper device and precision
+            self.to(device=self.device, dtype=self.precision)
+
+            # placeholder for final calibrated scale
+            calibrated_scale = []
+
+            # set model in eval mode and use variational distribution for inference
+            self.eval()
+            with torch.no_grad():
+                for batch_X, in dataloader:
+
+                    # move input to GPU
+                    batch_X = batch_X.to(device=self.device)
+
+                    # invoke GP model with learnt variational distribution - output is MultivariateNormal
+                    output = self(batch_X)
+
+                    # sample from the variational distribution
+                    function_samples = output(torch.Size([self.n_random_samples]))  # (r, n, d) or (r, n, (d+d^2)/2)
+
+                    # unsqueeze to distribute computation
+                    x_logvar = torch.unsqueeze(batch_X[:, n_dims:], dim=0)  # (1, n, d)
+                    x_std = torch.exp(x_logvar / 2.)
+
+                    cauchy_scale = x_std * torch.exp(function_samples)  # (r, n, d)
+                    cauchy_scale = torch.mean(cauchy_scale, dim=0)
+
+                    calibrated_scale.append(cauchy_scale.to(dtype=torch.float32, device="cpu"))
+
+            calibrated_scale = torch.cat(calibrated_scale, dim=0)
+
+        return calibrated_scale.numpy()
diff --git a/netcal/regression/gp/GPNormal.py b/netcal/regression/gp/GPNormal.py
new file mode 100644
index 0000000..9a84e6f
--- /dev/null
+++ b/netcal/regression/gp/GPNormal.py
@@ -0,0 +1,240 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Iterable, Union
+import numpy as np
+
+import torch
+from torch.utils.data import DataLoader, TensorDataset
+import pyro
+
+from netcal.regression.gp import AbstractGP
+from netcal.regression.gp.likelihood import ScaledNormalLikelihood, ScaledMultivariateNormalLikelihood
+
+
+class GPNormal(AbstractGP):
+    """
+    GP-Normal recalibration method for regression uncertainty calibration using a temperature scaling for the
+    variance of a normal distribution but using the Gaussian process (GP) parameter estimation to adaptively
+    obtain the scaling parameter for each input individually.
+    The temperature scaling for the variance [1]_, [2]_ seeks to preserve a parametric Gaussian distribution as
+    calibration output and aims to reach *variance calibration*. That is, matching the predicted variance with the
+    observed "error variance" aka mean squared error.
+    In contrast to the standard approach, the GP-Normal [3]_ uses a Gaussian process (GP) from [4]_ to flexibly obtain
+    a recalibration weight for each sample individually.
+    Thus, the GP-Normal seeks for a mixed form of **variance calibration** in a more flexible way towards
+    **distribution calibration** for Gaussians.
+    Note that this method does not change the mean but only the predicted variance.
+
+    **Mathematical background:** Let :math:`f_Y(y)` denote the uncalibrated probability density function (PDF),
+    targeting the probability distribution for :math:`Y`. In our case, the PDF is given as a Gaussian, so that
+    :math:`f_Y(y) = \\mathcal{N}\\big(y; \\mu_Y(X), \\sigma^2_Y(X)\\big)` with mean :math:`\\mu_Y(X)` and variance
+    :math:`\\sigma^2_Y(X)` obtained by a probabilistic regression model that depends on the input :math:`X`.
+    The calibrated PDF :math:`g_Y(y)` is the rescaled Gaussian with fixed mean and rescaled variance, so that
+
+    .. math::
+        g_Y(y) = \\mathcal{N}\\Big(y; \\mu_Y(X), \\big(\\theta_y \\cdot \\sigma_Y(X)\\big)^2\\Big) ,
+
+    where :math:`\\theta_y` is the adaptive rescaling weight for a certain :math:`y`.
+
+    In contrast to the standard temperature scaling approach by [1]_, [2]_, the GP-Normal utilizes a Gaussian process
+    to obtain :math:`\\theta_y`, so that
+
+    .. math::
+        \\theta_y \\sim \\text{gp}(0, k) ,
+
+    where :math:`k` is the kernel function (for a more detailed description of the underlying Gaussian process, see
+    documentation of parent class :class:`netcal.regression.gp.AbstractGP`).
+
+    Parameters
+    ----------
+    n_inducing_points: int
+        Number of inducing points used to approximate the input space. These inducing points are also optimized.
+    n_random_samples: int
+        Number of random samples used to sample from the parameter distribution during optimization and inference.
+    correlations : bool, default: False,
+        If True, perform covariance estimation recalibration if the input during fit/transform is given as multiple
+        independent distributions, e.g., by a mean and standard deviation vector for each sample.
+        If the input is given as a mean vector and a covariance matrix for each sample, this method applies
+        covariance recalibration by learning a recalibration weight for each entry.
+        If False, perform standard regression recalibration and output independent probability distributions.
+    n_epochs: int, default: 200
+        Number of optimization epochs.
+    batch_size: int, default: 256
+        Size of batches during optimization.
+    num_workers : int, optional, default: 0
+        Number of workers used for the dataloader.
+    lr: float, optional, default: 1e-2
+        Learning rate used for the Adam optimizer.
+    use_cuda: str or bool, optional, default: False
+        The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+        You can also pass a string "cuda:0", "cuda:1", etc. to specify the CUDA device.
+        If False, use CPU for optimization and inference.
+    jitter: float, optional, default: 1e-5
+        Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+        Gaussian process optimization.
+    name_prefix: str, optional, default: "gpnormal"
+        Name prefix internally used in Pyro to distinguish between parameter stores.
+
+    References
+    ----------
+    .. [1] Levi, Dan, et al.:
+       "Evaluating and calibrating uncertainty prediction in regression tasks."
+       arXiv preprint arXiv:1905.11659 (2019).
+       `Get source online <https://arxiv.org/pdf/1905.11659.pdf>`__
+
+    .. [2] Laves, Max-Heinrich, et al.:
+       "Well-calibrated regression uncertainty in medical imaging with deep learning."
+       Medical Imaging with Deep Learning. PMLR, 2020.
+       `Get source online <http://proceedings.mlr.press/v121/laves20a/laves20a.pdf>`__
+
+    .. [3] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+       "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+       European Conference on Computer Vision (ECCV) Workshops, 2022.
+       `Get source online <https://arxiv.org/pdf/2207.01242.pdf>`__
+
+    .. [4] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+       "Distribution calibration for regression."
+       International Conference on Machine Learning. PMLR, 2019.
+       `Get source online <http://proceedings.mlr.press/v97/song19a/song19a.pdf>`__
+    """
+
+    precision = torch.float64
+
+    def __init__(
+            self,
+            n_inducing_points: int = 12,
+            n_random_samples: int = 128,
+            *,
+            correlations: bool = False,
+            name_prefix: str = "gpnormal",
+            **kwargs
+    ):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        # call super constructor
+        super().__init__(
+            n_inducing_points=n_inducing_points,
+            n_random_samples=n_random_samples,
+            n_parameters=1,
+            correlations=correlations,
+            name_prefix=name_prefix,
+            **kwargs
+        )
+
+        # set likelihood and number of parameters per dim
+        if correlations:
+            self.likelihood = ScaledMultivariateNormalLikelihood
+        else:
+            self.likelihood = ScaledNormalLikelihood
+
+        # do not use inv_gamma and delta to rescale sampled parameters before exponential
+        self._learn_scale_shift = False
+
+    # -------------------------------------------------------------------------
+    # Pyro + GPyTorch functions
+
+    def transform(self, X: Union[Iterable[np.ndarray], np.ndarray]) -> np.ndarray:
+        """
+        Transform the given stddev to a distribution-calibrated one using the input
+        mean and stddev as priors for the underlying Gaussian process. If correlation=True, perform either recalibration
+        of given covariance matrices or learn local correlations between dimensions if only standard deviations
+        are provided as input. In this case, the function returns covariance matrices for each input sample.
+
+        Parameters
+        ----------
+        X : np.ndarray of shape (r, n, [d]) or Tuple of two np.ndarray, each of shape (n, [d])
+            Input data for calibration regression obtained by a model that performs inference with uncertainty.
+            Depending on the input format, this method handles the input differently:
+            If X is tuple of two NumPy arrays with shape (n, [d]) for each array, this method asserts the
+            first array as mean and the second one as the according stddev predictions with d dimensions (optionally).
+            If X is single NumPy array of shape (r, n), this methods asserts predictions obtained by a stochastic
+            inference model (e.g. network using MC dropout) with n samples and r stochastic forward passes. In this
+            case, the mean and stddev is computed automatically.
+
+        Returns
+        -------
+        np.ndarray of shape (n, d) or (n, d, d)
+            Recalibrated standard deviation for each sample in each dimension. If correlations=True, return
+            estimated/recalibrated covariance matrices for each input sample in n.
+        """
+
+        # get mean, variance and stddev of input
+        with torch.no_grad():
+            Xmean, Xvariance = self._get_input(X)
+
+        # concatenate mean and var of training points to a single pytorch tensor
+        n_dims = Xmean.shape[1]
+        X = torch.cat((Xmean, Xvariance), dim=1).to(dtype=self.precision)  # (n, 2*d)
+
+        # create PyTorch dataset and dataloader for optimization
+        dataset = TensorDataset(X)
+        dataloader = DataLoader(dataset, batch_size=self.batch_size, shuffle=False,
+                                num_workers=self.num_workers, pin_memory=True)
+
+        # set model in eval mode and use variational distribution for inference
+        self.eval()
+
+        # work in distinct pyro parameter store
+        with pyro.get_param_store().scope(self.pyro_scope):
+
+            # move self to the proper device and precision
+            self.to(device=self.device, dtype=self.precision)
+
+            # placeholder for final calibrated scale
+            calibrated_scale = []
+
+            # set model in eval mode and use variational distribution for inference
+            self.eval()
+            with torch.no_grad():
+                for batch_X, in dataloader:
+
+                    # move input to GPU
+                    batch_X = batch_X.to(device=self.device)
+
+                    # invoke GP model with learnt variational distribution - output is MultivariateNormal
+                    output = self(batch_X)
+
+                    # in the simple independent case, the output parameters are exponentiated and multiplied by
+                    # the baseline variance. Thus, we can use the mean of a LogNormal instead of sampling
+                    # for mean of LogNormal, only the diagonal of the covariance matrix is required
+                    if not self.correlations:
+
+                        mean, var = output.mean, output.variance
+                        logmean = torch.exp(mean + 0.5 * var)
+
+                        # perform variance scaling and store to global output
+                        x_var = torch.exp(batch_X[:, n_dims:])
+                        calibrated_var = x_var * logmean
+                        calibrated_scale.append(calibrated_var.to(dtype=torch.float32, device="cpu"))
+
+                    # in the more complex case of modelling covariances, we only use the exponential for the weights
+                    # for rescaling the diagonal variances. The correlations are not affected. Thus, use the computational
+                    # more expensive sampling to obtain a mean calibrated estimate.
+                    else:
+
+                        # sample from the variational distribution
+                        function_samples = output(torch.Size([self.n_random_samples]))  # (r, n, (d+d^2)/2)
+
+                        # unsqueeze to distribute computation
+                        x_var = torch.unsqueeze(batch_X[:, n_dims:], dim=0)  # (1, n, d) or (1, n, (d+d^2)/2)
+
+                        # rescale variance and introduce correlations. Finally, get mean of all covariance matrices.
+                        # positive-semidefiniteness is preserved under summing and multiplying by a positive constant
+                        covariance_matrix = ScaledMultivariateNormalLikelihood.rescale(x_var, function_samples)  # (r, n, d, d)
+                        covariance_matrix = torch.mean(covariance_matrix, dim=0)  # (n, d, d)
+
+                        calibrated_scale.append(covariance_matrix.to(dtype=torch.float32, device="cpu"))
+
+            # concatenate variances/covariances
+            calibrated_scale = torch.cat(calibrated_scale, dim=0)
+
+            # return standard deviations if 'correlations' is False
+            if not self.correlations:
+                calibrated_scale = torch.sqrt_(calibrated_scale)
+
+        return calibrated_scale.numpy()
diff --git a/netcal/regression/gp/README.md b/netcal/regression/gp/README.md
new file mode 100644
index 0000000..98b5db6
--- /dev/null
+++ b/netcal/regression/gp/README.md
@@ -0,0 +1,28 @@
+# Regression GP Calibration Package
+
+This package provides the framework for all Gaussian Process (GP) recalibration schemes.
+These are *GP-Beta* [2], GP-Normal [3], and GP-Cauchy [3]. The goal of regression calibration using a GP scheme is to achieve
+*distribution calibration*, i.e., to match the predicted moments (mean, variance) to the true observed ones.
+In contrast to *quantile calibration* [1], where only the marginal calibration is of interest, the *distribution calibration* [2] is more
+restrictive. It requires that the predicted moments should match the observed ones *given a certain probability
+distribution*. Therefore, the authors in [2] propose to use Gaussian process to estimate the recalibration
+parameters of a Beta calibration function locally (i.e., matching the observed moments of neighboring samples).
+The *GP-Normal* and the *GP-Cauchy* follow the same principle but return parametric output distributions after calibration.
+
+
+## References
+
+[1] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+   "Accurate uncertainties for deep learning using calibrated regression."
+   International Conference on Machine Learning. PMLR, 2018.
+   [Get source online](http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf)
+
+[2] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+   "Distribution calibration for regression."
+   International Conference on Machine Learning. PMLR, 2019.
+   [Get source online](http://proceedings.mlr.press/v97/song19a/song19a.pdf)
+
+[3] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+   "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+   ArXiv preprint arXiv:2207.01242, 2022.
+   [Get source online](https://arxiv.org/pdf/2207.01242.pdf)
\ No newline at end of file
diff --git a/netcal/regression/gp/__init__.py b/netcal/regression/gp/__init__.py
new file mode 100644
index 0000000..21c259c
--- /dev/null
+++ b/netcal/regression/gp/__init__.py
@@ -0,0 +1,37 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+"""
+.. include:: /../../netcal/regression/gp/README.md
+   :parser: myst_parser.sphinx_
+
+Available classes
+=================
+
+.. autosummary::
+   :toctree: _autosummary_regression_gp
+   :template: custom_class.rst
+
+   AbstractGP
+   GPBeta
+   GPNormal
+   GPCauchy
+
+Packages
+========
+
+.. autosummary::
+   :toctree: _autosummary_regression_gp_submodules
+
+   kernel
+   likelihood
+"""
+
+from .AbstractGP import AbstractGP
+from .GPBeta import GPBeta
+from .GPNormal import GPNormal
+from .GPCauchy import GPCauchy
diff --git a/netcal/regression/gp/kernel/GaussianRBFKernel.py b/netcal/regression/gp/kernel/GaussianRBFKernel.py
new file mode 100644
index 0000000..d57f093
--- /dev/null
+++ b/netcal/regression/gp/kernel/GaussianRBFKernel.py
@@ -0,0 +1,141 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+import numpy as np
+import torch
+import gpytorch
+
+
+class GaussianRBFKernel(gpytorch.kernels.Kernel):
+    """
+    Computes the Gaussian RBF kernel using input points defined as Gaussians.
+    This kernel has been proposed by [1]_.
+    Given input samples :math:`\\mathbf{x}_i, \\mathbf{x}_j \\in \\mathbb{R}^d` of dimension :math:`d` with
+    according covariances :math:`\\Sigma_i, \\Sigma_j \\in \\mathbb{R}^{d \\times d}` that define a
+    Gaussian for each input point. The kernel function is defined as
+
+    .. math::
+       k\\Big((\\mathbf{x}_i, \\Sigma_i), (\\mathbf{x}_j, \\Sigma_j)\\Big) = \\theta^d |\\Sigma_{ij}|^{-\\frac{1}{2}} \\exp \\Bigg( -\\frac{1}{2} (\\mathbf{x}_i-\\mathbf{x}_j)^\\top
+       \\Sigma_{ij}^{-1}(\\mathbf{x}_i-\\mathbf{x}_j)  \\Bigg) ,
+
+    with
+
+    .. math::
+       \\Sigma_{ij} = \\Sigma_i + \\Sigma_j + \\theta^2 \\mathbf{I} ,
+
+    where :math:`\\theta \\in \\mathbb{R}` is a lengthscale parameter. Since we're only using
+    independent normal distributions for each dimension, we only have diagonal covariance matrices.
+
+    References
+    ----------
+    .. [1] Song, L., Zhang, X., Smola, A., Gretton, A., & Schölkopf, B.:
+        "Tailoring density estimation via reproducing kernel moment matching."
+        In Proceedings of the 25th international conference on Machine learning (pp. 992-999), July 2008.
+        `Get source online <https://www.cs.uic.edu/~zhangx/pubDoc/xinhua_icml08.pdf>`__
+    """
+
+    has_lengthscale = True
+
+    def __init__(self, *args, cov: bool, **kwargs):
+        super().__init__(*args, **kwargs)
+        self.cov = cov
+
+    def forward(self, x1: torch.Tensor, x2: torch.Tensor, diag: bool = False, *args, **kwargs) -> torch.Tensor:
+        """
+        Computes the Gaussian moment-matching RBF kernel. Asserts both input variables as
+        2-D tensors holding the mean and variance matrices for each input point:
+        x1, x2 with shape (n, 2*d) and (m, 2*d), where n is number of samples in x1 and
+        m is the number of samples in x2, and d is number of feature dimensions.
+        Thus, mean of x1, x2 is given in (n, 0:d) and the variance in (n, d:).
+
+        Parameters
+        ----------
+        x1 : torch.Tensor of shape (n, 2*d)
+            First set of samples used for kernel computation consisting of mean and variance
+            for each input point.
+        x2 : torch.Tensor of shape (m, 2*d)
+            Second set of samples used for kernel computation consisting of mean and variance
+            for each input point.
+        diag : bool, optional, default: False
+            If True, return only the diagonal elements of the covariance matrix.
+
+        Returns
+        -------
+        torch.Tensor of shape (n, m)
+            Covariance kernel matrix for each input pair.
+        """
+
+        assert x1.ndim > 1, "GaussianRBFKernel: x1 must be at least 2-D with shape ([b], n, 2*d) " \
+                            "(cov=False) or ([b], n, d + (d^2+d)//2) (cov=True)"
+        assert x2.ndim > 1, "GaussianRBFKernel: x2 must be at least 2-D with shape ([b], n, 2*d) " \
+                            "(cov=False) or ([b], n, d + (d^2+d)//2) (cov=True)"
+
+        if self.cov:
+            # formula to reconstruct the true data dimension from mean + lower triangular cov shape
+            n_dims = int((np.sqrt(8 * x1.shape[-1] + 9) - 3) // 2)
+
+            # construct triangular lower matrices
+            tril_idx = torch.tril_indices(row=n_dims, col=n_dims, offset=0)
+            x1_var = torch.zeros(*x1.shape[:-1], n_dims, n_dims, dtype=x1.dtype, device=x1.device)  # ([b], n, d, d)
+            x2_var = torch.zeros(*x2.shape[:-1], n_dims, n_dims, dtype=x2.dtype, device=x2.device)  # ([b], n, d, d)
+
+            # insert parameters into lower triangular
+            x1_var[..., tril_idx[0], tril_idx[1]] = x1[..., n_dims:]
+            x2_var[..., tril_idx[0], tril_idx[1]] = x2[..., n_dims:]
+
+            # finally, reconstruct covariance matrices by LL^T computation
+            x1_var = torch.matmul(x1_var, x1_var.transpose(-2, -1))  # ([b], n, d, d)
+            x2_var = torch.matmul(x2_var, x2_var.transpose(-2, -1))  # ([b], n, d, d)
+
+            # construct sum over all covariance matrices
+            variances = x1_var[..., None, :, :] + x2_var[..., None, :, :, :] # ([b], n, m, d, d)
+
+            # add lengthscale parameter to diagonal
+            diagonal = torch.diagonal(variances, offset=0, dim1=-2, dim2=-1)
+            diagonal[:] = diagonal + torch.square(self.lengthscale)
+
+            # get inverse of covariance matrices
+            inv_cov = torch.linalg.inv(variances)  # ([b], n, m, d, d)
+
+            # get determinant of covariance matrices
+            determinant = torch.linalg.det(variances)  # ([b], n, m)
+
+        else:
+            n_dims = x1.shape[-1] // 2
+            x1_var = torch.exp(x1[..., n_dims:])  # ([b], n, d)
+            x2_var = torch.exp(x2[..., n_dims:])  # ([b], m, d)
+
+            # first, add all variances within a single batch and add squared lengthscale to each dimension
+            # the inverse covariance matrix is the inverse of the variances on the diagonal
+            variances = x1_var[..., None, :] + x2_var[..., None, :, :] + torch.square(self.lengthscale)  # ([b], n, m, d)
+            inv_cov = torch.diag_embed(1. / variances)  # ([b], n, m, d, d)
+
+            # since we only have a diagonal covariance matrix, take the product as the determinant
+            determinant = torch.prod(variances, dim=-1)  # ([b], n, m)
+
+        # get mean estimates
+        x1_loc = torch.unsqueeze(x1[..., :n_dims], dim=-1)  # ([b], n, d, 1)
+        x2_loc = torch.unsqueeze(x2[..., :n_dims], dim=-1)  # ([b], m, d, 1)
+
+        # compute mahalanobis distance
+        mean_diff = x1_loc[..., None, :, :] - x2_loc[..., None, :, :, :]  # ([b], n, m, d, 1)
+        mahalanobis = torch.matmul(
+            mean_diff.transpose(dim0=-1, dim1=-2),  # ([b], n, m, 1, d)
+            torch.matmul(inv_cov, mean_diff)  # ([b], n, m, d, 1)
+        )  # ([b], n, m, 1, 1)
+
+        # finally, put mahalanobis into exponential and squeeze the two last dims
+        exponent = torch.exp(-0.5 * mahalanobis)[..., 0, 0]  # ([b], n, m)
+        res = torch.pow(self.lengthscale, n_dims) * torch.div(exponent, torch.sqrt(determinant))  # ([b], n, m)
+
+        if not diag:
+            return res
+        else:
+            if torch.is_tensor(res):
+                return res.diagonal(dim1=-1, dim2=-2)
+            else:
+                return res.diag()  # For LazyTensor
diff --git a/netcal/regression/gp/kernel/README.md b/netcal/regression/gp/kernel/README.md
new file mode 100644
index 0000000..64cc4f4
--- /dev/null
+++ b/netcal/regression/gp/kernel/README.md
@@ -0,0 +1,3 @@
+# Kernels for GP
+
+Package with all custom definitions for the kernel functions that are used by the Gaussian process (GP) framework.
diff --git a/netcal/regression/gp/kernel/__init__.py b/netcal/regression/gp/kernel/__init__.py
new file mode 100644
index 0000000..6959a20
--- /dev/null
+++ b/netcal/regression/gp/kernel/__init__.py
@@ -0,0 +1,22 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+"""
+.. include:: /../../netcal/regression/gp/kernel/README.md
+   :parser: myst_parser.sphinx_
+
+Available classes
+=================
+
+.. autosummary::
+   :toctree: _autosummary_regression_gp_kernel
+   :template: custom_class.rst
+
+   GaussianRBFKernel
+"""
+
+from .GaussianRBFKernel import GaussianRBFKernel
diff --git a/netcal/regression/gp/likelihood/BetaLikelihood.py b/netcal/regression/gp/likelihood/BetaLikelihood.py
new file mode 100644
index 0000000..951d2ab
--- /dev/null
+++ b/netcal/regression/gp/likelihood/BetaLikelihood.py
@@ -0,0 +1,420 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Tuple, Union
+import numpy as np
+
+import torch
+import torch.nn.functional as F
+import pyro.distributions as dist
+
+
+class BetaLikelihood(dist.TorchDistribution):
+    """
+    Beta likelihood used to implement the basic functionality of the :class:`netcal.regression.gp.GPBeta`
+    recalibration method.
+    This function serves the standard beta calibration mapping for the cumulative distribution function (CDF) as well
+    as the derived beta link function for the recalibration of the probability density function (PDF).
+    Since the likelihood of the Gaussian process is calculated during model training using the PDF, this method
+    is required not only for the inference but also for the training of the :class:`netcal.regression.gp.GPBeta` method
+    [1]_.
+
+    **Mathematical background:** From the docstring of :class:`netcal.regression.gp.GPBeta`, we know that the GP-Beta
+    utilizes the beta calibration method [2]_ from confidence calibration (cf. :class:`netcal.scaling.BetaCalibration`)
+    for the recalibration of the CDF.
+    Let :math:`f_Y(y)` denote the uncalibrated probability density function (PDF), targeting the probability
+    distribution for :math:`Y`. Let :math:`\\tau_y \\in [0, 1]` denote a certain quantile on the uncalibrated CDF which
+    is denoted by :math:`\\tau_y = F_Y(y)`.
+    Furthermore, let :math:`g_Y(y)` and :math:`G_Y(y)` denote the recalibrated PDF and CDF, respectively.
+    The Beta calibration function :math:`\\mathbf{c}_\\beta(\\tau_y)` known from [2]_ is given by
+
+    .. math::
+        \\mathbf{c}_\\beta(\\tau_y) &= \\phi\\big( a \\log(\\tau_y) - b \\log(1-\\tau_y) + c \\big) \\\\
+        &= \\phi\\big( z(\\tau_y) \\big) ,
+
+    with recalibration parameters :math:`a,b \\in \\mathbb{R}_{>0}` and :math:`c \\in \\mathbb{R}`, and
+    :math:`\\phi(\\cdot)` as the sigmoid function [2]_.
+    In this case, we denote the logit of the beta calibration function :math:`\\mathbf{c}_\\beta(\\tau_y)` by
+
+    .. math::
+        z(\\tau_y) = a \\log(\\tau_y) - b \\log(1-\\tau_y) + c .
+
+    The beta calibration method serves as a mapping from the uncalibrated CDF to the calibrated one, so that
+
+    .. math::
+        G_Y(y) = \\mathbf{c}_\\beta\\big( F_Y(y) \\big)
+
+    holds. The PDF is recalibrated using the beta link function :math:`\\mathbf{r}_\\beta(\\tau_y)` [1]_ by
+
+    .. math::
+        g_Y(y) = \\frac{\\partial \\mathbf{c}_\\beta}{\\partial y}
+        = \\frac{\\partial \\mathbf{c}_\\beta}{\\partial \\tau_y} \\frac{\\partial \\tau_y}{\\partial y}
+        = \\mathbf{r}_\\beta(\\tau_y) f_Y(y) ,
+
+    where the beta link function is given by
+
+    .. math::
+        \\mathbf{r}_\\beta(\\tau_y) = \\Bigg(\\frac{a}{\\tau_y} + \\frac{b}{1-\\tau_y} \\Bigg)
+        \\mathbf{c}_\\beta(\\tau_y) \\big(1 - \\mathbf{c}_\\beta(\\tau_y)\\big) .
+
+    The recalibration parameters :math:`a,b` and :math:`c` are not directly infered by the GP but rather use the
+    underlying function parameters :math:`w_a, w_b, w_c \\in \\mathbb{R}`, so that
+
+    .. math::
+       a &= \\exp(\\gamma_a^{-1} w_a + \\delta_a) \\\\
+       b &= \\exp(\\gamma_b^{-1} w_b + \\delta_b) \\\\
+       c &= \\gamma_c^{-1} w_c + \\delta_c
+
+    are given as the beta distribution parameters to guarantee :math:`a, b > 0`.
+    During optimization, we need the log of the link function. We use a numerical more stable version:
+
+    .. math::
+       \\log\\big(\\mathbf{r}_\\beta(\\tau_y)\\big) = \\log \\Bigg(\\frac{a}{\\tau_y} + \\frac{b}{1-\\tau_y} \\Bigg) +
+       \\log \\Big( \\mathbf{c}_\\beta(\\tau_y) \\big(1 - \\mathbf{c}_\\beta(\\tau_y)\\big) \\Big)
+
+    The first part can be rewritten as:
+
+    .. math::
+       & \\log \\Bigg(\\frac{a}{\\tau_y} + \\frac{b}{1-\\tau_y} \\Bigg) \\\\
+       &= \\log \\Bigg( \\exp \\Big( \\log(a) - \\log(\\tau_y) \\Big) + \\exp \\Big( \\log(b) - \\log(1-\\tau_y) \\Big) \\Bigg) \\\\
+       &= \\log \\Bigg( \\exp \\Big( \\gamma_a^{-1} w_a + \\delta_a - \\log(\\tau_y) \\Big) + \\exp \\Big( \\gamma_b^{-1} w_b + \\delta_b - \\log(1-\\tau_y) \\Big) \\Bigg) \\\\
+       &= \\text{logsumexp} \\Bigg[ \\Big( \\gamma_a^{-1} w_a + \\delta_a - \\log(\\tau_y) \\Big), \\Big( \\gamma_b^{-1} w_b + \\delta_b - \\log(1-\\tau_y) \\Big) \\Bigg]
+
+    where :math:`\\text{logsumexp}` is a numerical stable version of :math:`\\log \\Big( \\sum_x \\exp(x) \\Big)` in PyTorch.
+    In addition, we can also simplify the expression for the log of the sigmoid functions that are used within
+    the computation of :math:`\\mathbf{c}_\\beta(\\tau_y)` by
+
+
+    .. math::
+       \\log(\\phi(x)) &= -\\log \\Big( \\exp(-x) + 1 \\Big), \\\\
+       \\log(1-\\phi(x)) &= -\\log \\Big( \\exp(x) + 1 \\Big)
+
+    which can also be expressed in terms of PyTorch's numerical more stable :math:`\\text{softplus}`
+    function :math:`\\log \\Big( \\exp(x) + 1 \\Big)`. Thus, the log of the link function can be expressed as
+
+    .. math::
+       \\log(r_\\beta(\\tau_y)) = &\\text{logsumexp} \\Bigg[ \\Big( \\gamma_a^{-1} w_a + \\delta_a - \\log(\\tau_y) \\Big),
+       \\Big( \\gamma_b^{-1} w_b + \\delta_b - \\log(1-\\tau_y) \\Big) \\Bigg] \\\\
+       &- \\Big(\\text{softplus}\\big(-z(x)\\big) + \\text{softplus}\\big(z(x)\\big)\\Big)
+
+    Parameters
+    ----------
+    loc: torch.Tensor, shape: ([[1], 1], n, d)
+        Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+        This class also supports broadcasting of the calculations to t sampling points (defining the non-parametric
+        PDF/CDF, first dim) and r random samples (second dim).
+    logvar: torch.Tensor, shape: ([[1], 1], n, d)
+        Log of the variance vector of the uncalibrated (Gaussian) probability distribution with n samples and d
+        dimensions. This class also supports broadcasting of the calculations to t sampling points (defining the
+        non-parametric PDF/CDF, first dim) and r random samples (second dim).
+    parameters: torch.Tensor, shape: ([[1], r], n, p*d)
+        Rescaling parameters of the beta link function **before applying the exponential** (for parameters :math:`a, b`)
+        with n samples d dimensions, r random samples and p as the number of parameters (p=3 in this case).
+
+    References
+    ----------
+    .. [1] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+       "Distribution calibration for regression."
+       International Conference on Machine Learning (pp. 5897-5906), 2019.
+       `Get source online <http://proceedings.mlr.press/v97/song19a/song19a.pdf>`__
+
+    .. [2] Kull, Meelis, Telmo Silva Filho, and Peter Flach:
+       "Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers"
+       Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
+       `Get source online <http://proceedings.mlr.press/v54/kull17a/kull17a.pdf>`__
+    """
+
+    def __init__(self, loc: torch.Tensor, logvar: torch.Tensor, parameters: torch.Tensor):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        # call super constructor with right batch_shape (necessary for Pyro) and save parameters as member variable
+        super().__init__(batch_shape=parameters.shape[:-1] + loc.shape[-1:], validate_args=False)
+        self.parameters = parameters
+
+        # recover the variance and initialize a normal distribution that reflects the uncalibrated distribution
+        var = torch.exp(logvar)
+        self._normal = dist.Normal(loc, torch.sqrt(var))
+
+    def log_prob(self, value: torch.Tensor) -> torch.Tensor:
+        """
+        Calculate the log-density at the points given by 'value' using the underlying uncalibrated distribution
+        :math:`f_Y(y)` that is rescaled by the calibration parameters.
+        This function implements the beta link function :math:`\\mathbf{r}_\\beta(\\tau_y)` and provides the
+        log-likelihood for the recalibrated PDF
+
+        .. math::
+            \\log\\big(g_Y(y)\\big) = \\log\\big(\\mathbf{r}_\\beta(\\tau_y) f_Y(y) \\big) .
+
+        Parameters
+        ----------
+        value : torch.Tensor, shape: ([[t], 1], n, d)
+            Points at which to calculate the log-likelihood with n samples and d dimensions.
+            The dimension t represents the points that define the non-parametric PDF/CDF on the x-axis.
+            The intermediate (second) dim is required when using multiple stochastic forward passes for
+            the rescaling parameters.
+
+        Returns
+        -------
+        torch.Tensor, shape: ([[t], r], n, d)
+            Log-likelihood of the recalibrated non-parametric distribution with
+            t points that define the non-parametric PDF/CDF on the x-axis, r stochastic forward passes for the rescaling
+            parameters, n samples and d dimensions.
+        """
+
+        # get cumulative and log_density for input
+        with torch.no_grad():
+            cumulative = self._normal.cdf(value)  # ([[t], 1], n, d)
+            log_density = self._normal.log_prob(value)  # ([[t], 1], n, d)
+
+            # prevent inf or NaN during log for cumulatives that ran into saturation {0, 1}
+            torch.clamp(cumulative, min=torch.finfo(cumulative.dtype).eps, max=1.-torch.finfo(cumulative.dtype).eps, out=cumulative)
+
+        param_a = self.parameters[..., 0::3]  # ([[1], r], n, d)
+        param_b = self.parameters[..., 1::3]  # ([[1], r], n, d)
+
+        # numerical stable variant of log
+        log_derivative_logit = torch.logsumexp(
+            torch.stack((
+                param_a - torch.log(cumulative),
+                param_b - torch.log(1. - cumulative),
+            ), dim=-1),  # ([[t], r], n, d, 2)
+            dim=-1
+        )  # ([[t], r], n, d)
+
+        # get logit of calibrated cumulative
+        logit = self._get_beta_logit(cumulative)
+
+        # log(sigmoid(x)) is -softplus(-x)
+        # log(1-sigmoid(x)) is -softplus(x)
+        log_derivative_sigmoid = -F.softplus(-logit) - F.softplus(logit)  # ([[t], r], n, d)
+
+        log_link = log_derivative_logit + log_derivative_sigmoid  # ([[t], r], n, d)
+
+        # broadcast log_density to sample dimension
+        linklikelihood = log_link + log_density  # ([[t], r], n, d)
+
+        return linklikelihood
+
+    def cdf(self, t: Union[int, torch.Tensor]) -> Tuple[torch.Tensor, torch.Tensor]:
+        """
+        Calculate cumulative distribution function (CDF) at the points given by 't' using
+        the underlying uncalibrated cumulative :math:`F_Y(y)` that is rescaled by the calibration parameters.
+        This function implements the beta calibration function :math:`\\mathbf{c}_\\beta(\\tau_y)` and provides the
+        recalibrated CDF
+
+        .. math::
+            G_Y(y) = \\mathbf{c}_\\beta\\big(F_y(y)\\big).
+
+        Furthermore, this method provides the sampling points to properly represent the x-values of the recalibrated
+        CDF. To obtain the relevant points (where the CDF is >>0 and <<1), we use an iterative approach to approximate
+        the most relevant x-values of the CDF.
+
+        Parameters
+        ----------
+        t : torch.Tensor, shape: ([[t], r], n, d)
+            Points at which to calculate the CDF with n samples and d dimensions.
+            The dimension t represents the points that define the non-parametric PDF/CDF on the x-axis.
+            The dimension r is required when using multiple stochastic forward passes for
+            the rescaling parameters.
+
+        Returns
+        -------
+        Tuple of torch.Tensor, both of shape: ([[t], r], n, d)
+            X- and y-values of the recalibrated cumulative distribution function (CDF) with
+            t points that define the non-parametric PDF/CDF on the x-axis, r stochastic forward passes for the rescaling
+            parameters, n samples and d dimensions.
+        """
+
+        # target quantile determines the points at which the CDF is not relevant any more
+        target_quantile = 1e-7
+
+        # max_iter is the maximum amount of iterations used to refine the sampling points
+        max_iter = 5
+
+        # if t is int, use t sampling points to describe the output distribution
+        if isinstance(t, int):
+
+            # get base boundaries by the inverse cumulative function
+            lower_bound_0 = self._normal.icdf(torch.tensor(target_quantile))  # ([[1], 1], n, d)
+            upper_bound_0 = self._normal.icdf(torch.tensor(1. - target_quantile))  # ([[1], 1], n, d)
+
+            # use the base quantile width 4 times (in each direction) to rescale the boundaries
+            width_0 = upper_bound_0 - lower_bound_0
+            lower_bound = lower_bound_0 - 4 * width_0
+            upper_bound = upper_bound_0 + 4 * width_0
+
+            # generate initial guess for the sampling points
+            sampling_points, cumulative = self._generate_sampling_points(
+                t, lower_bound.cpu().numpy(), upper_bound.cpu().numpy()
+            )
+
+            # use iterative approach to refine the sampling points
+            for it in range(max_iter + 1):
+                logit = self._get_beta_logit(cumulative)
+                calibrated = torch.sigmoid(logit)
+
+                # reached end of refinement loop
+                if it == max_iter:
+                    break
+
+                # copy back to numpy as we use the 'flip' function in the following
+                # in contrast to PyTorch, NumPy returns a view instead of making a copy of the data
+                calibrated = calibrated.cpu().numpy()  # # ([[t], r], n, d)
+
+                # get the indices where the desired relevance level is reached
+                # move the indices to the outer point (useful especially for very low resolutions) by decreasing
+                # lb - 1 and increasing ub + 1
+                lb_idx = np.argmax(calibrated >= target_quantile, axis=0) - 1  # ([r], n, d)
+                ub_idx = t - np.argmax(np.flip(calibrated, axis=0) < (1 - target_quantile), axis=0)  # ([r], n, d)
+
+                # depending on the random samples, use the minimum/maximum boundary idx
+                lb_idx = np.min(lb_idx, axis=0, keepdims=True)  # (1, n, d)
+                ub_idx = np.max(ub_idx, axis=0, keepdims=True)  # (1, n, d)
+
+                # avoid out-of-bounds indices
+                lb_idx[lb_idx < 0] = 0
+                ub_idx[ub_idx >= t] = t - 1
+
+                # take indices along first axis to get the right x-scores for the cumulative
+                lower_bound = np.take_along_axis(
+                    sampling_points.numpy(),
+                    indices=lb_idx[None, ...],
+                    axis=0,
+                )  # ([[1], r], n, d)
+
+                upper_bound = np.take_along_axis(
+                    sampling_points.numpy(),
+                    indices=ub_idx[None, ...],
+                    axis=0,
+                )  # ([[1], r], n, d)
+
+                # generate new set of sampling points
+                sampling_points, cumulative = self._generate_sampling_points(t, lower_bound, upper_bound)
+
+        # if t is np.ndarray, use this points as the base for the calibrated output distribution
+        elif isinstance(t, torch.Tensor):
+
+            sampling_points = t
+
+            # get cumulative and log_density for input
+            with torch.no_grad():
+                cumulative = self._normal.cdf(sampling_points)  # ([[t], 1], n, d)
+                torch.clamp(cumulative, min=torch.finfo(cumulative.dtype).eps,
+                            max=1. - torch.finfo(cumulative.dtype).eps, out=cumulative)
+
+            logit = self._get_beta_logit(cumulative)
+            calibrated = torch.sigmoid(logit)
+
+        else:
+            raise AttributeError("Parameter \'t\' must be either of type int or np.ndarray.")
+
+        # finally, move sampling points to the same device
+        sampling_points = sampling_points.to(device=calibrated.device)
+        return sampling_points, calibrated
+
+    def _generate_sampling_points(
+            self,
+            t: int,
+            lower_bound: np.ndarray,
+            upper_bound: np.ndarray
+    ) -> Tuple[torch.Tensor, torch.Tensor]:
+        """
+        Generate the sampling points between lower and upper bound.
+        This function is iteratively called to refine the set of sampling points to get a meaningful representation
+        of the recalibrated non-parametric distribution.
+
+        Parameters
+        ----------
+        t : int
+            Number of sampling points that define a non-parametric PDF/CDF on the x-axis.
+        lower_bound : np.ndarray, shape: ([[1], r], n, d)
+            Lower bound of the sampling points with r random samples, n data points and d dimensions.
+        upper_bound : np.ndarray, shape: ([[1], r], n, d)
+            Upper bound of the sampling points with r random samples, n data points and d dimensions.
+
+        Returns
+        -------
+        Tuple of torch.Tensor, both of shape ([[t], r], n, d)
+            X- and y-values of the recalibrated cumulative distribution function (CDF) with
+            t points that define the non-parametric PDF/CDF on the x-axis, r stochastic forward passes for the rescaling
+            parameters, n samples and d dimensions.
+        """
+
+        # use NumPy's linspace as it is capable of arrays as start- and endpoints.
+        sampling_points = torch.from_numpy(
+            np.linspace(lower_bound, upper_bound, t, axis=0)
+        )  # ([[t, 1], r], n, d)
+
+        # remove the unnecessary additional dimension
+        sampling_points = torch.squeeze(
+            sampling_points,
+            dim=1
+        ) if sampling_points.ndim == 5 else sampling_points  # ([[t], r], n, d)
+
+        # bring sampling points to the target precision
+        sampling_points = sampling_points.to(dtype=self._normal.loc.dtype)
+
+        # cumulative is required to examine the y-scores of the CDF to determine the new boundaries
+        cumulative = self._normal.cdf(
+            sampling_points.to(device=self._normal.loc.device)
+        )  # ([[t], r], n, d)
+
+        # clamp cumulative to be in open interval (0, 1)
+        torch.clamp(
+            cumulative,
+            min=torch.finfo(cumulative.dtype).eps,
+            max=1. - torch.finfo(cumulative.dtype).eps,
+            out=cumulative
+        )
+
+        return sampling_points, cumulative
+
+    def _get_beta_logit(self, cumulative: torch.Tensor) -> torch.Tensor:
+        """
+        Calculate the logit of the beta calibration function at the points given by "cumulative" using the
+        recalibration parameters.
+        The logit :math:`z(\\tau_y)` of the beta calibration function for a quantile :math:`\\tau_y \\in [0, 1]` is
+        defined by
+
+        .. math::
+            z(\\tau_y) = a \\log(\\tau_y) - b \\log(1-\\tau_y) + c .
+
+        Parameters
+        ----------
+        cumulative : torch.Tensor, shape: ([[t], 1], n, d)
+            Y-values of the (uncalibrated) CDF in :math:`[0, 1]` with t points that define the non-parametric PDF/CDF,
+            n samples and d dimensions.
+
+        Returns
+        -------
+        torch.Tensor, shape: ([[t], r], n, d)
+            Logit of the beta calibration function with t points that define the non-parametric PDF/CDF,
+            r stochastic forward passes for the rescaling parameters, n samples and d dimensions.
+        """
+
+        param_a = self.parameters[..., 0::3]  # ([[1], r], n, d)
+        param_b = self.parameters[..., 1::3]  # ([[1], r], n, d)
+        param_c = self.parameters[..., 2::3]  # ([[1], r], n, d)
+
+        # call exponential function on the first two parameters
+        parameters = torch.stack((
+            param_a.exp(),
+            param_b.exp(),
+            param_c),
+            dim=-1
+        )  # ([[1], r], n, d, 3)
+
+        # construct input array
+        input = torch.stack(
+            (torch.log(cumulative), -torch.log(1. - cumulative), torch.ones_like(cumulative)),
+            dim=-1
+        )  # ([[t], 1], n, d, 3)
+
+        # get calibrated cumulative
+        logit = torch.sum(parameters * input, dim=-1)  # ([[t], r], n, d)
+
+        return logit
diff --git a/netcal/regression/gp/likelihood/CauchyLikelihood.py b/netcal/regression/gp/likelihood/CauchyLikelihood.py
new file mode 100644
index 0000000..74bc81d
--- /dev/null
+++ b/netcal/regression/gp/likelihood/CauchyLikelihood.py
@@ -0,0 +1,64 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+import torch
+import pyro.distributions as dist
+
+
+class CauchyLikelihood(dist.Cauchy):
+    """
+    Standard likelihood of a Cauchy distribution used within :class:`netcal.regression.gp.GPCauchy`
+    where the scaling parameter :math:`\\lambda` is obtained by
+    combining the uncalibrated standard deviation with a rescaling parameter obtained by a Gaussian process.
+    This method provides the likelihood for the :class:`netcal.regression.gp.GPCauchy` by applying a rescaling
+    of the uncalibrated input standard deviation by a recalibration parameter :math:`\\theta_y` [1]_, so that the
+    recalibrated probability density function (PDF) :math:`g_Y(y)` is given by
+
+    .. math::
+        g_Y(y) = \\text{Cauchy}\\Big(y; x_0=\\mu_Y(X), \\lambda=\\big(\\theta_y \\cdot \\sigma_Y(X)\\big)\\Big)
+
+    with :math:`\\mu_Y(X) \\in \\mathbb{R}` and :math:`\\sigma_Y(X) \\in \\mathbb{R}_{>0}` as the uncalibrated
+    mean and standard deviation, respectively, and :math:`x_0` as the mode of the Cauchy which is approximated by
+    the uncalibrated mean estimate.
+
+    Parameters
+    ----------
+    loc: torch.Tensor, shape: ([1], n, d)
+        Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+        This class also supports broadcasting of the calculations to r random samples (first dim).
+    logvar: torch.Tensor, shape: ([1], n, d)
+        Log of the variance vector of the uncalibrated (Gaussian) probability distribution with n samples and d
+        dimensions. This class also supports broadcasting of the calculations to r random samples (first dim).
+    parameters: torch.Tensor, shape: ([r], n, d)
+        Rescaling parameter of the GP-Cauchy with n samples d dimensions and r random samples.
+
+    References
+    ----------
+    .. [1] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+       "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+       European Conference on Computer Vision (ECCV) Workshops, 2022.
+       `Get source online <https://arxiv.org/pdf/2207.01242.pdf>`__
+    """
+
+    def __init__(self, loc: torch.Tensor, logvar: torch.Tensor, parameters: torch.Tensor):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        scale = torch.exp(logvar / 2.)  # is stddev sqrt(exp(logvar)) = exp(logvar / 2.)
+        transformed_scale = scale * parameters.exp()
+        super().__init__(loc, transformed_scale, validate_args=False)
+
+    def expand(self, batch_shape, _instance=None):
+        """ Expand-method. Reimplementation required when sub-classing the Cauchy distribution of Pyro. """
+
+        new = self._get_checked_instance(CauchyLikelihood, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.loc = self.loc.expand(batch_shape)
+        new.scale = self.scale.expand(batch_shape)
+        super(CauchyLikelihood, new).__init__(new.loc, new.scale, validate_args=False)
+        new._validate_args = self._validate_args
+
+        return new
diff --git a/netcal/regression/gp/likelihood/README.md b/netcal/regression/gp/likelihood/README.md
new file mode 100644
index 0000000..dfffd4d
--- /dev/null
+++ b/netcal/regression/gp/likelihood/README.md
@@ -0,0 +1,4 @@
+# Likelihoods for GP
+
+Package with all custom definitions for the likelihood functions that are used by the Gaussian process (GP) framework
+during training and inference.
\ No newline at end of file
diff --git a/netcal/regression/gp/likelihood/ScaledMultivariateNormalLikelihood.py b/netcal/regression/gp/likelihood/ScaledMultivariateNormalLikelihood.py
new file mode 100644
index 0000000..f0c891d
--- /dev/null
+++ b/netcal/regression/gp/likelihood/ScaledMultivariateNormalLikelihood.py
@@ -0,0 +1,172 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+import numpy as np
+import torch
+import pyro.distributions as dist
+
+
+class ScaledMultivariateNormalLikelihood(dist.MultivariateNormal):
+    """
+    Standard likelihood of a **multivariate** normal distribution used within :class:`netcal.regression.gp.GPNormal`
+    for *covariance estimation* and *covariance recalibration*.
+    This method provides the multivariate likelihood for the :class:`netcal.regression.gp.GPNormal` when
+    "correlations=True".
+    The input to this class is given as the LDL* decomposed (uncalibrated) covariance matrix
+    :math:`\\boldsymbol{\\Sigma}_{\\mathbf{Y}}(X) = \\mathbf{L}\\mathbf{D}\\mathbf{L}^{\\top}`.
+    Afterwards, this method applies a rescaling of the uncalibrated :math:`\\mathbf{L} \\in \\mathbb{R}^{d \\times d}`
+    and :math:`\\mathbf{D} \\in \\mathbb{R}^{d \\times d}` matrices by the
+    recalibration parameters :math:`\\theta_L \\in \\mathbb{R}^{d \\times d}` and
+    :math:`\\theta_D \\in \\mathbb{R}^{d \\times d}_{>0}` [1]_, so that the recalibrated
+    probability density function (PDF) :math:`g_{\\mathbf{Y}}(\\mathbf{y})` is given by
+
+    .. math::
+        g_{\\mathbf{Y}}(\\mathbf{y}) = \\mathcal{N}\\Big(\\mathbf{y}; \\boldsymbol{\\mu}_{\\mathbf{Y}}(X),
+        (\\theta_L \\odot \\mathbf{L})(\\theta_D \\odot \\mathbf{D})(\\theta_L \\odot \\mathbf{L})^{\\top} \\big) \\Big)
+
+    with :math:`\\boldsymbol{\\mu}_{\\mathbf{Y}}(X) \\in \\mathbb{R}` as the uncalibrated mean and :math:`\\odot` as
+    the element-wise matrix multiplication operator.
+
+    Parameters
+    ----------
+    loc: torch.Tensor, shape: ([1], n, d)
+        Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+        This class also supports broadcasting of the calculations to r random samples (first dim).
+    var: torch.Tensor, shape: ([1], n, (d^2+d) // 2)
+        LDL* decomposed covariance matrix (compressed form) of the uncalibrated (Gaussian) probability distribution
+        with n samples and d dimensions. This class also supports broadcasting of the calculations to r random samples
+        (first dim).
+    parameters: torch.Tensor, shape: ([r], n, (d+d^2) // 2)
+        Rescaling parameter of the GP-Normal for the decomposed covariance matrices with n samples d dimensions
+        and r random samples.
+
+    References
+    ----------
+    .. [1] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+       "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+       European Conference on Computer Vision (ECCV) Workshops, 2022.
+       `Get source online <https://arxiv.org/pdf/2207.01242.pdf>`__
+    """
+
+    def __init__(self, loc: torch.Tensor, var: torch.Tensor, parameters: torch.Tensor):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        # reconstruct and rescale the given input covariance matrices
+        covariance_matrix = self.rescale(var, parameters)
+
+        super().__init__(loc=loc, covariance_matrix=covariance_matrix, validate_args=False)
+
+    @staticmethod
+    def reconstruct(decomposed: torch.Tensor):
+        """
+        Reconstruct the lower :math:`\\mathbf{L}` and diagonal :math:`\\mathbf{D}` matrices from the flat input vector
+        given by "decomposed" since Pyro does not support an additional dimension internally.
+
+        Parameters
+        ----------
+        decomposed: torch.Tensor, shape: ([1], n, (d^2+d) // 2)
+            LDL* decomposed covariance matrix (compressed form) of the uncalibrated (Gaussian) probability distribution
+            with n samples and d dimensions.
+
+        Returns
+        -------
+        Tuple of torch.Tensor with (L, D)
+            Reconstructed lower triangular matrix and diagonal vector of the decomposed input covariance matrix.
+            L has shape ([1], n, d, d) and is lower triangualr.
+            D has shape ([1], n, d) and holds the diagonal elements.
+        """
+
+        # decomposed has shape (..., (d^2+d)//2)
+        # formula to reconstruct the true data dimension from mean + lower triangular cov shape
+        n_dims = int((np.sqrt(8 * decomposed.shape[-1] + 1) - 1) // 2)
+
+        # use LDL* decomposition but reconstruct input var from LL*
+        # get lower triangular indices (L matrix)
+        tril_idx = torch.tril_indices(row=n_dims, col=n_dims, offset=0)
+
+        # initialize identity matrix and place covariance estimates in the lower off-diagonal
+        lower = torch.zeros(
+            *decomposed.shape[:-1], n_dims, n_dims,
+            dtype=decomposed.dtype,
+            device=decomposed.device
+        )  # (..., d, d)
+
+        lower[..., tril_idx[0], tril_idx[1]] = decomposed
+        diagonal_view = torch.diagonal(lower, dim1=-2, dim2=-1)  # (..., d)
+        diagonal = diagonal_view.clone()
+
+        # since diagonal is simply a view on the lower, place ones inplace
+        diagonal_view[:] = 1.
+
+        return lower, diagonal
+
+    @staticmethod
+    def rescale(var: torch.Tensor, parameters: torch.Tensor):
+        """
+        This method applies the rescaling of the LDL* decomposed covariance matrices by computing
+        :math:`\\theta_L \\odot \\mathbf{L}` and :math:`\\theta_D \\odot \\mathbf{D}`.
+        Finally, the covariance matrix is recovered and returned.
+
+        Parameters
+        ----------
+        var: torch.Tensor, shape: ([1], n, (d^2+d) // 2)
+            LDL* decomposed covariance matrix (compressed form) of the uncalibrated (Gaussian) probability distribution
+            with n samples and d dimensions.
+        parameters: torch.Tensor, shape: ([r], n, (d+d^2) // 2)
+            Rescaling parameter of the GP-Normal for the decomposed covariance matrices with n samples d dimensions
+            and r random samples.
+
+        Returns
+        -------
+        torch.Tensor of shape ([r], n, d, d)
+            Rescaled covariance matrices with r stochastic forward passes for the rescaling
+            parameters, n samples and d dimensions.
+        """
+
+        lower_cov, diagonal_var = ScaledMultivariateNormalLikelihood.reconstruct(var)
+        lower_scale, diagonal_scale = ScaledMultivariateNormalLikelihood.reconstruct(parameters)
+
+        # diagonal var returns the standard devs on the diagonal
+        # use square method to reconstruct variances
+        diagonal_var = torch.square(diagonal_var)
+
+        # use exponential on diagonal variance scaling parameters to guarantee positive estimates
+        diagonal_scale = torch.exp(diagonal_scale)
+
+        # perform element-wise multiplication
+        lower_scale = lower_scale * lower_cov  # ([r], n, d, d)
+
+        # rescale diagonal variances
+        diagonal_scale = diagonal_scale * diagonal_var  # ([r], n, d)
+        diagonal_scale = torch.diag_embed(diagonal_scale)  # ([r], n, d, d)
+
+        # construct covariance matrix using LDL*
+        covariance_matrix = lower_scale @ diagonal_scale @ torch.transpose(lower_scale, dim0=-2, dim1=-1)  # ([r], n, d, d)
+
+        return covariance_matrix
+
+    def expand(self, batch_shape, _instance=None):
+        """ Expand-method. Reimplementation required when sub-classing the MultivariateNormal distribution of Pyro. """
+
+        new = self._get_checked_instance(ScaledMultivariateNormalLikelihood, _instance)
+        batch_shape = torch.Size(batch_shape)
+        loc_shape = batch_shape + self.event_shape
+        cov_shape = batch_shape + self.event_shape + self.event_shape
+        new.loc = self.loc.expand(loc_shape)
+        new._unbroadcasted_scale_tril = self._unbroadcasted_scale_tril
+        if 'covariance_matrix' in self.__dict__:
+            new.covariance_matrix = self.covariance_matrix.expand(cov_shape)
+            super(ScaledMultivariateNormalLikelihood, new).__init__(loc=new.loc, covariance_matrix=new.covariance_matrix, validate_args=False)
+        if 'scale_tril' in self.__dict__:
+            new.scale_tril = self.scale_tril.expand(cov_shape)
+            super(ScaledMultivariateNormalLikelihood, new).__init__(loc=new.loc, scale_tril=new.scale_tril, validate_args=False)
+        if 'precision_matrix' in self.__dict__:
+            new.precision_matrix = self.precision_matrix.expand(cov_shape)
+            super(ScaledMultivariateNormalLikelihood, new).__init__(loc=new.loc, precision_matrix=new.precision_matrix, validate_args=False)
+
+        new._validate_args = self._validate_args
+        return new
diff --git a/netcal/regression/gp/likelihood/ScaledNormalLikelihood.py b/netcal/regression/gp/likelihood/ScaledNormalLikelihood.py
new file mode 100644
index 0000000..ffddecf
--- /dev/null
+++ b/netcal/regression/gp/likelihood/ScaledNormalLikelihood.py
@@ -0,0 +1,62 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+import torch
+import pyro.distributions as dist
+
+
+class ScaledNormalLikelihood(dist.Normal):
+    """
+    Standard likelihood of a normal distribution used within :class:`netcal.regression.gp.GPNormal`
+    with additional rescaling parameters for the variance.
+    This method provides the likelihood for the :class:`netcal.regression.gp.GPNormal` by applying a rescaling
+    of the uncalibrated input variance by a recalibration parameter :math:`\\theta_y` [1]_, so that the recalibrated
+    probability density function (PDF) :math:`g_Y(y)` is given by
+
+    .. math::
+        g_Y(y) = \\mathcal{N}\\Big(y; \\mu_Y(X), \\big(\\theta_y \\cdot \\sigma_Y(X)\\big)^2\\Big)
+
+    with :math:`\\mu_Y(X) \\in \\mathbb{R}` and :math:`\\sigma_Y(X) \\in \\mathbb{R}_{>0}` as the uncalibrated
+    mean and standard deviation, respectively.
+
+    Parameters
+    ----------
+    loc: torch.Tensor, shape: ([1], n, d)
+        Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+        This class also supports broadcasting of the calculations to r random samples (first dim).
+    logvar: torch.Tensor, shape: ([1], n, d)
+        Log of the variance vector of the uncalibrated (Gaussian) probability distribution with n samples and d
+        dimensions. This class also supports broadcasting of the calculations to r random samples (first dim).
+    parameters: torch.Tensor, shape: ([r], n, d)
+        Rescaling parameter of the GP-Normal with n samples d dimensions and r random samples.
+
+    References
+    ----------
+    .. [1] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+       "Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection."
+       European Conference on Computer Vision (ECCV) Workshops, 2022.
+       `Get source online <https://arxiv.org/pdf/2207.01242.pdf>`__
+    """
+
+    def __init__(self, loc: torch.Tensor, logvar: torch.Tensor, parameters: torch.Tensor):
+        """ Constructor. For detailed parameter description, see class docs. """
+
+        var = torch.exp(logvar)
+        transformed_var = var * parameters.exp()
+        super().__init__(loc, torch.sqrt(transformed_var), validate_args=False)
+
+    def expand(self, batch_shape, _instance=None):
+        """ Expand-method. Reimplementation required when sub-classing the Normal distribution of Pyro. """
+
+        new = self._get_checked_instance(ScaledNormalLikelihood, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.loc = self.loc.expand(batch_shape)
+        new.scale = self.scale.expand(batch_shape)
+        super(ScaledNormalLikelihood, new).__init__(new.loc, new.scale, validate_args=False)
+        new._validate_args = self._validate_args
+
+        return new
diff --git a/netcal/regression/gp/likelihood/__init__.py b/netcal/regression/gp/likelihood/__init__.py
new file mode 100644
index 0000000..c94f2ab
--- /dev/null
+++ b/netcal/regression/gp/likelihood/__init__.py
@@ -0,0 +1,28 @@
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+"""
+.. include:: /../../netcal/regression/gp/likelihood/README.md
+   :parser: myst_parser.sphinx_
+
+Available classes
+=================
+
+.. autosummary::
+   :toctree: _autosummary_regression_gp_likelihood
+   :template: custom_class.rst
+
+   ScaledNormalLikelihood
+   ScaledMultivariateNormalLikelihood
+   BetaLikelihood
+   CauchyLikelihood
+"""
+
+from .ScaledNormalLikelihood import ScaledNormalLikelihood
+from .ScaledMultivariateNormalLikelihood import ScaledMultivariateNormalLikelihood
+from .BetaLikelihood import BetaLikelihood
+from .CauchyLikelihood import CauchyLikelihood

From e953ebc783b5f9b8c2961d2b620d1acf90901b17 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 09:57:49 +0200
Subject: [PATCH 10/21] Register new regression package. Register new helper
 functions. Update package version

---
 netcal/__init__.py | 26 ++++++++++++++++----------
 1 file changed, 16 insertions(+), 10 deletions(-)

diff --git a/netcal/__init__.py b/netcal/__init__.py
index 80fdd27..a8d0e87 100644
--- a/netcal/__init__.py
+++ b/netcal/__init__.py
@@ -1,19 +1,20 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
 """
-API Reference
-=============
-This is the detailled API reference for the confidence calibration framework. This framework can be used to
-obtain well-calibrated confidence estimates from biased estimators like Neural Networks.
-The API reference contains a detailled description of all available methods and their parameters. For
+API Reference of net:cal
+========================
+This is the detailed API reference for the net:cal calibration framework. This library can be used to
+obtain well-calibrated confidence or uncertainty estimates from biased estimators such as neural networks.
+The API reference contains a detailed description of all available methods and their parameters. For
 miscellaneous examples on how to use these methods, see readme below.
 
 Available packages
+------------------
 
 .. autosummary::
    :toctree: _autosummary
@@ -23,11 +24,15 @@
    regularization
    metrics
    presentation
+   regression
 
 
 Each calibration method must inherit the base class :class:`AbstractCalibration`. If you want to write your own method and
 include into the framework, include this class as the base class.
 
+Base class
+----------
+
 .. autosummary::
    :toctree: _autosummary_abstract_calibration
    :template: custom_class.rst
@@ -36,10 +41,11 @@
 
 """
 
-name = 'calibration'
-__version__ = '1.2.1'
+name = 'netcal'
+__version__ = '1.3.0'
 
 from .AbstractCalibration import AbstractCalibration
 from .Decorator import accepts, dimensions, global_accepts, global_dimensions
 from .Context import manual_seed, redirect
-from .Stats import hpdi
+from .Stats import hpdi, mv_cauchy_log_density
+from .Helper import squeeze_generic, meanvar, cumulative, is_in_quantile, cumulative_moments, density_from_cumulative

From bd02b50b10ff4d6a1a49136e4891b66c15715817 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 10:00:08 +0200
Subject: [PATCH 11/21] Update development artifact in regularization package

---
 docs/source/conf.py               | 42 ++++++++++++++++++++++---------
 docs/source/index.rst             |  3 ++-
 netcal/regularization/__init__.py |  1 -
 3 files changed, 32 insertions(+), 14 deletions(-)

diff --git a/docs/source/conf.py b/docs/source/conf.py
index d2634c0..df98123 100644
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -1,9 +1,9 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
-# This Source Code Form is subject to the terms of the Mozilla Public
-# License, v. 2.0. If a copy of the MPL was not distributed with this
-# file, You can obtain one at http://mozilla.org/MPL/2.0/.
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 # Configuration file for the Sphinx documentation builder.
 #
 # This file only contains a selection of the most common options. For a full
@@ -20,15 +20,16 @@
 import sys
 sys.path.insert(0, os.path.abspath('../../'))
 
+from netcal import __version__
+
 # -- Project information -----------------------------------------------------
 
-project = 'calibration-framework'
-copyright = '2019-2021, Ruhr West University of Applied Sciences, Bottrop, Germany AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany'
+project = 'netcal'
+copyright = '2019-2022, Ruhr West University of Applied Sciences, Bottrop, Germany AND e:fs TechHub GmbH, Gaimersheim, Germany'
 author = 'Fabian Kueppers'
 
 # The full version, including alpha/beta/rc tags
-release = '1.2.1'
-
+release = __version__
 
 # -- General configuration ---------------------------------------------------
 
@@ -45,9 +46,15 @@
 # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
 # ones.
 extensions = ['sphinx.ext.autodoc', 'sphinx.ext.coverage', 'sphinx.ext.napoleon',
-              'sphinx.ext.autosummary'
+              'sphinx.ext.autosummary', 'sphinx.ext.doctest', 'myst_parser'
 ]
 
+source_suffix = {
+    '.rst': 'restructuredtext',
+    '.txt': 'markdown',
+    '.md': 'markdown',
+}
+
 # Add any paths that contain templates here, relative to this directory.
 templates_path = ['_templates']
 
@@ -61,10 +68,21 @@
 
 # The theme to use for HTML and HTML Help pages.  See the documentation for
 # a list of builtin themes.
-#
-html_theme = 'default'
+
+extensions.append("sphinxjp.themes.basicstrap")
+html_theme = 'basicstrap'
+
+html_title = "net:cal API Reference"
+html_short_title = "net:cal API Reference"
+html_show_copyright = False
+html_show_sphinx = False
+html_sidebars = { '**': ['globaltoc.html', 'searchbox.html'] }
+
 
 # Add any paths that contain custom static files (such as style sheets) here,
 # relative to this directory. They are copied after the builtin static files,
 # so a file named "default.css" will overwrite the builtin "default.css".
 html_static_path = ['_static']
+
+html_logo = "img/logo/logo200x200.png"
+html_favicon = "img/logo/favicon.ico"
\ No newline at end of file
diff --git a/docs/source/index.rst b/docs/source/index.rst
index ef93093..a57659f 100644
--- a/docs/source/index.rst
+++ b/docs/source/index.rst
@@ -1,5 +1,6 @@
 .. automodule:: netcal
-.. include:: ../../README.rst
+.. include:: /../../README.md
+   :parser: myst_parser.sphinx_
 
 
 
diff --git a/netcal/regularization/__init__.py b/netcal/regularization/__init__.py
index 6fa628b..a18f154 100644
--- a/netcal/regularization/__init__.py
+++ b/netcal/regularization/__init__.py
@@ -24,6 +24,5 @@
 
 from .ConfidencePenalty import confidence_penalty
 from .ConfidencePenalty import ConfidencePenalty
-from .ECEPenalty import ECEPenalty
 from .MMCEPenalty import MMCEPenalty
 from .DCAPenalty import DCAPenalty

From 26601626c963dd8b1af6e85964781e7a7057fa0c Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 10:10:10 +0200
Subject: [PATCH 12/21] Update package documentation.

---
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_binning/netcal.binning.ENIR.doctree b/docs/build/doctrees/_autosummary/_autosummary_binning/netcal.binning.ENIR.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.doctree b/docs/build/doctrees/_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_metric/netcal.metrics.ECE.doctree b/docs/build/doctrees/_autosummary/_autosummary_metric/netcal.metrics.ECE.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_metric/netcal.metrics.MCE.doctree b/docs/build/doctrees/_autosummary/_autosummary_metric/netcal.metrics.MCE.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_metric/netcal.metrics.PICP.doctree b/docs/build/doctrees/_autosummary/_autosummary_metric/netcal.metrics.PICP.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.doctree b/docs/build/doctrees/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MCE.doctree b/docs/build/doctrees/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MCE.doctree
new file mode 100644
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.doctree b/docs/build/doctrees/_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.doctree
new file mode 100644
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityDiagram.doctree b/docs/build/doctrees/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityDiagram.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityQCE.doctree b/docs/build/doctrees/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityQCE.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regression/netcal.regression.GPCauchy.doctree b/docs/build/doctrees/_autosummary/_autosummary_regression/netcal.regression.GPCauchy.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regression/netcal.regression.GPNormal.doctree b/docs/build/doctrees/_autosummary/_autosummary_regression/netcal.regression.GPNormal.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regression/netcal.regression.VarianceScaling.doctree b/docs/build/doctrees/_autosummary/_autosummary_regression/netcal.regression.VarianceScaling.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPCauchy.doctree b/docs/build/doctrees/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPCauchy.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regression_gp/netcal.regression.gp.doctree b/docs/build/doctrees/_autosummary/_autosummary_regression_gp/netcal.regression.gp.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.doctree b/docs/build/doctrees/_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.doctree b/docs/build/doctrees/_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.doctree b/docs/build/doctrees/_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.doctree b/docs/build/doctrees/_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.doctree b/docs/build/doctrees/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.doctree
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diff --git a/docs/build/doctrees/_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.doctree b/docs/build/doctrees/_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.doctree
new file mode 100644
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-  <div class="section" id="netcal-binning-bbq">
-<h1>netcal.binning.BBQ<a class="headerlink" href="#netcal-binning-bbq" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.binning.BBQ">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.binning.</code><code class="sig-name descname">BBQ</code><span class="sig-paren">(</span><em class="sig-param">score_function: str = 'BIC'</em>, <em class="sig-param">equal_intervals: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">independent_probabilities: bool = False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.BBQ" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.AbstractCalibration.AbstractCalibration</span></code></p>
-<p>Bayesian Binning into Quantiles (BBQ) <a class="footnote-reference brackets" href="#id2" id="id1">1</a>. This method utilizes multiple <a class="reference internal" href="netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.binning.html#binning-methods-for-confidence-calibration">Binning Methods for Confidence Calibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.binning.html#available-classes">Available classes</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.binning.HistogramBinning.html">netcal.binning.HistogramBinning</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.binning.IsotonicRegression.html">netcal.binning.IsotonicRegression</a></li>
+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.binning.BBQ</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.binning.BBQ"><code class="docutils literal notranslate"><span class="pre">BBQ</span></code></a></li>
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+  <section id="netcal-binning-bbq">
+<h1>netcal.binning.BBQ<a class="headerlink" href="#netcal-binning-bbq" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.binning.BBQ">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.binning.</span></span><span class="sig-name descname"><span class="pre">BBQ</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">score_function</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'BIC'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">independent_probabilities</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.BBQ" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bayesian Binning into Quantiles (BBQ).
+This method has been proposed by <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+This method utilizes multiple <a class="reference internal" href="netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a>
 instances with different amounts of bins and computes a weighted sum of all methods to obtain a
 well-calibrated confidence estimate. The scoring function “BDeu”, which is proposed in the original paper,
 is currently not supported.</p>
@@ -77,7 +215,7 @@ <h1>netcal.binning.BBQ<a class="headerlink" href="#netcal-binning-bbq" title="Pe
 <p>Using the elbow method to sort out models with a low relative score, the weights for each model can be obtained
 by normalizing over all model posterior scores.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>score_function</strong> (<em>str</em><em>, </em><em>default='BIC'</em>) – define score functions:
 - ‘BIC’: Bayesian-Information-Criterion
@@ -95,22 +233,19 @@ <h1>netcal.binning.BBQ<a class="headerlink" href="#netcal-binning-bbq" title="Pe
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
 “Obtaining well calibrated probabilities using bayesian binning.”
 Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
 <a class="reference external" href="https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958">Get source online</a></p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([score_function, equal_intervals, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([score_function, equal_intervals, ...])</p></td>
 <td><p>Constructor.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
@@ -129,235 +264,58 @@ <h1>netcal.binning.BBQ<a class="headerlink" href="#netcal-binning-bbq" title="Pe
 <td><p>Load model from saved torch dump.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.binning.BBQ.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.BBQ.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.binning.BBQ.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; BBQ<a class="headerlink" href="#netcal.binning.BBQ.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build BBQ calibration model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="#netcal.binning.BBQ" title="netcal.binning.BBQ"><code class="xref py py-class docutils literal notranslate"><span class="pre">BBQ</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="#netcal.binning.BBQ" title="netcal.binning.BBQ">BBQ</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.BBQ.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.BBQ.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.BBQ.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.BBQ.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.BBQ.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.BBQ.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.BBQ.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.BBQ.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.BBQ.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.binning.BBQ.BBQ<a class="headerlink" href="#netcal.binning.BBQ.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.BBQ.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.binning.BBQ.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.BBQ.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.binning.BBQ.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with uncalibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-</div>
+</section>
 
 
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-  <div class="section" id="netcal-binning-enir">
-<h1>netcal.binning.ENIR<a class="headerlink" href="#netcal-binning-enir" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.binning.ENIR">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.binning.</code><code class="sig-name descname">ENIR</code><span class="sig-paren">(</span><em class="sig-param">score_function: str = 'BIC'</em>, <em class="sig-param">quick_init: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">independent_probabilities: bool = False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.ENIR" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.AbstractCalibration.AbstractCalibration</span></code></p>
-<p>Ensemble of Near Isotonic Regression (ENIR) models <a class="footnote-reference brackets" href="#id2" id="id1">1</a>. These models allow - in contrast to standard
+              <li><a href="netcal.binning.BBQ.html" title="netcal.binning.BBQ" accesskey="P">previous </a></li>
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+<li class="toctree-l4"><a class="reference internal" href="#netcal.binning.ENIR"><code class="docutils literal notranslate"><span class="pre">ENIR</span></code></a></li>
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+  <section id="netcal-binning-enir">
+<h1>netcal.binning.ENIR<a class="headerlink" href="#netcal-binning-enir" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.binning.ENIR">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.binning.</span></span><span class="sig-name descname"><span class="pre">ENIR</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">score_function</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'BIC'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">quick_init</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">independent_probabilities</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.ENIR" title="Permalink to this definition">¶</a></dt>
+<dd><p>Ensemble of Near Isotonic Regression (ENIR) models.
+This method has initially been proposed by <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+These models allow - in contrast to standard
 <a class="reference internal" href="netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression" title="netcal.binning.IsotonicRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">IsotonicRegression</span></code></a> method - a violation of the monotony restrictions. Using the <em>modified
 Pool-Adjacent-Violators Algorithm (mPAVA)</em>, this method build multiple Near Isotonic Regression models
 and weights them by a certain score function.</p>
@@ -77,7 +215,7 @@ <h1>netcal.binning.ENIR<a class="headerlink" href="#netcal-binning-enir" title="
 <p>Using the elbow method to sort out models with a low relative score, the weights for each model can be obtained
 by normalizing over all model posterior scores.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>score_function</strong> (<em>str</em><em>, </em><em>default='BIC'</em>) – define score functions:
 - ‘BIC’: Bayesian-Information-Criterion
@@ -94,22 +232,19 @@ <h1>netcal.binning.ENIR<a class="headerlink" href="#netcal-binning-enir" title="
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Naeini, Mahdi Pakdaman, and Gregory F. Cooper:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Naeini, Mahdi Pakdaman, and Gregory F. Cooper:
 “Binary classifier calibration using an ensemble of near isotonic regression models.”
 2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE, 2016.
 <a class="reference external" href="https://ieeexplore.ieee.org/iel7/7837023/7837813/07837860.pdf">Get source online</a></p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([score_function, quick_init, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([score_function, quick_init, ...])</p></td>
 <td><p>Constructor.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
@@ -128,235 +263,58 @@ <h1>netcal.binning.ENIR<a class="headerlink" href="#netcal-binning-enir" title="
 <td><p>Load model from saved torch dump.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.binning.ENIR.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.ENIR.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.binning.ENIR.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; ENIR<a class="headerlink" href="#netcal.binning.ENIR.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build ENIR calibration model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="#netcal.binning.ENIR" title="netcal.binning.ENIR"><code class="xref py py-class docutils literal notranslate"><span class="pre">ENIR</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="#netcal.binning.ENIR" title="netcal.binning.ENIR">ENIR</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.ENIR.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.ENIR.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.ENIR.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.ENIR.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.ENIR.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.ENIR.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.ENIR.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.ENIR.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.ENIR.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.binning.ENIR.ENIR<a class="headerlink" href="#netcal.binning.ENIR.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.ENIR.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.binning.ENIR.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.ENIR.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.binning.ENIR.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with uncalibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
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-  <div class="section" id="netcal-binning-histogrambinning">
-<h1>netcal.binning.HistogramBinning<a class="headerlink" href="#netcal-binning-histogrambinning" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.binning.HistogramBinning">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.binning.</code><code class="sig-name descname">HistogramBinning</code><span class="sig-paren">(</span><em class="sig-param">bins: Union[int</em>, <em class="sig-param">Iterable[int]] = 10</em>, <em class="sig-param">equal_intervals: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">independent_probabilities: bool = False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.HistogramBinning" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.AbstractCalibration.AbstractCalibration</span></code></p>
-<p>Simple Histogram Binning calibration method <a class="footnote-reference brackets" href="#id4" id="id1">1</a>. Each prediction is sorted into a bin
+              <li><a href="../netcal.binning.html" title="netcal.binning" accesskey="P">previous </a></li>
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+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.binning.HistogramBinning</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.binning.HistogramBinning"><code class="docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a></li>
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+                  
+  <section id="netcal-binning-histogrambinning">
+<h1>netcal.binning.HistogramBinning<a class="headerlink" href="#netcal-binning-histogrambinning" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.binning.HistogramBinning">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.binning.</span></span><span class="sig-name descname"><span class="pre">HistogramBinning</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">independent_probabilities</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.HistogramBinning" title="Permalink to this definition">¶</a></dt>
+<dd><p>Simple Histogram Binning calibration method.
+This method has been proposed by <a class="footnote-reference brackets" href="#id4" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+Each prediction is sorted into a bin
 and assigned its calibrated confidence estimate. This method normally works for binary
-classification. For multiclass classification, this method is applied into a 1-vs-all manner <a class="footnote-reference brackets" href="#id5" id="id2">2</a>.</p>
+classification. For multiclass classification, this method is applied into a 1-vs-all manner <a class="footnote-reference brackets" href="#id5" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.</p>
 <p>The bin boundaries are either chosen to be equal length intervals or to equalize the number of samples in each bin.</p>
 <p>On object detection, use a multidimensional binning to include additional information of the box
-regression branch <a class="footnote-reference brackets" href="#id7" id="id3">3</a>.</p>
+regression branch <a class="footnote-reference brackets" href="#id6" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the Histogram Binning.
 On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
@@ -76,33 +213,32 @@ <h1>netcal.binning.HistogramBinning<a class="headerlink" href="#netcal-binning-h
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Zadrozny, Bianca and Elkan, Charles:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Zadrozny, Bianca and Elkan, Charles:
 “Obtaining calibrated probability estimates from decision trees and naive bayesian classifiers.”
 In ICML, pp. 609–616, 2001.
 <a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.3039&amp;rep=rep1&amp;type=pdf">Get source online</a></p>
-</dd>
-<dt class="label" id="id5"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Zadrozny, Bianca and Elkan, Charles:
+</aside>
+<aside class="footnote brackets" id="id5" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Zadrozny, Bianca and Elkan, Charles:
 “Transforming classifier scores into accurate multiclass probability estimates.”
 In KDD, pp. 694–699, 2002.
 <a class="reference external" href="https://www.researchgate.net/profile/Charles_Elkan/publication/2571315_Transforming_Classifier_Scores_into_Accurate_Multiclass_Probability_Estimates/links/0fcfd509ae852a8bb9000000.pdf">Get source online</a></p>
-</dd>
-<dt class="label" id="id7"><span class="brackets"><a class="fn-backref" href="#id3">3</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
-The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.</p>
-</dd>
-</dl>
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.</p>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
 <td><p>Create an instance of <cite>HistogramBinning</cite>.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
@@ -124,256 +260,58 @@ <h1>netcal.binning.HistogramBinning<a class="headerlink" href="#netcal-binning-h
 <td><p>Load model from saved torch dump.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state])</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.HistogramBinning.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">tensorboard: bool = False</em>, <em class="sig-param">log_dir: str = None</em><span class="sig-paren">)</span> &#x2192; HistogramBinning<a class="headerlink" href="#netcal.binning.HistogramBinning.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Function call to build the calibration model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number (only for compatibility here)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning">HistogramBinning</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.HistogramBinning.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.get_degrees_of_freedom">
-<code class="sig-name descname">get_degrees_of_freedom</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; int<a class="headerlink" href="#netcal.binning.HistogramBinning.get_degrees_of_freedom" title="Permalink to this definition">¶</a></dt>
-<dd><p>Needed for BIC. Returns the degree of freedom. This simply returns the
-number of bins.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>Integer with degree of freedom.</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>int</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.HistogramBinning.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.HistogramBinning.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.HistogramBinning.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.binning.HistogramBinning.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.binning.HistogramBinning.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.HistogramBinning.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">num_samples: int = 1</em>, <em class="sig-param">random_state: int = None</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.binning.HistogramBinning.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with uncalibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p></li>
-<li><p><strong>num_samples</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1000</em>) – Number of samples generated on MCMC sampling or Variational Inference - only for compatibility and
-not used by Histogram Binning!</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-</div>
+</section>
 
 
+                </div>
+              </div>
+            </div>
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-  <div class="section" id="netcal-binning-isotonicregression">
-<h1>netcal.binning.IsotonicRegression<a class="headerlink" href="#netcal-binning-isotonicregression" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.binning.IsotonicRegression">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.binning.</code><code class="sig-name descname">IsotonicRegression</code><span class="sig-paren">(</span><em class="sig-param">detection: bool = False</em>, <em class="sig-param">independent_probabilities: bool = False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.AbstractCalibration.AbstractCalibration</span></code></p>
-<p>Isotonic Regression method <a class="footnote-reference brackets" href="#id2" id="id1">1</a>. This method is similar to <a class="reference internal" href="netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a> but with dynamic bin sizes
+              <li><a href="netcal.binning.HistogramBinning.html" title="netcal.binning.HistogramBinning" accesskey="P">previous </a></li>
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+            
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+  <section id="netcal-binning-isotonicregression">
+<h1>netcal.binning.IsotonicRegression<a class="headerlink" href="#netcal-binning-isotonicregression" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.binning.IsotonicRegression">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.binning.</span></span><span class="sig-name descname"><span class="pre">IsotonicRegression</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">independent_probabilities</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression" title="Permalink to this definition">¶</a></dt>
+<dd><p>Isotonic Regression method.
+This method has initially been proposed by <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+This method is similar to <a class="reference internal" href="netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning"><code class="xref py py-class docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a> but with dynamic bin sizes
 and boundaries. A piecewise constant function gets fit to ground truth labels sorted by
 given confidence estimates.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
 with shape (n_samples, [n_classes]).
@@ -68,20 +205,17 @@ <h1>netcal.binning.IsotonicRegression<a class="headerlink" href="#netcal-binning
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Zadrozny, Bianca and Elkan, Charles:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Zadrozny, Bianca and Elkan, Charles:
 “Transforming classifier scores into accurate multiclass probability estimates.”
 In KDD, pp. 694–699, 2002.
 <a class="reference external" href="https://www.researchgate.net/profile/Charles_Elkan/publication/2571315_Transforming_Classifier_Scores_into_Accurate_Multiclass_Probability_Estimates/links/0fcfd509ae852a8bb9000000.pdf">Get source online</a></p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([detection, independent_probabilities])</p></td>
 <td><p>Create an instance of <cite>IsotonicRegression</cite>.</p></td>
@@ -102,235 +236,58 @@ <h1>netcal.binning.IsotonicRegression<a class="headerlink" href="#netcal-binning
 <td><p>Load model from saved torch dump.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; IsotonicRegression<a class="headerlink" href="#netcal.binning.IsotonicRegression.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build Isotonic Regression model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="#netcal.binning.IsotonicRegression" title="netcal.binning.IsotonicRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">IsotonicRegression</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="#netcal.binning.IsotonicRegression" title="netcal.binning.IsotonicRegression">IsotonicRegression</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.binning.IsotonicRegression.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.binning.IsotonicRegression.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.binning.IsotonicRegression.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.binning.IsotonicRegression.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with uncalibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-</div>
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-  <div class="section" id="netcal-metrics-ace">
-<h1>netcal.metrics.ACE<a class="headerlink" href="#netcal-metrics-ace" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.metrics.ACE">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.metrics.</code><code class="sig-name descname">ACE</code><span class="sig-paren">(</span><em class="sig-param">bins: Union[int</em>, <em class="sig-param">Iterable[int]] = 10</em>, <em class="sig-param">equal_intervals: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">sample_threshold: int = 1</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.ACE" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.Miscalibration._Miscalibration</span></code></p>
-<p>Average Calibration Error (ACE).
-This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1">1</a> or as Detection Average Calibration Error (D-ACE)
-<a class="footnote-reference brackets" href="#id4" id="id2">2</a> on object detection tasks. This metrics measures the average difference between accuracy and confidence by
-grouping all samples into <span class="math notranslate nohighlight">\(K\)</span> bins and calculating</p>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.metrics.html#metrics-package-to-measure-miscalibration">Metrics Package to Measure Miscalibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.metrics.html#available-classes">Available classes</a><ul class="current">
+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.metrics.ACE</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.metrics.ACE"><code class="docutils literal notranslate"><span class="pre">ACE</span></code></a></li>
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+    </p>
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+                  
+  <section id="netcal-metrics-ace">
+<h1>netcal.metrics.ACE<a class="headerlink" href="#netcal-metrics-ace" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.ACE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">ACE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.ACE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Average Calibration Error (ACE) for classification and Detection Average Calibration Error (D-ACE) for
+object detection or segmentation.
+This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> or as Detection Average Calibration Error (D-ACE)
+<a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> on object detection tasks. This metrics measures the average difference between accuracy and confidence by
+grouping all samples into <span class="math notranslate nohighlight">\(B\)</span> bins and calculating</p>
 <div class="math notranslate nohighlight">
-\[ACE = \frac{1}{K} \sum_{i=1}^K |\text{acc}_i - \text{conf}_i| ,\]</div>
-<p>where <span class="math notranslate nohighlight">\(\text{acc}_i\)</span> and <span class="math notranslate nohighlight">\(\text{conf}_i\)</span> denote the accuracy and average confidence in the i-th bin.
-The main difference to <a class="reference internal" href="netcal.metrics.ECE.html#netcal.metrics.ECE" title="netcal.metrics.ECE"><code class="xref py py-class docutils literal notranslate"><span class="pre">ECE</span></code></a> is that each bin is weighted equally.</p>
+\[ACE = \frac{1}{B} \sum_{b=1}^B |\text{acc}(b) - \text{conf}(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{acc}(b)\)</span> and <span class="math notranslate nohighlight">\(\text{conf}(b)\)</span> denote the accuracy and average confidence in the b-th bin.
+The main difference to <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.confidence.ECE</span></code> is that each bin is weighted equally.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the Histogram Binning.
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the ACE.
 On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
 If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
 <li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
@@ -76,234 +221,90 @@ <h1>netcal.metrics.ACE<a class="headerlink" href="#netcal-metrics-ace" title="Pe
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id3"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi:
 “Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection.”
 Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.
 <a class="reference external" href="https://openreview.net/pdf?id=S1lG7aTnqQ">Get source online</a></p>
-</dd>
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
 The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 <a class="reference external" href="https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf">Get source online</a></p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
 <td><p>Constructor.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
 <td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, ...])</p></td>
 <td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
 <td><p>Check input data.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, …)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
 <td><p>Determine miscalibration based on passed histograms.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
 <td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.metrics.ACE.binning">
-<code class="sig-name descname">binning</code><span class="sig-paren">(</span><em class="sig-param">bin_bounds: List</em>, <em class="sig-param">samples: numpy.ndarray</em>, <em class="sig-param">*values: Iterable</em>, <em class="sig-param">nan: float = 0.0</em><span class="sig-paren">)</span> &#x2192; Tuple<a class="headerlink" href="#netcal.metrics.ACE.binning" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform binning on value (and all additional values passed) based on samples.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>bin_bounds</strong> (<em>list</em><em>, </em><em>length=samples.shape</em><em>[</em><em>1</em><em>]</em>) – Binning boundaries used for each dimension given in ‘samples’ parameter.</p></li>
-<li><p><strong>samples</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – Array used to group all samples into bins.</p></li>
-<li><p><strong>*values</strong> (<em>instances np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>1</em><em>)</em>) – Arrays whose values are binned.</p></li>
-<li><p><strong>nan</strong> (<em>float</em><em>, </em><em>optional default: 0.0</em>) – If a bin has no samples or less than defined sample_threshold, the according bin is marked as
-NaN. Specify fill float to insert instead of NaN.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length equal to the amount of passed value arrays with binning schemes and an additional histogram</em></p></li>
-<li><p><em>with number of samples in each bin as well as an index tuple containing the bin indices.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ACE.measure">
-<code class="sig-name descname">measure</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None, return_map: bool = False, return_num_samples: bool = False, return_uncertainty_map: bool = False</em><span class="sig-paren">)</span> &#x2192; Union[float, Tuple]<a class="headerlink" href="#netcal.metrics.ACE.measure" title="Permalink to this definition">¶</a></dt>
-<dd><p>Measure calibration by given predictions with confidence and the according ground truth.
-Assume binary predictions with y=1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>iterable of np.ndarray</em><em>, or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes/n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>iterable of np.ndarray with same length as X</em><em> or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.</p></li>
-<li><p><strong>batched</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – Multiple predictions can be evaluated at once (e.g. cross-validation examinations) using batched-mode.
-All predictions given by X and y are separately evaluated and their results are averaged afterwards
-for visualization.</p></li>
-<li><p><strong>uncertainty</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – <p>Define uncertainty handling if input X has been sampled e.g. by Monte-Carlo dropout or similar methods
-that output an ensemble of predictions per sample. Choose one of the following options:
-- flatten:  treat everything as a separate prediction - this option will yield into a slightly better</p>
-<blockquote>
-<div><p>calibration performance but without the visualization of a prediction interval.</p>
-</div></blockquote>
-<ul>
-<li><dl class="simple">
-<dt>mean:     compute Monte-Carlo integration to obtain a simple confidence estimate for a sample</dt><dd><p>(mean) with a standard deviation that is visualized.</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p></li>
-<li><p><strong>return_map</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, return map with miscalibration metric separated into all remaining dimension bins.</p></li>
-<li><p><strong>return_num_samples</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, also return the number of samples in each bin.</p></li>
-<li><p><strong>return_uncertainty_map</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, also return the average deviation of the confidence within each bin.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Always returns Average Calibration Error.
-If ‘return_map’ is True, return tuple and append miscalibration map over all bins.
-If ‘return_num_samples’ is True, return tuple and append the number of samples in each bin (excluding confidence dimension).
-If ‘return_uncertainty’ is True, return tuple and append the average standard deviation of confidence within each bin (excluding confidence dimension).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>float or tuple of (float, np.ndarray, [np.ndarray, [np.ndarray]])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ACE.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None</em><span class="sig-paren">)</span> &#x2192; Tuple[List[numpy.ndarray], List[numpy.ndarray], List[numpy.ndarray], List, int]<a class="headerlink" href="#netcal.metrics.ACE.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Check input data. For detailed documentation of the input parameters, check “_measure” method.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ACE.process">
-<code class="sig-name descname">process</code><span class="sig-paren">(</span><em class="sig-param">metric: str</em>, <em class="sig-param">acc_hist: numpy.ndarray</em>, <em class="sig-param">conf_hist: numpy.ndarray</em>, <em class="sig-param">variance_hist: numpy.ndarray</em>, <em class="sig-param">num_samples_hist: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; Tuple[float, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]<a class="headerlink" href="#netcal.metrics.ACE.process" title="Permalink to this definition">¶</a></dt>
-<dd><p>Determine miscalibration based on passed histograms.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>metric</strong> (<em>str</em>) – Identifier to specify the used metric. Must be one of ‘ace’, ‘ece’ or ‘mce’.</p></li>
-<li><p><strong>acc_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average accuracy in each bin.</p></li>
-<li><p><strong>conf_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average confidence in each bin.</p></li>
-<li><p><strong>variance_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average variance in each bin. This array is currently not used but
-might be utilized in the future.</p></li>
-<li><p><strong>num_samples_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with number of samples in each bin.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length 6 (miscalibration score, miscalibration map, accuracy map, confidence map, variance map, num samples map)</em></p></li>
-<li><p><em>All maps without confidence dimension.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ACE.reduce">
-<code class="sig-name descname">reduce</code><span class="sig-paren">(</span><em class="sig-param">histogram: numpy.ndarray</em>, <em class="sig-param">distribution: numpy.ndarray</em>, <em class="sig-param">axis: int</em>, <em class="sig-param">reduce_result: Tuple = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.ACE.reduce" title="Permalink to this definition">¶</a></dt>
-<dd><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.
-If ‘reduce_result’ is given, reuse the data distribution of the previous result instead of the distribution
-given by ‘distribution’ parameter.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ACE.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[Iterable[int], int]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.metrics.ACE.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter
-‘axes_to_keep’ even if the dimension is of size 1.</p>
 </dd></dl>
 
-</dd></dl>
-
-</div>
+</section>
 
 
+                </div>
+              </div>
+            </div>
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-  <div class="section" id="netcal-metrics-ece">
-<h1>netcal.metrics.ECE<a class="headerlink" href="#netcal-metrics-ece" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.metrics.ECE">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.metrics.</code><code class="sig-name descname">ECE</code><span class="sig-paren">(</span><em class="sig-param">bins: Union[int</em>, <em class="sig-param">Iterable[int]] = 10</em>, <em class="sig-param">equal_intervals: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">sample_threshold: int = 1</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.ECE" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.Miscalibration._Miscalibration</span></code></p>
-<p>Expected Calibration Error (ECE).
-This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1">1</a> or as Detection Expected Calibration Error on object
-detection tasks <a class="footnote-reference brackets" href="#id4" id="id2">2</a>. This metrics measures the expected difference between accuracy and confidence by grouping
-all samples (size <span class="math notranslate nohighlight">\(N\)</span>) into <span class="math notranslate nohighlight">\(K\)</span> bins
-and calculating</p>
+
+          </ul>
+
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+<h3><a href="../../index.html">Table of Contents</a></h3>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="../netcal.binning.html">netcal.binning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../netcal.scaling.html">netcal.scaling</a></li>
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+<li class="toctree-l1 current"><a class="reference internal" href="../netcal.metrics.html">netcal.metrics</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../netcal.metrics.html#metrics-package-to-measure-miscalibration">Metrics Package to Measure Miscalibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.metrics.html#available-classes">Available classes</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.metrics.ACE.html">netcal.metrics.ACE</a></li>
+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.metrics.ECE</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.metrics.ECE"><code class="docutils literal notranslate"><span class="pre">ECE</span></code></a></li>
+</ul>
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+  <section id="netcal-metrics-ece">
+<h1>netcal.metrics.ECE<a class="headerlink" href="#netcal-metrics-ece" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.ECE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">ECE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.ECE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Expected Calibration Error (ECE) for classification and Detection Expected Calibration Error (D-ECE) for
+object detection or segmentation.
+This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> or as Detection Expected Calibration Error (D-ECE) on object
+detection tasks <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. This metrics measures the expected difference between accuracy/precision and confidence
+by grouping all samples (size <span class="math notranslate nohighlight">\(N\)</span>) into <span class="math notranslate nohighlight">\(B\)</span> bins, so that the ECE is computed by</p>
 <div class="math notranslate nohighlight">
-\[ECE = \sum_{i=1}^K \frac{|B_i|}{N} |\text{acc}_i - \text{conf}_i| ,\]</div>
-<p>where <span class="math notranslate nohighlight">\(\text{acc}_i\)</span> and <span class="math notranslate nohighlight">\(\text{conf}_i\)</span> denote the accuracy and average confidence in the i-th bin
-and <span class="math notranslate nohighlight">\(|B_i|\)</span> denote the number of samples in bin <span class="math notranslate nohighlight">\(B_i\)</span>.</p>
+\[ECE = \sum_{b=1}^B \frac{N_b}{N} |\text{acc}(b) - \text{conf}(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{acc}(b)\)</span> and <span class="math notranslate nohighlight">\(\text{conf}(b)\)</span> denote the accuracy and average confidence in the i-th bin
+and <span class="math notranslate nohighlight">\(N_b\)</span> denote the number of samples in bin <span class="math notranslate nohighlight">\(b\)</span>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the Histogram Binning.
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the Expected Calibration Error.
 On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
 If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
 <li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
@@ -77,234 +221,90 @@ <h1>netcal.metrics.ECE<a class="headerlink" href="#netcal-metrics-ece" title="Pe
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id3"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
 “Obtaining well calibrated probabilities using bayesian binning.”
 Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
 <a class="reference external" href="https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958">Get source online</a></p>
-</dd>
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
 The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 <a class="reference external" href="https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf">Get source online</a>.</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
 <td><p>Constructor.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
 <td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, ...])</p></td>
 <td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
 <td><p>Check input data.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, …)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
 <td><p>Determine miscalibration based on passed histograms.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
 <td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.metrics.ECE.binning">
-<code class="sig-name descname">binning</code><span class="sig-paren">(</span><em class="sig-param">bin_bounds: List</em>, <em class="sig-param">samples: numpy.ndarray</em>, <em class="sig-param">*values: Iterable</em>, <em class="sig-param">nan: float = 0.0</em><span class="sig-paren">)</span> &#x2192; Tuple<a class="headerlink" href="#netcal.metrics.ECE.binning" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform binning on value (and all additional values passed) based on samples.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>bin_bounds</strong> (<em>list</em><em>, </em><em>length=samples.shape</em><em>[</em><em>1</em><em>]</em>) – Binning boundaries used for each dimension given in ‘samples’ parameter.</p></li>
-<li><p><strong>samples</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – Array used to group all samples into bins.</p></li>
-<li><p><strong>*values</strong> (<em>instances np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>1</em><em>)</em>) – Arrays whose values are binned.</p></li>
-<li><p><strong>nan</strong> (<em>float</em><em>, </em><em>optional default: 0.0</em>) – If a bin has no samples or less than defined sample_threshold, the according bin is marked as
-NaN. Specify fill float to insert instead of NaN.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length equal to the amount of passed value arrays with binning schemes and an additional histogram</em></p></li>
-<li><p><em>with number of samples in each bin as well as an index tuple containing the bin indices.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ECE.measure">
-<code class="sig-name descname">measure</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None, return_map: bool = False, return_num_samples: bool = False, return_uncertainty_map: bool = False</em><span class="sig-paren">)</span> &#x2192; Union[float, Tuple]<a class="headerlink" href="#netcal.metrics.ECE.measure" title="Permalink to this definition">¶</a></dt>
-<dd><p>Measure calibration by given predictions with confidence and the according ground truth.
-Assume binary predictions with y=1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>iterable of np.ndarray</em><em>, or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes/n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>iterable of np.ndarray with same length as X</em><em> or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.</p></li>
-<li><p><strong>batched</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – Multiple predictions can be evaluated at once (e.g. cross-validation examinations) using batched-mode.
-All predictions given by X and y are separately evaluated and their results are averaged afterwards
-for visualization.</p></li>
-<li><p><strong>uncertainty</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – <p>Define uncertainty handling if input X has been sampled e.g. by Monte-Carlo dropout or similar methods
-that output an ensemble of predictions per sample. Choose one of the following options:
-- flatten:  treat everything as a separate prediction - this option will yield into a slightly better</p>
-<blockquote>
-<div><p>calibration performance but without the visualization of a prediction interval.</p>
-</div></blockquote>
-<ul>
-<li><dl class="simple">
-<dt>mean:     compute Monte-Carlo integration to obtain a simple confidence estimate for a sample</dt><dd><p>(mean) with a standard deviation that is visualized.</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p></li>
-<li><p><strong>return_map</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, return map with miscalibration metric separated into all remaining dimension bins.</p></li>
-<li><p><strong>return_num_samples</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, also return the number of samples in each bin.</p></li>
-<li><p><strong>return_uncertainty_map</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, also return the average deviation of the confidence within each bin.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Always returns Expected Calibration Error.
-If ‘return_map’ is True, return tuple and append miscalibration map over all bins.
-If ‘return_num_samples’ is True, return tuple and append the number of samples in each bin (excluding confidence dimension).
-If ‘return_uncertainty’ is True, return tuple and append the average standard deviation of confidence within each bin (excluding confidence dimension).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>float or tuple of (float, np.ndarray, [np.ndarray, [np.ndarray]])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ECE.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None</em><span class="sig-paren">)</span> &#x2192; Tuple[List[numpy.ndarray], List[numpy.ndarray], List[numpy.ndarray], List, int]<a class="headerlink" href="#netcal.metrics.ECE.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Check input data. For detailed documentation of the input parameters, check “_measure” method.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ECE.process">
-<code class="sig-name descname">process</code><span class="sig-paren">(</span><em class="sig-param">metric: str</em>, <em class="sig-param">acc_hist: numpy.ndarray</em>, <em class="sig-param">conf_hist: numpy.ndarray</em>, <em class="sig-param">variance_hist: numpy.ndarray</em>, <em class="sig-param">num_samples_hist: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; Tuple[float, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]<a class="headerlink" href="#netcal.metrics.ECE.process" title="Permalink to this definition">¶</a></dt>
-<dd><p>Determine miscalibration based on passed histograms.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>metric</strong> (<em>str</em>) – Identifier to specify the used metric. Must be one of ‘ace’, ‘ece’ or ‘mce’.</p></li>
-<li><p><strong>acc_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average accuracy in each bin.</p></li>
-<li><p><strong>conf_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average confidence in each bin.</p></li>
-<li><p><strong>variance_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average variance in each bin. This array is currently not used but
-might be utilized in the future.</p></li>
-<li><p><strong>num_samples_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with number of samples in each bin.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length 6 (miscalibration score, miscalibration map, accuracy map, confidence map, variance map, num samples map)</em></p></li>
-<li><p><em>All maps without confidence dimension.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ECE.reduce">
-<code class="sig-name descname">reduce</code><span class="sig-paren">(</span><em class="sig-param">histogram: numpy.ndarray</em>, <em class="sig-param">distribution: numpy.ndarray</em>, <em class="sig-param">axis: int</em>, <em class="sig-param">reduce_result: Tuple = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.ECE.reduce" title="Permalink to this definition">¶</a></dt>
-<dd><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.
-If ‘reduce_result’ is given, reuse the data distribution of the previous result instead of the distribution
-given by ‘distribution’ parameter.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.ECE.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[Iterable[int], int]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.metrics.ECE.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter
-‘axes_to_keep’ even if the dimension is of size 1.</p>
 </dd></dl>
 
-</dd></dl>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.metrics.html#metrics-package-to-measure-miscalibration">Metrics Package to Measure Miscalibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.metrics.html#available-classes">Available classes</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.metrics.ACE.html">netcal.metrics.ACE</a></li>
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+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.metrics.ENCE</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.metrics.ENCE"><code class="docutils literal notranslate"><span class="pre">ENCE</span></code></a></li>
+</ul>
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+  <section id="netcal-metrics-ence">
+<h1>netcal.metrics.ENCE<a class="headerlink" href="#netcal-metrics-ence" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.ENCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">ENCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.ENCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Expected Normalized Calibration Error (ENCE) for a regression calibration evaluation to test for
+<em>variance calibration</em>. A probabilistic regression model takes <span class="math notranslate nohighlight">\(X\)</span> as input and outputs a
+mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and a standard deviation <span class="math notranslate nohighlight">\(\sigma_Y(X)\)</span> targeting the ground-truth <span class="math notranslate nohighlight">\(y\)</span>.
+Similar to the <a class="reference internal" href="../_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE" title="netcal.metrics.confidence.ECE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.confidence.ECE</span></code></a>, the ENCE applies a binning scheme with <span class="math notranslate nohighlight">\(B\)</span> bins
+over the predicted standard deviation <span class="math notranslate nohighlight">\(\sigma_Y(X)\)</span> and measures the absolute (normalized) difference
+between root mean squared error (RMSE) and root mean variance (RMV) <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+Thus, the ENCE <a class="footnote-reference brackets" href="#id3" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{ENCE} := \frac{1}{B} \sum^B_{b=1} \frac{|RMSE(b) - RMV(b)|}{RMV(b)} ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(RMSE(b)\)</span> and <span class="math notranslate nohighlight">\(RMV(b)\)</span> are the root mean squared error and the root mean variance within
+bin <span class="math notranslate nohighlight">\(b\)</span>, respectively.</p>
+<p>If multiple dimensions are given, the ENCE is measured for each dimension separately.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the ENCE binning.
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id2">2</a>)</span>
+<p>Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, sample_threshold])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, *[, kind, range_])</p></td>
+<td><p>Measure the ENCE for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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-  <div class="section" id="netcal-metrics-mce">
-<h1>netcal.metrics.MCE<a class="headerlink" href="#netcal-metrics-mce" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.metrics.MCE">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.metrics.</code><code class="sig-name descname">MCE</code><span class="sig-paren">(</span><em class="sig-param">bins: Union[int</em>, <em class="sig-param">Iterable[int]] = 10</em>, <em class="sig-param">equal_intervals: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">sample_threshold: int = 1</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.MCE" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.Miscalibration._Miscalibration</span></code></p>
-<p>Maximum Calibration Error (MCE).
-This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1">1</a> or as Detection Maximum calibration error (D-MCE) on
-object detection <a class="footnote-reference brackets" href="#id4" id="id2">2</a>. This metrics measures the maximum difference between accuracy and confidence over all bins
-by grouping all samples into <span class="math notranslate nohighlight">\(K\)</span> bins and calculating</p>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.metrics.html#metrics-package-to-measure-miscalibration">Metrics Package to Measure Miscalibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.metrics.html#available-classes">Available classes</a><ul class="current">
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+<li class="toctree-l4"><a class="reference internal" href="#netcal.metrics.MCE"><code class="docutils literal notranslate"><span class="pre">MCE</span></code></a></li>
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+  <section id="netcal-metrics-mce">
+<h1>netcal.metrics.MCE<a class="headerlink" href="#netcal-metrics-mce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.MCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">MCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.MCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Maximum Calibration Error (MCE) for classification and Detection Maximum Calibration Error (D-MCE) for
+object detection or segmentation.
+This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> or as Detection Maximum calibration error (D-MCE) on
+object detection <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. This metrics measures the maximum difference between accuracy and confidence over all bins
+by grouping all samples into <span class="math notranslate nohighlight">\(B\)</span> bins and calculating</p>
 <div class="math notranslate nohighlight">
-\[MCE = \max_{i \in \{1, ..., K\}} |\text{acc}_i - \text{conf}_i| ,\]</div>
-<p>where <span class="math notranslate nohighlight">\(\text{acc}_i\)</span> and <span class="math notranslate nohighlight">\(\text{conf}_i\)</span> denote the accuracy and average confidence in the i-th bin.</p>
+\[MCE = \max_{b \in \{1, ..., B\}} |\text{acc}(b) - \text{conf}(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{acc}(b)\)</span> and <span class="math notranslate nohighlight">\(\text{conf}(b)\)</span> denote the accuracy and average confidence in the b-th bin.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the Histogram Binning.
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the MCE.
 On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
 If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
 <li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
@@ -75,234 +220,90 @@ <h1>netcal.metrics.MCE<a class="headerlink" href="#netcal-metrics-mce" title="Pe
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id3"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
 “Obtaining well calibrated probabilities using bayesian binning.”
 Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
 <a class="reference external" href="https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958">Get source online</a></p>
-</dd>
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
 The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 <a class="reference external" href="https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf">Get source online</a></p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
 <td><p>Constructor.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
 <td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, ...])</p></td>
 <td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
 <td><p>Check input data.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, …)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
 <td><p>Determine miscalibration based on passed histograms.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
 <td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.metrics.MCE.binning">
-<code class="sig-name descname">binning</code><span class="sig-paren">(</span><em class="sig-param">bin_bounds: List</em>, <em class="sig-param">samples: numpy.ndarray</em>, <em class="sig-param">*values: Iterable</em>, <em class="sig-param">nan: float = 0.0</em><span class="sig-paren">)</span> &#x2192; Tuple<a class="headerlink" href="#netcal.metrics.MCE.binning" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform binning on value (and all additional values passed) based on samples.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>bin_bounds</strong> (<em>list</em><em>, </em><em>length=samples.shape</em><em>[</em><em>1</em><em>]</em>) – Binning boundaries used for each dimension given in ‘samples’ parameter.</p></li>
-<li><p><strong>samples</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – Array used to group all samples into bins.</p></li>
-<li><p><strong>*values</strong> (<em>instances np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>1</em><em>)</em>) – Arrays whose values are binned.</p></li>
-<li><p><strong>nan</strong> (<em>float</em><em>, </em><em>optional default: 0.0</em>) – If a bin has no samples or less than defined sample_threshold, the according bin is marked as
-NaN. Specify fill float to insert instead of NaN.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length equal to the amount of passed value arrays with binning schemes and an additional histogram</em></p></li>
-<li><p><em>with number of samples in each bin as well as an index tuple containing the bin indices.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.MCE.measure">
-<code class="sig-name descname">measure</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None, return_map: bool = False, return_num_samples: bool = False, return_uncertainty_map: bool = False</em><span class="sig-paren">)</span> &#x2192; Union[float, Tuple]<a class="headerlink" href="#netcal.metrics.MCE.measure" title="Permalink to this definition">¶</a></dt>
-<dd><p>Measure calibration by given predictions with confidence and the according ground truth.
-Assume binary predictions with y=1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>iterable of np.ndarray</em><em>, or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes/n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>iterable of np.ndarray with same length as X</em><em> or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.</p></li>
-<li><p><strong>batched</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – Multiple predictions can be evaluated at once (e.g. cross-validation examinations) using batched-mode.
-All predictions given by X and y are separately evaluated and their results are averaged afterwards
-for visualization.</p></li>
-<li><p><strong>uncertainty</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – <p>Define uncertainty handling if input X has been sampled e.g. by Monte-Carlo dropout or similar methods
-that output an ensemble of predictions per sample. Choose one of the following options:
-- flatten:  treat everything as a separate prediction - this option will yield into a slightly better</p>
-<blockquote>
-<div><p>calibration performance but without the visualization of a prediction interval.</p>
-</div></blockquote>
-<ul>
-<li><dl class="simple">
-<dt>mean:     compute Monte-Carlo integration to obtain a simple confidence estimate for a sample</dt><dd><p>(mean) with a standard deviation that is visualized.</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p></li>
-<li><p><strong>return_map</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, return map with miscalibration metric separated into all remaining dimension bins.</p></li>
-<li><p><strong>return_num_samples</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, also return the number of samples in each bin.</p></li>
-<li><p><strong>return_uncertainty_map</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, also return the average deviation of the confidence within each bin.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Always returns Maximum Calibration Error.
-If ‘return_map’ is True, return tuple and append miscalibration map over all bins.
-If ‘return_num_samples’ is True, return tuple and append the number of samples in each bin (excluding confidence dimension).
-If ‘return_uncertainty’ is True, return tuple and append the average standard deviation of confidence within each bin (excluding confidence dimension).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>float or tuple of (float, np.ndarray, [np.ndarray, [np.ndarray]])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.MCE.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None</em><span class="sig-paren">)</span> &#x2192; Tuple[List[numpy.ndarray], List[numpy.ndarray], List[numpy.ndarray], List, int]<a class="headerlink" href="#netcal.metrics.MCE.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Check input data. For detailed documentation of the input parameters, check “_measure” method.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.MCE.process">
-<code class="sig-name descname">process</code><span class="sig-paren">(</span><em class="sig-param">metric: str</em>, <em class="sig-param">acc_hist: numpy.ndarray</em>, <em class="sig-param">conf_hist: numpy.ndarray</em>, <em class="sig-param">variance_hist: numpy.ndarray</em>, <em class="sig-param">num_samples_hist: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; Tuple[float, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]<a class="headerlink" href="#netcal.metrics.MCE.process" title="Permalink to this definition">¶</a></dt>
-<dd><p>Determine miscalibration based on passed histograms.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>metric</strong> (<em>str</em>) – Identifier to specify the used metric. Must be one of ‘ace’, ‘ece’ or ‘mce’.</p></li>
-<li><p><strong>acc_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average accuracy in each bin.</p></li>
-<li><p><strong>conf_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average confidence in each bin.</p></li>
-<li><p><strong>variance_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average variance in each bin. This array is currently not used but
-might be utilized in the future.</p></li>
-<li><p><strong>num_samples_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with number of samples in each bin.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length 6 (miscalibration score, miscalibration map, accuracy map, confidence map, variance map, num samples map)</em></p></li>
-<li><p><em>All maps without confidence dimension.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.MCE.reduce">
-<code class="sig-name descname">reduce</code><span class="sig-paren">(</span><em class="sig-param">histogram: numpy.ndarray</em>, <em class="sig-param">distribution: numpy.ndarray</em>, <em class="sig-param">axis: int</em>, <em class="sig-param">reduce_result: Tuple = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.MCE.reduce" title="Permalink to this definition">¶</a></dt>
-<dd><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.
-If ‘reduce_result’ is given, reuse the data distribution of the previous result instead of the distribution
-given by ‘distribution’ parameter.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.MCE.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[Iterable[int], int]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.metrics.MCE.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter
-‘axes_to_keep’ even if the dimension is of size 1.</p>
 </dd></dl>
 
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-  <div class="section" id="netcal-metrics-mmce">
-<h1>netcal.metrics.MMCE<a class="headerlink" href="#netcal-metrics-mmce" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.metrics.MMCE">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.metrics.</code><code class="sig-name descname">MMCE</code><span class="sig-paren">(</span><em class="sig-param">detection: bool = False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.MMCE" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
-<p>Maximum Mean Calibration Error (MMCE) <a class="footnote-reference brackets" href="#id2" id="id1">1</a>.
-A differentiable approximation to the Expected Calibration Error (ECE) using a
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.metrics.html#metrics-package-to-measure-miscalibration">Metrics Package to Measure Miscalibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.metrics.html#available-classes">Available classes</a><ul class="current">
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+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.metrics.MMCE</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.metrics.MMCE"><code class="docutils literal notranslate"><span class="pre">MMCE</span></code></a></li>
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+  <section id="netcal-metrics-mmce">
+<h1>netcal.metrics.MMCE<a class="headerlink" href="#netcal-metrics-mmce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.MMCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">MMCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.MMCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Maximum Mean Calibration Error (MMCE).
+The MMCE <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is a differentiable approximation to the Expected Calibration Error (ECE) using a
 reproducing _kernel Hilbert space (RKHS).
-Using a dataset <span class="math notranslate nohighlight">\(\mathcal{D}\)</span> of size <span class="math notranslate nohighlight">\(N\)</span> consisting of the ground truth labels <span class="math notranslate nohighlight">\(\hat{y} \in \{1, ..., K \}\)</span>
-with input <span class="math notranslate nohighlight">\(\hat{y} \in \mathcal{X}\)</span>, the MMCE is calculated by using a scoring classifier <span class="math notranslate nohighlight">\(\hat{p}=h(x)\)</span>
-that returns the highest probability for a certain class in conjunction with the predicted label
-information <span class="math notranslate nohighlight">\(y \in \{1, ..., K \}\)</span> and is defined by</p>
+Using a dataset <span class="math notranslate nohighlight">\(\mathcal{D}\)</span> of size <span class="math notranslate nohighlight">\(N\)</span> consisting of the ground truth labels
+<span class="math notranslate nohighlight">\(\hat{y} \in \{1, ..., K \}\)</span> with input <span class="math notranslate nohighlight">\(x \in \mathcal{X}\)</span>, the MMCE is calculated by using
+a scoring classifier <span class="math notranslate nohighlight">\(\hat{p}=h(x)\)</span> that returns the highest probability for a certain class in conjunction
+with the predicted label information <span class="math notranslate nohighlight">\(y \in \{1, ..., K \}\)</span> and is defined by</p>
 <div class="math notranslate nohighlight">
 \[MMCE = \sqrt{\sum_{i, j \in \mathcal{D}} \frac{1}{N^2}(\mathbb{1}(\hat{y}_i = y_i) - \hat{p}_i) (\mathbb{1}(\hat{y}_j = y_j) - \hat{p}_j)k(\hat{p}_i, \hat{p}_j)} ,\]</div>
 <p>with <span class="math notranslate nohighlight">\(\mathbb{1}(*)\)</span> as the indicator function and a Laplacian _kernel <span class="math notranslate nohighlight">\(k\)</span> defined by</p>
 <div class="math notranslate nohighlight">
 \[k(\hat{p}_i, \hat{p}_j) = \exp(-2.5 |\hat{p}_i - \hat{p}_j|) .\]</div>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – Detection mode is currently not supported for MMCE!
 If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
 with shape (n_samples, [n_classes]).
@@ -73,20 +217,17 @@ <h1>netcal.metrics.MMCE<a class="headerlink" href="#netcal-metrics-mmce" title="
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain:
 “Trainable calibration measures for neural networks from _kernel mean embeddings.”
 International Conference on Machine Learning. 2018.
 <a class="reference external" href="http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf">Get source online</a>.</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([detection])</p></td>
 <td><p>Constructor.</p></td>
@@ -96,94 +237,48 @@ <h1>netcal.metrics.MMCE<a class="headerlink" href="#netcal-metrics-mmce" title="
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.metrics.MMCE.measure">
-<code class="sig-name descname">measure</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.MMCE.measure" title="Permalink to this definition">¶</a></dt>
-<dd><p>Measure calibration by given predictions with confidence and the according ground truth.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>iterable of np.ndarray</em><em>, or </em><em>np.ndarray of shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.</p></li>
-<li><p><strong>y</strong> (<em>iterable of np.ndarray with same length as X</em><em> or </em><em>np.ndarray of shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
-If iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.</p></li>
-<li><p><strong>batched</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – Multiple predictions can be evaluated at once (e.g. cross-validation examinations) using batched-mode.
-All predictions given by X and y are separately evaluated and their results are averaged afterwards
-for visualization.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Returns Maximum Mean Calibration Error.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>float</p>
-</dd>
-</dl>
 </dd></dl>
 
-</dd></dl>
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+  <section id="netcal-metrics-nll">
+<h1>netcal.metrics.NLL<a class="headerlink" href="#netcal-metrics-nll" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.NLL">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">NLL</span></span><a class="headerlink" href="#netcal.metrics.NLL" title="Permalink to this definition">¶</a></dt>
+<dd><p>Negative log likelihood (NLL) for probabilistic regression models.
+If a probabilistic forecaster outputs a probability density function (PDF) <span class="math notranslate nohighlight">\(f_Y(y)\)</span> targeting the ground-truth
+<span class="math notranslate nohighlight">\(y\)</span>, the negative log likelihood is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{NLL} = -\sum^N_{n=1} \log\big(f_Y(y)\big) ,\]</div>
+<p>with <span class="math notranslate nohighlight">\(N\)</span> as the number of samples within the examined data set.</p>
+<p><strong>Note:</strong> the input field for the standard deviation might also be given as quadratic NumPy arrays of shape
+(n, d, d) with d dimensions. In this case, this method asserts covariance matrices as input
+for each sample and the NLL is calculated for multivariate distributions.</p>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, *[, kind, reduction])</p></td>
+<td><p>Measures the negative log likelihood (NLL) for probabilistic regression models.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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-  <div class="section" id="netcal-metrics-picp">
-<h1>netcal.metrics.PICP<a class="headerlink" href="#netcal-metrics-picp" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.metrics.PICP">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.metrics.</code><code class="sig-name descname">PICP</code><span class="sig-paren">(</span><em class="sig-param">bins: Union[int</em>, <em class="sig-param">Iterable[int]] = 10</em>, <em class="sig-param">equal_intervals: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">sample_threshold: int = 1</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.PICP" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.Miscalibration._Miscalibration</span></code></p>
-<p>Compute Prediction Interval Coverage Probability (PICP) <a class="footnote-reference brackets" href="#id3" id="id1">1</a>,[2]_ and Mean Prediction Interval Width (MPIW) <a class="footnote-reference brackets" href="#id4" id="id2">2</a>.
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+<li class="toctree-l4"><a class="reference internal" href="#netcal.metrics.PICP"><code class="docutils literal notranslate"><span class="pre">PICP</span></code></a></li>
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+  <section id="netcal-metrics-picp">
+<h1>netcal.metrics.PICP<a class="headerlink" href="#netcal-metrics-picp" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.PICP">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">PICP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.PICP" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute Prediction Interval Coverage Probability (PICP) and Mean Prediction Interval Width (MPIW).
+These metrics have been proposed by <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
 This metric is used for Bayesian models to determine the quality of the uncertainty estimates.
 In Bayesian mode, an uncertainty estimate is attached to each sample. The PICP measures the probability, that
 the true (observed) accuracy falls into the p% prediction interval. The uncertainty is well-calibrated, if
 the PICP is equal to p%. Simultaneously, the MPIW measures the mean width of all prediction intervals to evaluate
 the sharpness of the uncertainty estimates.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the Histogram Binning.
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the PICP.
 On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
 If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
 <li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
@@ -74,234 +218,90 @@ <h1>netcal.metrics.PICP<a class="headerlink" href="#netcal-metrics-picp" title="
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id3"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Kuleshov, V.; Fenner, N. &amp; Ermon, S.:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Kuleshov, V.; Fenner, N. &amp; Ermon, S.:
 “Accurate Uncertainties for Deep Learning Using Calibrated Regression.”
 International Conference on Machine Learning (ICML), 2018
 <a class="reference external" href="http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf">Get source online</a></p>
-</dd>
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez:
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez:
 “Quality of Uncertainty Quantification for Bayesian Neural Network Inference.”
 Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019
 <a class="reference external" href="https://arxiv.org/pdf/1906.09686.pdf">Get source online</a></p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
 <td><p>Constructor.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">accuracy</span></code>(X, y[, batched, uncertainty])</p></td>
-<td><p>Measure the accuracy of each point by binning.</p></td>
-</tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
 <td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, p, use_hpd, batched, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction])</p></td>
 <td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
 <td><p>Check input data.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, …)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
 <td><p>Determine miscalibration based on passed histograms.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
 <td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.metrics.PICP.accuracy">
-<code class="sig-name descname">accuracy</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = 'mean'</em><span class="sig-paren">)</span> &#x2192; Tuple[List[numpy.ndarray], List[numpy.ndarray], List[numpy.ndarray], List[numpy.ndarray], List, int]<a class="headerlink" href="#netcal.metrics.PICP.accuracy" title="Permalink to this definition">¶</a></dt>
-<dd><p>Measure the accuracy of each point by binning.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.PICP.binning">
-<code class="sig-name descname">binning</code><span class="sig-paren">(</span><em class="sig-param">bin_bounds: List</em>, <em class="sig-param">samples: numpy.ndarray</em>, <em class="sig-param">*values: Iterable</em>, <em class="sig-param">nan: float = 0.0</em><span class="sig-paren">)</span> &#x2192; Tuple<a class="headerlink" href="#netcal.metrics.PICP.binning" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform binning on value (and all additional values passed) based on samples.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>bin_bounds</strong> (<em>list</em><em>, </em><em>length=samples.shape</em><em>[</em><em>1</em><em>]</em>) – Binning boundaries used for each dimension given in ‘samples’ parameter.</p></li>
-<li><p><strong>samples</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – Array used to group all samples into bins.</p></li>
-<li><p><strong>*values</strong> (<em>instances np.ndarray of shape</em><em> (</em><em>n_samples</em><em>, </em><em>1</em><em>)</em>) – Arrays whose values are binned.</p></li>
-<li><p><strong>nan</strong> (<em>float</em><em>, </em><em>optional default: 0.0</em>) – If a bin has no samples or less than defined sample_threshold, the according bin is marked as
-NaN. Specify fill float to insert instead of NaN.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length equal to the amount of passed value arrays with binning schemes and an additional histogram</em></p></li>
-<li><p><em>with number of samples in each bin as well as an index tuple containing the bin indices.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.metrics.PICP.measure">
-<code class="sig-name descname">measure</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], p: float = 0.05, use_hpd: bool = True, batched: bool = False, uncertainty: str = 'mean', return_map: bool = False</em><span class="sig-paren">)</span> &#x2192; NamedTuple<a class="headerlink" href="#netcal.metrics.PICP.measure" title="Permalink to this definition">¶</a></dt>
-<dd><p>Measure calibration by given predictions with confidence and the according ground truth.
-Assume binary predictions with y=1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>iterable of np.ndarray</em><em>, or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes/n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>iterable of np.ndarray with same length as X</em><em> or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.</p></li>
-<li><p><strong>p</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 0.05</em>) – Confidence level.</p></li>
-<li><p><strong>use_hpd</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, use highest posterior density (HPD) interval to determine the prediction interval width.
-Use variance with Gaussian assumption otherwise.</p></li>
-<li><p><strong>batched</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – Multiple predictions can be evaluated at once (e.g. cross-validation examinations) using batched-mode.
-All predictions given by X and y are separately evaluated and their results are averaged afterwards
-for visualization.</p></li>
-<li><p><strong>uncertainty</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;mean&quot;</em>) – Mode to measure mean estimate and uncertainty of the samples in Bayesian mode. Must be one
-of “mean” (mean of all samples), “mode” (mode of all samples), “median” (median of all samples) or
-“flatten” (no uncertainty will be computed, all samples are seen as independent predictions).</p></li>
-<li><p><strong>return_map</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, return map with PICP and MPIW metric separated into all remaining dimension bins.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>Namedtuple PICPResult with fields “picp” and “mpiw”, where each field either holds the PICP/MPIW score</em></p></li>
-<li><p><em>or a tuple of (float, np.ndarray)</em> – Always returns a named tuple with PICP (prediction interval coverage probability) and MPIW
-(mean prediction interval width).
-If ‘return_map’ is True, each field holds a tuple for the metric itself and the PICP/MPIW distribution
-over all bins.</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.PICP.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None</em><span class="sig-paren">)</span> &#x2192; Tuple[List[numpy.ndarray], List[numpy.ndarray], List[numpy.ndarray], List, int]<a class="headerlink" href="#netcal.metrics.PICP.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Check input data. For detailed documentation of the input parameters, check “_measure” method.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.PICP.process">
-<code class="sig-name descname">process</code><span class="sig-paren">(</span><em class="sig-param">metric: str</em>, <em class="sig-param">acc_hist: numpy.ndarray</em>, <em class="sig-param">conf_hist: numpy.ndarray</em>, <em class="sig-param">variance_hist: numpy.ndarray</em>, <em class="sig-param">num_samples_hist: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; Tuple[float, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray]<a class="headerlink" href="#netcal.metrics.PICP.process" title="Permalink to this definition">¶</a></dt>
-<dd><p>Determine miscalibration based on passed histograms.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>metric</strong> (<em>str</em>) – Identifier to specify the used metric. Must be one of ‘ace’, ‘ece’ or ‘mce’.</p></li>
-<li><p><strong>acc_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average accuracy in each bin.</p></li>
-<li><p><strong>conf_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average confidence in each bin.</p></li>
-<li><p><strong>variance_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with average variance in each bin. This array is currently not used but
-might be utilized in the future.</p></li>
-<li><p><strong>num_samples_hist</strong> (<em>np.ndarray of shape</em><em> (</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>n_bins</em><em>, </em><em>[</em><em>..</em><em>]</em><em>]</em><em>]</em><em>)</em>) – Histogram with number of samples in each bin.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>tuple of length 6 (miscalibration score, miscalibration map, accuracy map, confidence map, variance map, num samples map)</em></p></li>
-<li><p><em>All maps without confidence dimension.</em></p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.PICP.reduce">
-<code class="sig-name descname">reduce</code><span class="sig-paren">(</span><em class="sig-param">histogram: numpy.ndarray</em>, <em class="sig-param">distribution: numpy.ndarray</em>, <em class="sig-param">axis: int</em>, <em class="sig-param">reduce_result: Tuple = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.PICP.reduce" title="Permalink to this definition">¶</a></dt>
-<dd><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.
-If ‘reduce_result’ is given, reuse the data distribution of the previous result instead of the distribution
-given by ‘distribution’ parameter.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.metrics.PICP.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[Iterable[int], int]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.metrics.PICP.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter
-‘axes_to_keep’ even if the dimension is of size 1.</p>
-</dd></dl>
-
-</dd></dl>
-
-</div>
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+  <section id="netcal-metrics-pinballloss">
+<h1>netcal.metrics.PinballLoss<a class="headerlink" href="#netcal-metrics-pinballloss" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.PinballLoss">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">PinballLoss</span></span><a class="headerlink" href="#netcal.metrics.PinballLoss" title="Permalink to this definition">¶</a></dt>
+<dd><p>Synonym for Quantile loss. For documentation, see <a class="reference internal" href="../_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QuantileLoss.html#netcal.metrics.regression.QuantileLoss" title="netcal.metrics.regression.QuantileLoss"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.regression.QuantileLoss</span></code></a>.</p>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-metrics-qce">
+<h1>netcal.metrics.QCE<a class="headerlink" href="#netcal-metrics-qce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.QCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">QCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">marginal</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.QCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Marginal Quantile Calibration Error (M-QCE) and Conditional Quantile Calibration Error (C-QCE) which both measure
+the gap between predicted quantiles and observed quantile coverage also for multivariate distributions.
+The M-QCE and C-QCE have originally been proposed by <a class="footnote-reference brackets" href="#id6" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+The derivation of both metrics are based on
+the Normalized Estimation Error Squared (NEES) known from object tracking <a class="footnote-reference brackets" href="#id7" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+The derivation of both metrics is shown in the following.</p>
+<p><strong>Definition of standard NEES:</strong>
+Given mean prediction <span class="math notranslate nohighlight">\(\hat{\boldsymbol{y}} \in \mathbb{R}^M\)</span>, ground-truth
+<span class="math notranslate nohighlight">\(\boldsymbol{y} \in \mathbb{R}^M\)</span>, and
+estimated covariance matrix <span class="math notranslate nohighlight">\(\hat{\boldsymbol{\Sigma}} \in \mathbb{R}^{M \times M}\)</span> using
+<span class="math notranslate nohighlight">\(M\)</span> dimensions, the NEES is defined as</p>
+<div class="math notranslate nohighlight">
+\[\epsilon = (\boldsymbol{y} - \hat{\boldsymbol{y}})^\top \hat{\boldsymbol{\Sigma}}^{-1}
+(\boldsymbol{y} - \hat{\boldsymbol{y}}) .\]</div>
+<p>The average NEES is defined as the mean error over <span class="math notranslate nohighlight">\(N\)</span> trials in a Monte-Carlo simulation for
+Kalman-Filter testing, so that</p>
+<div class="math notranslate nohighlight">
+\[\bar{\epsilon} = \frac{1}{N} \sum^N_{i=1} \epsilon_i .\]</div>
+<p>Under the condition, that <span class="math notranslate nohighlight">\(\mathbb{E}[\boldsymbol{y} - \hat{\boldsymbol{y}}] = \boldsymbol{0}\)</span> (zero mean),
+a <span class="math notranslate nohighlight">\(\chi^2\)</span>-test is performed to evaluate the estimated uncertainty. This test is accepted, if</p>
+<div class="math notranslate nohighlight">
+\[\bar{\epsilon} \leq \chi^2_M(\tau),\]</div>
+<p>where <span class="math notranslate nohighlight">\(\chi^2_M(\tau)\)</span> is the PPF score obtained by a <span class="math notranslate nohighlight">\(\chi^2\)</span> distribution
+with <span class="math notranslate nohighlight">\(M\)</span> degrees of freedom, for a certain quantile level <span class="math notranslate nohighlight">\(\tau \in [0, 1]\)</span>.</p>
+<p><strong>Marginal Quantile Calibration Error (M-QCE):</strong>
+In the case of regression calibration testing, we are interested in the gap between predicted quantile levels and
+observed quantile coverage probability for a certain set of quantile levels. We assert <span class="math notranslate nohighlight">\(N\)</span> observations of our
+test set that are used to estimate the NEES, so that we can compute the expected deviation between predicted
+quantile level and observed quantile coverage by</p>
+<div class="math notranslate nohighlight">
+\[\text{M-QCE}(\tau) := \mathbb{E} \Big[ \big| \mathbb{P} \big( \epsilon \leq \chi^2_M(\tau) \big) - \tau \big| \Big] ,\]</div>
+<p>which is the definition of the Marginal Quantile Calibration Error (M-QCE) <a class="footnote-reference brackets" href="#id6" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+The M-QCE is calculated by</p>
+<div class="math notranslate nohighlight">
+\[\text{M-QCE}(\tau) = \Bigg| \frac{1}{N} \sum^N_{n=1} \mathbb{1} \big( \epsilon_n \leq \chi^2_M(\tau) \big) - \tau \Bigg|\]</div>
+<p><strong>Conditional Quantile Calibration Error (C-QCE):</strong>
+The M-QCE measures the marginal calibration error which is more suitable to test for <em>quantile calibration</em>.
+However, similar to <a class="reference internal" href="../_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.UCE.html#netcal.metrics.regression.UCE" title="netcal.metrics.regression.UCE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.regression.UCE</span></code></a> and <a class="reference internal" href="../_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.ENCE.html#netcal.metrics.regression.ENCE" title="netcal.metrics.regression.ENCE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.regression.ENCE</span></code></a>,
+we want to induce a dependency on the estimated covariance, since we require
+that</p>
+<div class="math notranslate nohighlight">
+\[ \begin{align}\begin{aligned}&amp;\mathbb{E}[(\boldsymbol{y} - \hat{\boldsymbol{y}})(\boldsymbol{y} - \hat{\boldsymbol{y}})^\top |
+\hat{\boldsymbol{\Sigma}} = \boldsymbol{\Sigma}] = \boldsymbol{\Sigma},\\&amp;\forall \boldsymbol{\Sigma} \in \mathbb{R}^{M \times M}, \boldsymbol{\Sigma} \succcurlyeq 0,
+\boldsymbol{\Sigma}^\top = \boldsymbol{\Sigma} .\end{aligned}\end{align} \]</div>
+<p>To estimate the a <em>covariance</em> dependent QCE, we apply a binning scheme (similar to the
+<a class="reference internal" href="../_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE" title="netcal.metrics.confidence.ECE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.confidence.ECE</span></code></a>) over the square root of the <em>standardized generalized variance</em> (SGV) <a class="footnote-reference brackets" href="#id8" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>,
+that is defined as</p>
+<div class="math notranslate nohighlight">
+\[\sigma_G = \sqrt{\text{det}(\hat{\boldsymbol{\Sigma}})^{\frac{1}{M}}} .\]</div>
+<p>Using the generalized standard deviation, it is possible to get a summarized statistic across different
+combinations of correlations to denote the distribution’s dispersion. Thus, the Conditional Quantile Calibration
+Error (C-QCE) <a class="footnote-reference brackets" href="#id6" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{C-QCE}(\tau) := \mathbb{E}_{\sigma_G, X}\Big[\Big|\mathbb{P}\big(\epsilon \leq \chi^2_M(\tau) | \sigma_G\big) - \tau \Big|\Big] ,\]</div>
+<p>To approximate the expectation over the generalized standard deviation, we use a binning scheme with <span class="math notranslate nohighlight">\(B\)</span> bins
+(similar to the ECE) and <span class="math notranslate nohighlight">\(N_b\)</span> samples per bin to compute the weighted sum across all bins, so that</p>
+<div class="math notranslate nohighlight">
+\[\text{C-QCE}(\tau) \approx \sum^B_{b=1} \frac{N_b}{N} | \text{freq}(b) - \tau |\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{freq}(b)\)</span> is the coverage frequency within bin <span class="math notranslate nohighlight">\(b\)</span> and given by</p>
+<div class="math notranslate nohighlight">
+\[\text{freq}(b) = \frac{1}{N_b} \sum_{n \in \mathcal{M}_b} \mathbb{1}\big(\epsilon_i \leq \chi^2_M(\tau)\big) ,\]</div>
+<p>with <span class="math notranslate nohighlight">\(\mathcal{M}_b\)</span> as the set of indices within bin <span class="math notranslate nohighlight">\(b\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used for the internal binning.
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>marginal</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, compute the M-QCE. This is the marginal probability over all samples falling into the desired
+quantiles. If False, use the C-QCE.
+The C-QCE uses a binning scheme by the gerneralized standard deviation to measure the conditional probability
+over all samples falling into the desired quantiles w.r.t. the generalized standard deviation.</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id3">2</a>,<a role="doc-backlink" href="#id5">3</a>)</span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Y. Bar-Shalom, X. R. Li, and T. Kirubarajan:
+“Estimation with applications to tracking and navigation.”
+Theory algorithms and software. John Wiley &amp; Sons, 2004.</p>
+</aside>
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">3</a><span class="fn-bracket">]</span></span>
+<p>A. SenGupta:
+“Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions.”
+Journal of Multivariate Analysis, vol. 23, no. 2, pp. 209–219, 1987.
+<a class="reference external" href="https://pdf.sciencedirectassets.com/272481/1-s2.0-S0047259X87X8001X/1-s2.0-0047259X87901539/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEB0aCXVzLWVhc3QtMSJHMEUCIAo6pl1vIu8%2F8ZEnEt6OKsA92ajSFy8%2BgjC8Tt9Tr360AiEAiVljbWcKBWAkrSpyT3LCCiX1Wug9gDf9WqxygiF%2B1G8q0gQIRhAEGgwwNTkwMDM1NDY4NjUiDLFU4Fzvuej7%2FpkSSCqvBNybwrdLhAP1yVFKRn0AQPK3G5t2wOY5ssTpqbS1HQzoz1EvOo%2BvWNeXPrWTo%2FhUvw8knQEWp9wA7a5wGdsbnmaBmCAWUFStKxSib9htTLAX1Ij5NCh%2ByA%2BiJwvPk4SXcRAJx4zQfJ8N%2FM2jcA3Lji7VPDYR8jNu7FfMd54veXYuqzUDoIdhVWIF4Czx0fwqngck9errYuNVSQCGSaW28m3%2BCr3%2FiePEQrXJcX0K7Q3z5D0%2FHGJvMsw%2FDqugg9gjWAFCquBO6EL9ircGBmzVsYnx8pKPZfa84aHZgGJPwvJp01o6qvUEdBZXbC5pmvDNAwIkguMahAHfNM3ffVDfyIVzRq1WrZIAKLYfgqFiGpNd3kGEUX5dGbSggAvxNXP7JX%2BifNsde9cIhzhqpjS0Z8BoOW8AGbXq9n15qEK%2F6xKJttpIhouxiadU6DtW%2BSDDFXDgdMVs1xU%2FE6dnWtl%2BQeA5VX4ITvTQMAjHOqu22lXEmOpHOmZ8fGKG5QTmz4iShixLGsgxpUMp2Wz%2F2OlCwt64m0sbI7zXr3YkUpyR019fs6IHJ28EVbeHsvp9xLrc5qltKHN3aoBmK4ZK0SFi%2FqHLhuz1HmWzCRQ0%2FkShcOXz80ttPlaHuX54VdVptvSy%2F1obsurjYuaR2HG9rO3lIneMgwKwwodZcKlu%2Fyo4WUCIk%2FhfKZrOWqVfAqqFPjWomg4CX787OIoqP%2FTz8H6sueGWk7HoeJKgSIW4yEISjNkwpdH7lQY6qQHS3GFk4XwFQEzwimYc%2B59DxQowARFI3PgPN%2F4FzUV5OHhm5G8455Dzm4T6R6E1%2F%2B86lSLdpH9JCkbDXBPJndiHTqXwBUej4wSWPASAvqQ6neC1lcJAqimCB7zn17je6g1dCi80xg1rZ6qU0c5BGtRqsCAB2NZlNn8jul1%2BM%2BiBF8SLE4xoNnT5kwEI%2FnnY81jvJw1kf4DspI9S8sAI2Z3efRca%2FBTIwgVw&amp;X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20220701T132912Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=300&amp;X-Amz-Credential=ASIAQ3PHCVTYZE6GY4EQ%2F20220701%2Fus-east-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=416cca57ae51cdc7c137e60fa5eba2ba651152e29e6b3485feeeb45f66aaeebb&amp;hash=f03a242d7d2e0652dfaa7c5e3fb713736b321247242986106eaa5412f136af12&amp;host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&amp;pii=0047259X87901539&amp;tid=spdf-4216aa85-a41c-4358-8d5e-3e877785fe29&amp;sid=4e9c65da63ee0949f79bfc42fc03dd438d5egxrqb&amp;type=client&amp;ua=4d545d0256065c055303&amp;rr=723f7d3c3edc2199">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, marginal, sample_threshold])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction, ...])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
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+<li class="toctree-l4"><a class="reference internal" href="#netcal.metrics.QuantileLoss"><code class="docutils literal notranslate"><span class="pre">QuantileLoss</span></code></a></li>
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+  <section id="netcal-metrics-quantileloss">
+<h1>netcal.metrics.QuantileLoss<a class="headerlink" href="#netcal-metrics-quantileloss" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.QuantileLoss">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">QuantileLoss</span></span><a class="headerlink" href="#netcal.metrics.QuantileLoss" title="Permalink to this definition">¶</a></dt>
+<dd><p>Pinball aka quantile loss within regression calibration to test for <em>quantile calibration</em> of a probabilistic
+regression model. The Pinball loss is an asymmetric loss that measures the quality of the predicted
+quantiles. Given a probabilistic regression model that outputs a probability density function (PDF) <span class="math notranslate nohighlight">\(f_Y(y)\)</span>
+targeting the ground-truth <span class="math notranslate nohighlight">\(y\)</span>, we further denote the cumulative as <span class="math notranslate nohighlight">\(F_Y(y)\)</span> and the (inverse)
+percent point function (PPF) as <span class="math notranslate nohighlight">\(F_Y^{-1}(\tau)\)</span> for a certain quantile level <span class="math notranslate nohighlight">\(\tau \in [0, 1]\)</span>.</p>
+<p>The Pinball loss is given by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}L_{\text{Pin}}(\tau) =
+\begin{cases}
+     \big( y-F_Y^{-1}(\tau) \big)\tau \quad &amp;\text{if } y \geq F_Y^{-1}(\tau)\\
+     \big( F_Y^{-1}(\tau)-y \big)(1-\tau) \quad &amp;\text{if } y &lt; F_Y^{-1}(\tau)
+\end{cases} .\end{split}\]</div>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
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+  <section id="netcal-metrics-uce">
+<h1>netcal.metrics.UCE<a class="headerlink" href="#netcal-metrics-uce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.UCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.</span></span><span class="sig-name descname"><span class="pre">UCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.UCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Uncertainty Calibration Error (UCE) for a regression calibration evaluation to test for
+<em>variance calibration</em>. A probabilistic regression model takes <span class="math notranslate nohighlight">\(X\)</span> as input and outputs a
+mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and a variance <span class="math notranslate nohighlight">\(\sigma_Y^2(X)\)</span> targeting the ground-truth <span class="math notranslate nohighlight">\(y\)</span>.
+Similar to the <a class="reference internal" href="../_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE" title="netcal.metrics.confidence.ECE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.confidence.ECE</span></code></a>, the UCE applies a binning scheme with <span class="math notranslate nohighlight">\(B\)</span> bins
+over the predicted variance <span class="math notranslate nohighlight">\(\sigma_Y^2(X)\)</span> and measures the absolute difference
+between mean squared error (MSE) and mean variance (RMV) <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+Thus, the UCE <a class="footnote-reference brackets" href="#id3" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{UCE} := \sum^B_{b=1} \frac{N_b}{N} |MSE(b) - MV(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(MSE(b)\)</span> and <span class="math notranslate nohighlight">\(MV(b)\)</span> are the mean squared error and the mean variance within
+bin <span class="math notranslate nohighlight">\(b\)</span>, respectively, and <span class="math notranslate nohighlight">\(N_b\)</span> is the number of samples within bin <span class="math notranslate nohighlight">\(b\)</span>.</p>
+<p>If multiple dimensions are given, the UCE is measured for each dimension separately.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the UCE binning.
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id2">2</a>)</span>
+<p>Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, sample_threshold])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, *[, kind, range_])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
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+  <section id="netcal-metrics-confidence-ace">
+<h1>netcal.metrics.confidence.ACE<a class="headerlink" href="#netcal-metrics-confidence-ace" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.confidence.ACE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.confidence.</span></span><span class="sig-name descname"><span class="pre">ACE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.confidence.ACE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Average Calibration Error (ACE) for classification and Detection Average Calibration Error (D-ACE) for
+object detection or segmentation.
+This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> or as Detection Average Calibration Error (D-ACE)
+<a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> on object detection tasks. This metrics measures the average difference between accuracy and confidence by
+grouping all samples into <span class="math notranslate nohighlight">\(B\)</span> bins and calculating</p>
+<div class="math notranslate nohighlight">
+\[ACE = \frac{1}{B} \sum_{b=1}^B |\text{acc}(b) - \text{conf}(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{acc}(b)\)</span> and <span class="math notranslate nohighlight">\(\text{conf}(b)\)</span> denote the accuracy and average confidence in the b-th bin.
+The main difference to <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.confidence.ECE</span></code> is that each bin is weighted equally.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the ACE.
+On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
+the number of samples in each bin.</p></li>
+<li><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
+with shape (n_samples, [n_classes]).
+If True, the input array ‘X’ is treated as a box predictions with several box features (at least
+box confidence must be present) with shape (n_samples, [n_box_features]).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi:
+“Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection.”
+Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.
+<a class="reference external" href="https://openreview.net/pdf?id=S1lG7aTnqQ">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+“Multivariate Confidence Calibration for Object Detection.”
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
+<a class="reference external" href="https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, ...])</p></td>
+<td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-metrics-confidence-ece">
+<h1>netcal.metrics.confidence.ECE<a class="headerlink" href="#netcal-metrics-confidence-ece" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.confidence.ECE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.confidence.</span></span><span class="sig-name descname"><span class="pre">ECE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.confidence.ECE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Expected Calibration Error (ECE) for classification and Detection Expected Calibration Error (D-ECE) for
+object detection or segmentation.
+This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> or as Detection Expected Calibration Error (D-ECE) on object
+detection tasks <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. This metrics measures the expected difference between accuracy/precision and confidence
+by grouping all samples (size <span class="math notranslate nohighlight">\(N\)</span>) into <span class="math notranslate nohighlight">\(B\)</span> bins, so that the ECE is computed by</p>
+<div class="math notranslate nohighlight">
+\[ECE = \sum_{b=1}^B \frac{N_b}{N} |\text{acc}(b) - \text{conf}(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{acc}(b)\)</span> and <span class="math notranslate nohighlight">\(\text{conf}(b)\)</span> denote the accuracy and average confidence in the i-th bin
+and <span class="math notranslate nohighlight">\(N_b\)</span> denote the number of samples in bin <span class="math notranslate nohighlight">\(b\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the Expected Calibration Error.
+On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
+the number of samples in each bin.</p></li>
+<li><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
+with shape (n_samples, [n_classes]).
+If True, the input array ‘X’ is treated as a box predictions with several box features (at least
+box confidence must be present) with shape (n_samples, [n_box_features]).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
+“Obtaining well calibrated probabilities using bayesian binning.”
+Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
+<a class="reference external" href="https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+“Multivariate Confidence Calibration for Object Detection.”
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
+<a class="reference external" href="https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf">Get source online</a>.</p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, ...])</p></td>
+<td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+<li class="toctree-l6"><a class="reference internal" href="#netcal.metrics.confidence.MCE"><code class="docutils literal notranslate"><span class="pre">MCE</span></code></a></li>
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+  <section id="netcal-metrics-confidence-mce">
+<h1>netcal.metrics.confidence.MCE<a class="headerlink" href="#netcal-metrics-confidence-mce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.confidence.MCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.confidence.</span></span><span class="sig-name descname"><span class="pre">MCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.confidence.MCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Maximum Calibration Error (MCE) for classification and Detection Maximum Calibration Error (D-MCE) for
+object detection or segmentation.
+This metric is used on classification <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> or as Detection Maximum calibration error (D-MCE) on
+object detection <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. This metrics measures the maximum difference between accuracy and confidence over all bins
+by grouping all samples into <span class="math notranslate nohighlight">\(B\)</span> bins and calculating</p>
+<div class="math notranslate nohighlight">
+\[MCE = \max_{b \in \{1, ..., B\}} |\text{acc}(b) - \text{conf}(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{acc}(b)\)</span> and <span class="math notranslate nohighlight">\(\text{conf}(b)\)</span> denote the accuracy and average confidence in the b-th bin.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the MCE.
+On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
+the number of samples in each bin.</p></li>
+<li><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
+with shape (n_samples, [n_classes]).
+If True, the input array ‘X’ is treated as a box predictions with several box features (at least
+box confidence must be present) with shape (n_samples, [n_box_features]).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht:
+“Obtaining well calibrated probabilities using bayesian binning.”
+Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
+<a class="reference external" href="https://www.aaai.org/ocs/index.php/AAAI/AAAI15/paper/download/9667/9958">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+“Multivariate Confidence Calibration for Object Detection.”
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
+<a class="reference external" href="https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched, uncertainty, ...])</p></td>
+<td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-metrics-confidence-mmce">
+<h1>netcal.metrics.confidence.MMCE<a class="headerlink" href="#netcal-metrics-confidence-mmce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.confidence.MMCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.confidence.</span></span><span class="sig-name descname"><span class="pre">MMCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.confidence.MMCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Maximum Mean Calibration Error (MMCE).
+The MMCE <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is a differentiable approximation to the Expected Calibration Error (ECE) using a
+reproducing _kernel Hilbert space (RKHS).
+Using a dataset <span class="math notranslate nohighlight">\(\mathcal{D}\)</span> of size <span class="math notranslate nohighlight">\(N\)</span> consisting of the ground truth labels
+<span class="math notranslate nohighlight">\(\hat{y} \in \{1, ..., K \}\)</span> with input <span class="math notranslate nohighlight">\(x \in \mathcal{X}\)</span>, the MMCE is calculated by using
+a scoring classifier <span class="math notranslate nohighlight">\(\hat{p}=h(x)\)</span> that returns the highest probability for a certain class in conjunction
+with the predicted label information <span class="math notranslate nohighlight">\(y \in \{1, ..., K \}\)</span> and is defined by</p>
+<div class="math notranslate nohighlight">
+\[MMCE = \sqrt{\sum_{i, j \in \mathcal{D}} \frac{1}{N^2}(\mathbb{1}(\hat{y}_i = y_i) - \hat{p}_i) (\mathbb{1}(\hat{y}_j = y_j) - \hat{p}_j)k(\hat{p}_i, \hat{p}_j)} ,\]</div>
+<p>with <span class="math notranslate nohighlight">\(\mathbb{1}(*)\)</span> as the indicator function and a Laplacian _kernel <span class="math notranslate nohighlight">\(k\)</span> defined by</p>
+<div class="math notranslate nohighlight">
+\[k(\hat{p}_i, \hat{p}_j) = \exp(-2.5 |\hat{p}_i - \hat{p}_j|) .\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – Detection mode is currently not supported for MMCE!
+If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
+with shape (n_samples, [n_classes]).
+If True, the input array ‘X’ is treated as a box predictions with several box features (at least
+box confidence must be present) with shape (n_samples, [n_box_features]).</p>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain:
+“Trainable calibration measures for neural networks from _kernel mean embeddings.”
+International Conference on Machine Learning. 2018.
+<a class="reference external" href="http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf">Get source online</a>.</p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([detection])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y[, batched])</p></td>
+<td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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diff --git a/docs/build/html/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.ENCE.html b/docs/build/html/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.ENCE.html
new file mode 100644
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+  <section id="netcal-metrics-regression-ence">
+<h1>netcal.metrics.regression.ENCE<a class="headerlink" href="#netcal-metrics-regression-ence" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.regression.ENCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.regression.</span></span><span class="sig-name descname"><span class="pre">ENCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.regression.ENCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Expected Normalized Calibration Error (ENCE) for a regression calibration evaluation to test for
+<em>variance calibration</em>. A probabilistic regression model takes <span class="math notranslate nohighlight">\(X\)</span> as input and outputs a
+mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and a standard deviation <span class="math notranslate nohighlight">\(\sigma_Y(X)\)</span> targeting the ground-truth <span class="math notranslate nohighlight">\(y\)</span>.
+Similar to the <a class="reference internal" href="netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE" title="netcal.metrics.confidence.ECE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.confidence.ECE</span></code></a>, the ENCE applies a binning scheme with <span class="math notranslate nohighlight">\(B\)</span> bins
+over the predicted standard deviation <span class="math notranslate nohighlight">\(\sigma_Y(X)\)</span> and measures the absolute (normalized) difference
+between root mean squared error (RMSE) and root mean variance (RMV) <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+Thus, the ENCE <a class="footnote-reference brackets" href="#id3" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{ENCE} := \frac{1}{B} \sum^B_{b=1} \frac{|RMSE(b) - RMV(b)|}{RMV(b)} ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(RMSE(b)\)</span> and <span class="math notranslate nohighlight">\(RMV(b)\)</span> are the root mean squared error and the root mean variance within
+bin <span class="math notranslate nohighlight">\(b\)</span>, respectively.</p>
+<p>If multiple dimensions are given, the ENCE is measured for each dimension separately.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the ENCE binning.
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id2">2</a>)</span>
+<p>Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, sample_threshold])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, *[, kind, range_])</p></td>
+<td><p>Measure the ENCE for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
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+<li class="toctree-l6"><a class="reference internal" href="#netcal.metrics.regression.NLL"><code class="docutils literal notranslate"><span class="pre">NLL</span></code></a></li>
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+  <section id="netcal-metrics-regression-nll">
+<h1>netcal.metrics.regression.NLL<a class="headerlink" href="#netcal-metrics-regression-nll" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.regression.NLL">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.regression.</span></span><span class="sig-name descname"><span class="pre">NLL</span></span><a class="headerlink" href="#netcal.metrics.regression.NLL" title="Permalink to this definition">¶</a></dt>
+<dd><p>Negative log likelihood (NLL) for probabilistic regression models.
+If a probabilistic forecaster outputs a probability density function (PDF) <span class="math notranslate nohighlight">\(f_Y(y)\)</span> targeting the ground-truth
+<span class="math notranslate nohighlight">\(y\)</span>, the negative log likelihood is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{NLL} = -\sum^N_{n=1} \log\big(f_Y(y)\big) ,\]</div>
+<p>with <span class="math notranslate nohighlight">\(N\)</span> as the number of samples within the examined data set.</p>
+<p><strong>Note:</strong> the input field for the standard deviation might also be given as quadratic NumPy arrays of shape
+(n, d, d) with d dimensions. In this case, this method asserts covariance matrices as input
+for each sample and the NLL is calculated for multivariate distributions.</p>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, *[, kind, reduction])</p></td>
+<td><p>Measures the negative log likelihood (NLL) for probabilistic regression models.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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+  <section id="netcal-metrics-regression-picp">
+<h1>netcal.metrics.regression.PICP<a class="headerlink" href="#netcal-metrics-regression-picp" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.regression.PICP">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.regression.</span></span><span class="sig-name descname"><span class="pre">PICP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.regression.PICP" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute Prediction Interval Coverage Probability (PICP) and Mean Prediction Interval Width (MPIW).
+These metrics have been proposed by <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+This metric is used for Bayesian models to determine the quality of the uncertainty estimates.
+In Bayesian mode, an uncertainty estimate is attached to each sample. The PICP measures the probability, that
+the true (observed) accuracy falls into the p% prediction interval. The uncertainty is well-calibrated, if
+the PICP is equal to p%. Simultaneously, the MPIW measures the mean width of all prediction intervals to evaluate
+the sharpness of the uncertainty estimates.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the PICP.
+On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>equal_intervals</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: True</em>) – If True, the bins have the same width. If False, the bins are splitted to equalize
+the number of samples in each bin.</p></li>
+<li><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
+with shape (n_samples, [n_classes]).
+If True, the input array ‘X’ is treated as a box predictions with several box features (at least
+box confidence must be present) with shape (n_samples, [n_box_features]).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the process metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Kuleshov, V.; Fenner, N. &amp; Ermon, S.:
+“Accurate Uncertainties for Deep Learning Using Calibrated Regression.”
+International Conference on Machine Learning (ICML), 2018
+<a class="reference external" href="http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez:
+“Quality of Uncertainty Quantification for Bayesian Neural Network Inference.”
+Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019
+<a class="reference external" href="https://arxiv.org/pdf/1906.09686.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction])</p></td>
+<td><p>Measure calibration by given predictions with confidence and the according ground truth.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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diff --git a/docs/build/html/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PinballLoss.html b/docs/build/html/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PinballLoss.html
new file mode 100644
index 0000000..5b99282
--- /dev/null
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+<li><a class="reference internal" href="#netcal.metrics.regression.PinballLoss"><code class="docutils literal notranslate"><span class="pre">PinballLoss</span></code></a></li>
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+<li class="toctree-l6"><a class="reference internal" href="#netcal.metrics.regression.PinballLoss"><code class="docutils literal notranslate"><span class="pre">PinballLoss</span></code></a></li>
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+  <section id="netcal-metrics-regression-pinballloss">
+<h1>netcal.metrics.regression.PinballLoss<a class="headerlink" href="#netcal-metrics-regression-pinballloss" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.regression.PinballLoss">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.regression.</span></span><span class="sig-name descname"><span class="pre">PinballLoss</span></span><a class="headerlink" href="#netcal.metrics.regression.PinballLoss" title="Permalink to this definition">¶</a></dt>
+<dd><p>Synonym for Quantile loss. For documentation, see <a class="reference internal" href="netcal.metrics.regression.QuantileLoss.html#netcal.metrics.regression.QuantileLoss" title="netcal.metrics.regression.QuantileLoss"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.regression.QuantileLoss</span></code></a>.</p>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-metrics-regression-qce">
+<h1>netcal.metrics.regression.QCE<a class="headerlink" href="#netcal-metrics-regression-qce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.regression.QCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.regression.</span></span><span class="sig-name descname"><span class="pre">QCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">marginal</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.regression.QCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Marginal Quantile Calibration Error (M-QCE) and Conditional Quantile Calibration Error (C-QCE) which both measure
+the gap between predicted quantiles and observed quantile coverage also for multivariate distributions.
+The M-QCE and C-QCE have originally been proposed by <a class="footnote-reference brackets" href="#id6" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+The derivation of both metrics are based on
+the Normalized Estimation Error Squared (NEES) known from object tracking <a class="footnote-reference brackets" href="#id7" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+The derivation of both metrics is shown in the following.</p>
+<p><strong>Definition of standard NEES:</strong>
+Given mean prediction <span class="math notranslate nohighlight">\(\hat{\boldsymbol{y}} \in \mathbb{R}^M\)</span>, ground-truth
+<span class="math notranslate nohighlight">\(\boldsymbol{y} \in \mathbb{R}^M\)</span>, and
+estimated covariance matrix <span class="math notranslate nohighlight">\(\hat{\boldsymbol{\Sigma}} \in \mathbb{R}^{M \times M}\)</span> using
+<span class="math notranslate nohighlight">\(M\)</span> dimensions, the NEES is defined as</p>
+<div class="math notranslate nohighlight">
+\[\epsilon = (\boldsymbol{y} - \hat{\boldsymbol{y}})^\top \hat{\boldsymbol{\Sigma}}^{-1}
+(\boldsymbol{y} - \hat{\boldsymbol{y}}) .\]</div>
+<p>The average NEES is defined as the mean error over <span class="math notranslate nohighlight">\(N\)</span> trials in a Monte-Carlo simulation for
+Kalman-Filter testing, so that</p>
+<div class="math notranslate nohighlight">
+\[\bar{\epsilon} = \frac{1}{N} \sum^N_{i=1} \epsilon_i .\]</div>
+<p>Under the condition, that <span class="math notranslate nohighlight">\(\mathbb{E}[\boldsymbol{y} - \hat{\boldsymbol{y}}] = \boldsymbol{0}\)</span> (zero mean),
+a <span class="math notranslate nohighlight">\(\chi^2\)</span>-test is performed to evaluate the estimated uncertainty. This test is accepted, if</p>
+<div class="math notranslate nohighlight">
+\[\bar{\epsilon} \leq \chi^2_M(\tau),\]</div>
+<p>where <span class="math notranslate nohighlight">\(\chi^2_M(\tau)\)</span> is the PPF score obtained by a <span class="math notranslate nohighlight">\(\chi^2\)</span> distribution
+with <span class="math notranslate nohighlight">\(M\)</span> degrees of freedom, for a certain quantile level <span class="math notranslate nohighlight">\(\tau \in [0, 1]\)</span>.</p>
+<p><strong>Marginal Quantile Calibration Error (M-QCE):</strong>
+In the case of regression calibration testing, we are interested in the gap between predicted quantile levels and
+observed quantile coverage probability for a certain set of quantile levels. We assert <span class="math notranslate nohighlight">\(N\)</span> observations of our
+test set that are used to estimate the NEES, so that we can compute the expected deviation between predicted
+quantile level and observed quantile coverage by</p>
+<div class="math notranslate nohighlight">
+\[\text{M-QCE}(\tau) := \mathbb{E} \Big[ \big| \mathbb{P} \big( \epsilon \leq \chi^2_M(\tau) \big) - \tau \big| \Big] ,\]</div>
+<p>which is the definition of the Marginal Quantile Calibration Error (M-QCE) <a class="footnote-reference brackets" href="#id6" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+The M-QCE is calculated by</p>
+<div class="math notranslate nohighlight">
+\[\text{M-QCE}(\tau) = \Bigg| \frac{1}{N} \sum^N_{n=1} \mathbb{1} \big( \epsilon_n \leq \chi^2_M(\tau) \big) - \tau \Bigg|\]</div>
+<p><strong>Conditional Quantile Calibration Error (C-QCE):</strong>
+The M-QCE measures the marginal calibration error which is more suitable to test for <em>quantile calibration</em>.
+However, similar to <a class="reference internal" href="netcal.metrics.regression.UCE.html#netcal.metrics.regression.UCE" title="netcal.metrics.regression.UCE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.regression.UCE</span></code></a> and <a class="reference internal" href="netcal.metrics.regression.ENCE.html#netcal.metrics.regression.ENCE" title="netcal.metrics.regression.ENCE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.regression.ENCE</span></code></a>,
+we want to induce a dependency on the estimated covariance, since we require
+that</p>
+<div class="math notranslate nohighlight">
+\[ \begin{align}\begin{aligned}&amp;\mathbb{E}[(\boldsymbol{y} - \hat{\boldsymbol{y}})(\boldsymbol{y} - \hat{\boldsymbol{y}})^\top |
+\hat{\boldsymbol{\Sigma}} = \boldsymbol{\Sigma}] = \boldsymbol{\Sigma},\\&amp;\forall \boldsymbol{\Sigma} \in \mathbb{R}^{M \times M}, \boldsymbol{\Sigma} \succcurlyeq 0,
+\boldsymbol{\Sigma}^\top = \boldsymbol{\Sigma} .\end{aligned}\end{align} \]</div>
+<p>To estimate the a <em>covariance</em> dependent QCE, we apply a binning scheme (similar to the
+<a class="reference internal" href="netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE" title="netcal.metrics.confidence.ECE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.confidence.ECE</span></code></a>) over the square root of the <em>standardized generalized variance</em> (SGV) <a class="footnote-reference brackets" href="#id8" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>,
+that is defined as</p>
+<div class="math notranslate nohighlight">
+\[\sigma_G = \sqrt{\text{det}(\hat{\boldsymbol{\Sigma}})^{\frac{1}{M}}} .\]</div>
+<p>Using the generalized standard deviation, it is possible to get a summarized statistic across different
+combinations of correlations to denote the distribution’s dispersion. Thus, the Conditional Quantile Calibration
+Error (C-QCE) <a class="footnote-reference brackets" href="#id6" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{C-QCE}(\tau) := \mathbb{E}_{\sigma_G, X}\Big[\Big|\mathbb{P}\big(\epsilon \leq \chi^2_M(\tau) | \sigma_G\big) - \tau \Big|\Big] ,\]</div>
+<p>To approximate the expectation over the generalized standard deviation, we use a binning scheme with <span class="math notranslate nohighlight">\(B\)</span> bins
+(similar to the ECE) and <span class="math notranslate nohighlight">\(N_b\)</span> samples per bin to compute the weighted sum across all bins, so that</p>
+<div class="math notranslate nohighlight">
+\[\text{C-QCE}(\tau) \approx \sum^B_{b=1} \frac{N_b}{N} | \text{freq}(b) - \tau |\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{freq}(b)\)</span> is the coverage frequency within bin <span class="math notranslate nohighlight">\(b\)</span> and given by</p>
+<div class="math notranslate nohighlight">
+\[\text{freq}(b) = \frac{1}{N_b} \sum_{n \in \mathcal{M}_b} \mathbb{1}\big(\epsilon_i \leq \chi^2_M(\tau)\big) ,\]</div>
+<p>with <span class="math notranslate nohighlight">\(\mathcal{M}_b\)</span> as the set of indices within bin <span class="math notranslate nohighlight">\(b\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used for the internal binning.
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>marginal</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, compute the M-QCE. This is the marginal probability over all samples falling into the desired
+quantiles. If False, use the C-QCE.
+The C-QCE uses a binning scheme by the gerneralized standard deviation to measure the conditional probability
+over all samples falling into the desired quantiles w.r.t. the generalized standard deviation.</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id3">2</a>,<a role="doc-backlink" href="#id5">3</a>)</span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Y. Bar-Shalom, X. R. Li, and T. Kirubarajan:
+“Estimation with applications to tracking and navigation.”
+Theory algorithms and software. John Wiley &amp; Sons, 2004.</p>
+</aside>
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">3</a><span class="fn-bracket">]</span></span>
+<p>A. SenGupta:
+“Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions.”
+Journal of Multivariate Analysis, vol. 23, no. 2, pp. 209–219, 1987.
+<a class="reference external" href="https://pdf.sciencedirectassets.com/272481/1-s2.0-S0047259X87X8001X/1-s2.0-0047259X87901539/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEB0aCXVzLWVhc3QtMSJHMEUCIAo6pl1vIu8%2F8ZEnEt6OKsA92ajSFy8%2BgjC8Tt9Tr360AiEAiVljbWcKBWAkrSpyT3LCCiX1Wug9gDf9WqxygiF%2B1G8q0gQIRhAEGgwwNTkwMDM1NDY4NjUiDLFU4Fzvuej7%2FpkSSCqvBNybwrdLhAP1yVFKRn0AQPK3G5t2wOY5ssTpqbS1HQzoz1EvOo%2BvWNeXPrWTo%2FhUvw8knQEWp9wA7a5wGdsbnmaBmCAWUFStKxSib9htTLAX1Ij5NCh%2ByA%2BiJwvPk4SXcRAJx4zQfJ8N%2FM2jcA3Lji7VPDYR8jNu7FfMd54veXYuqzUDoIdhVWIF4Czx0fwqngck9errYuNVSQCGSaW28m3%2BCr3%2FiePEQrXJcX0K7Q3z5D0%2FHGJvMsw%2FDqugg9gjWAFCquBO6EL9ircGBmzVsYnx8pKPZfa84aHZgGJPwvJp01o6qvUEdBZXbC5pmvDNAwIkguMahAHfNM3ffVDfyIVzRq1WrZIAKLYfgqFiGpNd3kGEUX5dGbSggAvxNXP7JX%2BifNsde9cIhzhqpjS0Z8BoOW8AGbXq9n15qEK%2F6xKJttpIhouxiadU6DtW%2BSDDFXDgdMVs1xU%2FE6dnWtl%2BQeA5VX4ITvTQMAjHOqu22lXEmOpHOmZ8fGKG5QTmz4iShixLGsgxpUMp2Wz%2F2OlCwt64m0sbI7zXr3YkUpyR019fs6IHJ28EVbeHsvp9xLrc5qltKHN3aoBmK4ZK0SFi%2FqHLhuz1HmWzCRQ0%2FkShcOXz80ttPlaHuX54VdVptvSy%2F1obsurjYuaR2HG9rO3lIneMgwKwwodZcKlu%2Fyo4WUCIk%2FhfKZrOWqVfAqqFPjWomg4CX787OIoqP%2FTz8H6sueGWk7HoeJKgSIW4yEISjNkwpdH7lQY6qQHS3GFk4XwFQEzwimYc%2B59DxQowARFI3PgPN%2F4FzUV5OHhm5G8455Dzm4T6R6E1%2F%2B86lSLdpH9JCkbDXBPJndiHTqXwBUej4wSWPASAvqQ6neC1lcJAqimCB7zn17je6g1dCi80xg1rZ6qU0c5BGtRqsCAB2NZlNn8jul1%2BM%2BiBF8SLE4xoNnT5kwEI%2FnnY81jvJw1kf4DspI9S8sAI2Z3efRca%2FBTIwgVw&amp;X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20220701T132912Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=300&amp;X-Amz-Credential=ASIAQ3PHCVTYZE6GY4EQ%2F20220701%2Fus-east-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=416cca57ae51cdc7c137e60fa5eba2ba651152e29e6b3485feeeb45f66aaeebb&amp;hash=f03a242d7d2e0652dfaa7c5e3fb713736b321247242986106eaa5412f136af12&amp;host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&amp;pii=0047259X87901539&amp;tid=spdf-4216aa85-a41c-4358-8d5e-3e877785fe29&amp;sid=4e9c65da63ee0949f79bfc42fc03dd438d5egxrqb&amp;type=client&amp;ua=4d545d0256065c055303&amp;rr=723f7d3c3edc2199">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, marginal, sample_threshold])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction, ...])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
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+  <section id="netcal-metrics-regression-quantileloss">
+<h1>netcal.metrics.regression.QuantileLoss<a class="headerlink" href="#netcal-metrics-regression-quantileloss" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.regression.QuantileLoss">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.regression.</span></span><span class="sig-name descname"><span class="pre">QuantileLoss</span></span><a class="headerlink" href="#netcal.metrics.regression.QuantileLoss" title="Permalink to this definition">¶</a></dt>
+<dd><p>Pinball aka quantile loss within regression calibration to test for <em>quantile calibration</em> of a probabilistic
+regression model. The Pinball loss is an asymmetric loss that measures the quality of the predicted
+quantiles. Given a probabilistic regression model that outputs a probability density function (PDF) <span class="math notranslate nohighlight">\(f_Y(y)\)</span>
+targeting the ground-truth <span class="math notranslate nohighlight">\(y\)</span>, we further denote the cumulative as <span class="math notranslate nohighlight">\(F_Y(y)\)</span> and the (inverse)
+percent point function (PPF) as <span class="math notranslate nohighlight">\(F_Y^{-1}(\tau)\)</span> for a certain quantile level <span class="math notranslate nohighlight">\(\tau \in [0, 1]\)</span>.</p>
+<p>The Pinball loss is given by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}L_{\text{Pin}}(\tau) =
+\begin{cases}
+     \big( y-F_Y^{-1}(\tau) \big)\tau \quad &amp;\text{if } y \geq F_Y^{-1}(\tau)\\
+     \big( F_Y^{-1}(\tau)-y \big)(1-\tau) \quad &amp;\text{if } y &lt; F_Y^{-1}(\tau)
+\end{cases} .\end{split}\]</div>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, q, *[, kind, reduction])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
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+<li class="toctree-l6"><a class="reference internal" href="#netcal.metrics.regression.UCE"><code class="docutils literal notranslate"><span class="pre">UCE</span></code></a></li>
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+  <section id="netcal-metrics-regression-uce">
+<h1>netcal.metrics.regression.UCE<a class="headerlink" href="#netcal-metrics-regression-uce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.metrics.regression.UCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.metrics.regression.</span></span><span class="sig-name descname"><span class="pre">UCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.metrics.regression.UCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Uncertainty Calibration Error (UCE) for a regression calibration evaluation to test for
+<em>variance calibration</em>. A probabilistic regression model takes <span class="math notranslate nohighlight">\(X\)</span> as input and outputs a
+mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and a variance <span class="math notranslate nohighlight">\(\sigma_Y^2(X)\)</span> targeting the ground-truth <span class="math notranslate nohighlight">\(y\)</span>.
+Similar to the <a class="reference internal" href="netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE" title="netcal.metrics.confidence.ECE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.confidence.ECE</span></code></a>, the UCE applies a binning scheme with <span class="math notranslate nohighlight">\(B\)</span> bins
+over the predicted variance <span class="math notranslate nohighlight">\(\sigma_Y^2(X)\)</span> and measures the absolute difference
+between mean squared error (MSE) and mean variance (RMV) <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+Thus, the UCE <a class="footnote-reference brackets" href="#id3" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined by</p>
+<div class="math notranslate nohighlight">
+\[\text{UCE} := \sum^B_{b=1} \frac{N_b}{N} |MSE(b) - MV(b)| ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(MSE(b)\)</span> and <span class="math notranslate nohighlight">\(MV(b)\)</span> are the mean squared error and the mean variance within
+bin <span class="math notranslate nohighlight">\(b\)</span>, respectively, and <span class="math notranslate nohighlight">\(N_b\)</span> is the number of samples within bin <span class="math notranslate nohighlight">\(b\)</span>.</p>
+<p>If multiple dimensions are given, the UCE is measured for each dimension separately.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the UCE binning.
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p></li>
+<li><p><strong>sample_threshold</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1</em>) – Bins with an amount of samples below this threshold are not included into the miscalibration metrics.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id2">2</a>)</span>
+<p>Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, sample_threshold])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code>(bin_bounds, samples, *values[, nan])</p></td>
+<td><p>Perform binning on value (and all additional values passed) based on samples.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">frequency</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Measure the frequency of each point by binning.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">measure</span></code>(X, y, *[, kind, range_])</p></td>
+<td><p>Measure quantile loss for given input data either as tuple consisting of mean and stddev estimates or as NumPy array consisting of a sample distribution.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X, y[, batched, uncertainty])</p></td>
+<td><p>Check input data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">process</span></code>(metric, acc_hist, conf_hist, ...)</p></td>
+<td><p>Determine miscalibration based on passed histograms.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reduce</span></code>(histogram, distribution, axis[, ...])</p></td>
+<td><p>Calculate the weighted mean on a given histogram based on a dedicated data distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
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+          <div class="document" role="main">
+            <div class="documentwrapper">
+              <div class="bodywrapper">
+                <div class="body">
+                  
+  <section id="module-netcal.metrics.confidence">
+<span id="netcal-metrics-confidence"></span><h1>netcal.metrics.confidence<a class="headerlink" href="#module-netcal.metrics.confidence" title="Permalink to this heading">¶</a></h1>
+<section id="metrics-for-confidence-calibration">
+<h2>Metrics for Confidence Calibration<a class="headerlink" href="#metrics-for-confidence-calibration" title="Permalink to this heading">¶</a></h2>
+<p>Methods for measuring miscalibration in the context of confidence calibration.</p>
+<p>The common methods for confidence calibration evaluation are given with the
+<em>netcal.metrics.confidence.ECE</em> (ECE), <em>netcal.metrics.confidence.MCE</em> (MCE), and
+<em>netcal.metrics.confidence.ACE</em> (ACE). Each method bins the samples by their confidence and measures the
+accuracy in each bin. The ECE gives the mean gap between confidence and observed accuracy in each bin weighted by the
+number of samples. The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights
+each bin equally.</p>
+<p>A further metric is the Maximum Mean Calibration Error (MMCE) which is a differentiable variant of the ECE that
+might also be used as a regularization technique during model training.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.confidence.ACE.html#netcal.metrics.confidence.ACE" title="netcal.metrics.confidence.ACE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ACE</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Average Calibration Error (ACE) for classification and Detection Average Calibration Error (D-ACE) for object detection or segmentation.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE" title="netcal.metrics.confidence.ECE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ECE</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Expected Calibration Error (ECE) for classification and Detection Expected Calibration Error (D-ECE) for object detection or segmentation.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.confidence.MCE.html#netcal.metrics.confidence.MCE" title="netcal.metrics.confidence.MCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MCE</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Maximum Calibration Error (MCE) for classification and Detection Maximum Calibration Error (D-MCE) for object detection or segmentation.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.confidence.MMCE.html#netcal.metrics.confidence.MMCE" title="netcal.metrics.confidence.MMCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MMCE</span></code></a>([detection])</p></td>
+<td><p>Maximum Mean Calibration Error (MMCE).</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+</section>
+
+
+                </div>
+              </div>
+            </div>
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+<li><a class="reference internal" href="#metrics-for-regression-uncertainty-calibration">Metrics for Regression Uncertainty Calibration</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../netcal.binning.html">netcal.binning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../netcal.scaling.html">netcal.scaling</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../netcal.regularization.html">netcal.regularization</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../netcal.metrics.html">netcal.metrics</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../netcal.metrics.html#metrics-package-to-measure-miscalibration">Metrics Package to Measure Miscalibration</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../netcal.metrics.html#available-classes">Available classes</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.metrics.html#packages">Packages</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.metrics.confidence.html">netcal.metrics.confidence</a></li>
+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.metrics.regression</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#metrics-for-regression-uncertainty-calibration">Metrics for Regression Uncertainty Calibration</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#available-classes">Available classes</a><ul>
+<li class="toctree-l5"><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.QuantileLoss.html">netcal.metrics.regression.QuantileLoss</a></li>
+<li class="toctree-l5"><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.PinballLoss.html">netcal.metrics.regression.PinballLoss</a></li>
+<li class="toctree-l5"><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.ENCE.html">netcal.metrics.regression.ENCE</a></li>
+<li class="toctree-l5"><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.UCE.html">netcal.metrics.regression.UCE</a></li>
+<li class="toctree-l5"><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.PICP.html">netcal.metrics.regression.PICP</a></li>
+<li class="toctree-l5"><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.QCE.html">netcal.metrics.regression.QCE</a></li>
+<li class="toctree-l5"><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.NLL.html">netcal.metrics.regression.NLL</a></li>
+</ul>
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+</ul>
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+  <section id="module-netcal.metrics.regression">
+<span id="netcal-metrics-regression"></span><h1>netcal.metrics.regression<a class="headerlink" href="#module-netcal.metrics.regression" title="Permalink to this heading">¶</a></h1>
+<section id="metrics-for-regression-uncertainty-calibration">
+<h2>Metrics for Regression Uncertainty Calibration<a class="headerlink" href="#metrics-for-regression-uncertainty-calibration" title="Permalink to this heading">¶</a></h2>
+<p>Methods for measuring miscalibration in the context of regression uncertainty calibration for probabilistic
+regression models.</p>
+<p>The common methods for regression uncertainty evaluation are <em>netcal.metrics.regression.PinballLoss</em> (Pinball
+loss), the <em>netcal.metrics.regression.NLL</em> (NLL), and the <em>netcal.metrics.regression.QCE</em> (M-QCE and
+C-QCE). The Pinball loss as well as the Marginal/Conditional Quantile Calibration Error (M-QCE and C-QCE) evaluate
+the quality of the estimated quantiles compared to the observed ground-truth quantile coverage. The NLL is a proper
+scoring rule to measure the overall quality of the predicted probability distributions.</p>
+<p>Further metrics are the <em>netcal.metrics.regression.UCE</em> (UCE) and the <em>netcal.metrics.regression.ENCE</em>
+(ENCE) which both apply a binning scheme over the predicted standard deviation/variance and test for <em>variance
+calibration</em>.</p>
+<p>For a detailed description of the available metrics within regression calibration, see the module doc of
+<em>netcal.regression</em>.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.QuantileLoss.html#netcal.metrics.regression.QuantileLoss" title="netcal.metrics.regression.QuantileLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QuantileLoss</span></code></a>()</p></td>
+<td><p>Pinball aka quantile loss within regression calibration to test for <em>quantile calibration</em> of a probabilistic regression model.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.PinballLoss.html#netcal.metrics.regression.PinballLoss" title="netcal.metrics.regression.PinballLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PinballLoss</span></code></a>()</p></td>
+<td><p>Synonym for Quantile loss.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.ENCE.html#netcal.metrics.regression.ENCE" title="netcal.metrics.regression.ENCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ENCE</span></code></a>([bins, sample_threshold])</p></td>
+<td><p>Expected Normalized Calibration Error (ENCE) for a regression calibration evaluation to test for <em>variance calibration</em>.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.UCE.html#netcal.metrics.regression.UCE" title="netcal.metrics.regression.UCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UCE</span></code></a>([bins, sample_threshold])</p></td>
+<td><p>Uncertainty Calibration Error (UCE) for a regression calibration evaluation to test for <em>variance calibration</em>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.PICP.html#netcal.metrics.regression.PICP" title="netcal.metrics.regression.PICP"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PICP</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Compute Prediction Interval Coverage Probability (PICP) and Mean Prediction Interval Width (MPIW).</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.QCE.html#netcal.metrics.regression.QCE" title="netcal.metrics.regression.QCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QCE</span></code></a>([bins, marginal, sample_threshold])</p></td>
+<td><p>Marginal Quantile Calibration Error (M-QCE) and Conditional Quantile Calibration Error (C-QCE) which both measure the gap between predicted quantiles and observed quantile coverage also for multivariate distributions.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.regression.NLL.html#netcal.metrics.regression.NLL" title="netcal.metrics.regression.NLL"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NLL</span></code></a>()</p></td>
+<td><p>Negative log likelihood (NLL) for probabilistic regression models.</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+</section>
+
+
+                </div>
+              </div>
+            </div>
+          </div>
+        </div>
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+        
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diff --git a/docs/build/html/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html b/docs/build/html/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html
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-  <div class="section" id="netcal-presentation-reliabilitydiagram">
-<h1>netcal.presentation.ReliabilityDiagram<a class="headerlink" href="#netcal-presentation-reliabilitydiagram" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.presentation.ReliabilityDiagram">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.presentation.</code><code class="sig-name descname">ReliabilityDiagram</code><span class="sig-paren">(</span><em class="sig-param">bins: Union[int</em>, <em class="sig-param">Iterable[int]] = 10</em>, <em class="sig-param">equal_intervals: bool = True</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">sample_threshold: int = 1</em>, <em class="sig-param">fmin: float = None</em>, <em class="sig-param">fmax: float = None</em>, <em class="sig-param">metric: str = 'ECE'</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.presentation.ReliabilityDiagram" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
-<p>Plot Confidence Histogram and Reliability Diagram to visualize miscalibration.
+
+          </ul>
+
+        </div>
+      </div>
+    </div>
+    
+
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+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.presentation.ReliabilityDiagram</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.presentation.ReliabilityDiagram"><code class="docutils literal notranslate"><span class="pre">ReliabilityDiagram</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.presentation.ReliabilityRegression.html">netcal.presentation.ReliabilityRegression</a></li>
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+  <section id="netcal-presentation-reliabilitydiagram">
+<h1>netcal.presentation.ReliabilityDiagram<a class="headerlink" href="#netcal-presentation-reliabilitydiagram" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.presentation.ReliabilityDiagram">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.presentation.</span></span><span class="sig-name descname"><span class="pre">ReliabilityDiagram</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_intervals</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fmin</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fmax</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">metric</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'ECE'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.presentation.ReliabilityDiagram" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot Confidence Histogram and Reliability Diagram to visualize miscalibration in the context of
+confidence calibration.
 On classification, plot the gaps between average confidence and observed accuracy bin-wise over the confidence
-space <a class="footnote-reference brackets" href="#id4" id="id1">1</a>, <a class="footnote-reference brackets" href="#id5" id="id2">2</a>.
-On detection, plot the miscalibration w.r.t. the additional regression information provided (1-D or 2-D) <a class="footnote-reference brackets" href="#id7" id="id3">3</a>.</p>
+space <a class="footnote-reference brackets" href="#id4" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id5" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+On detection, plot the miscalibration w.r.t. the additional regression information provided (1-D or 2-D) <a class="footnote-reference brackets" href="#id6" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the ACE/ECE/MCE.
 On detection mode: if int, use same amount of bins for each dimension (nx1 = nx2 = … = bins).
@@ -74,167 +209,82 @@ <h1>netcal.presentation.ReliabilityDiagram<a class="headerlink" href="#netcal-pr
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
 “On Calibration of Modern Neural Networks.”
 Proceedings of the 34th International Conference on Machine Learning-Volume 70. JMLR. org, 2017.
 <a class="reference external" href="https://arxiv.org/abs/1706.04599">Get source online</a></p>
-</dd>
-<dt class="label" id="id5"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>A. Niculescu-Mizil and R. Caruana:
+</aside>
+<aside class="footnote brackets" id="id5" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>A. Niculescu-Mizil and R. Caruana:
 “Predicting good probabilities with supervised learning.”
 Proceedings of the 22nd International Conference on Machine Learning, 2005, pp. 625–632.
 <a class="reference external" href="https://www.cs.cornell.edu/~alexn/papers/calibration.icml05.crc.rev3.pdf">Get source online</a></p>
-</dd>
-<dt class="label" id="id7"><span class="brackets"><a class="fn-backref" href="#id3">3</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
 The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.
 <a class="reference external" href="https://openaccess.thecvf.com/content_CVPRW_2020/papers/w20/Kuppers_Multivariate_Confidence_Calibration_for_Object_Detection_CVPRW_2020_paper.pdf">Get source online</a></p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins, equal_intervals, detection, ...])</p></td>
 <td><p>Constructor.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">plot</span></code>(X, y[, batched, uncertainty, filename, …])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">plot</span></code>(X, y, *[, batched, uncertainty, ...])</p></td>
 <td><p>Reliability diagram to visualize miscalibration.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.presentation.ReliabilityDiagram.plot">
-<code class="sig-name descname">plot</code><span class="sig-paren">(</span><em class="sig-param">X: Union[Iterable[numpy.ndarray], numpy.ndarray], y: Union[Iterable[numpy.ndarray], numpy.ndarray], batched: bool = False, uncertainty: str = None, filename: str = None, tikz: bool = False, title_suffix: str = None, feature_names: List[str] = None, **save_args</em><span class="sig-paren">)</span> &#x2192; Union[matplotlib.figure.Figure, str]<a class="headerlink" href="#netcal.presentation.ReliabilityDiagram.plot" title="Permalink to this definition">¶</a></dt>
-<dd><p>Reliability diagram to visualize miscalibration. This could be either in classical way for confidences only
-or w.r.t. additional properties (like x/y-coordinates of detection boxes, width, height, etc.). The additional
-properties get binned. Afterwards, the miscalibration will be calculated for each bin. This is
-visualized as a 2-D plots.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>iterable of np.ndarray</em><em>, or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes/n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If this is an iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>iterable of np.ndarray with same length as X</em><em> or </em><em>np.ndarray of shape=</em><em>(</em><em>[</em><em>n_bayes</em><em>]</em><em>, </em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).
-If 3-D, interpret first dimension as samples from an Bayesian estimator with mulitple data points
-for a single sample (e.g. variational inference or MC dropout samples).
-If iterable over multiple instances of np.ndarray and parameter batched=True,
-interpret this parameter as multiple predictions that should be averaged.</p></li>
-<li><p><strong>batched</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – Multiple predictions can be evaluated at once (e.g. cross-validation examinations) using batched-mode.
-All predictions given by X and y are separately evaluated and their results are averaged afterwards
-for visualization.</p></li>
-<li><p><strong>uncertainty</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – <p>Define uncertainty handling if input X has been sampled e.g. by Monte-Carlo dropout or similar methods
-that output an ensemble of predictions per sample. Choose one of the following options:
-- flatten:  treat everything as a separate prediction - this option will yield into a slightly better</p>
-<blockquote>
-<div><p>calibration performance but without the visualization of a prediction interval.</p>
-</div></blockquote>
-<ul>
-<li><dl class="simple">
-<dt>mean:     compute Monte-Carlo integration to obtain a simple confidence estimate for a sample</dt><dd><p>(mean) with a standard deviation that is visualized.</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p></li>
-<li><p><strong>filename</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Optional filename to save the plotted figure.</p></li>
-<li><p><strong>tikz</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, use ‘tikzplotlib’ package to return tikz-code for Latex rather than a Matplotlib figure.</p></li>
-<li><p><strong>title_suffix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Suffix for plot title.</p></li>
-<li><p><strong>feature_names</strong> (<em>list</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Names of the additional features that are attached to the axes of a reliability diagram.</p></li>
-<li><p><strong>**save_args</strong> (<em>args</em>) – Additional arguments passed to ‘matplotlib.pyplot.Figure.savefig’ function if ‘tikz’ is False.
-If ‘tikz’ is True, the argument are passed to ‘tikzplotlib.get_tikz_code’ function.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>matplotlib.pyplot.Figure if ‘tikz’ is False else str with tikz code.</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – <ul class="simple">
-<li><p>If parameter metric is not string or string is not ‘ACE’, ‘ECE’ or ‘MCE’
-    - If parameter ‘feature_names’ is set but length does not fit to second dim of X
-    - If no ground truth samples are provided
-    - If length of bins parameter does not match the number of features given by X
-    - If more than 3 feature dimensions (including confidence) are provided</p></li>
-</ul>
-</p>
-</dd>
-</dl>
 </dd></dl>
 
-</dd></dl>
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+  <section id="netcal-presentation-reliabilityqce">
+<h1>netcal.presentation.ReliabilityQCE<a class="headerlink" href="#netcal-presentation-reliabilityqce" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.presentation.ReliabilityQCE">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.presentation.</span></span><span class="sig-name descname"><span class="pre">ReliabilityQCE</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bins</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">ndarray</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.presentation.ReliabilityQCE" title="Permalink to this definition">¶</a></dt>
+<dd><p>Visualizes the Conditional Quantile Calibration Error (C-QCE) in the scope of regression calibration as a bar chart
+for probabilistic regression models.
+See <a class="reference internal" href="../_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QCE.html#netcal.metrics.regression.QCE" title="netcal.metrics.regression.QCE"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.metrics.regression.QCE</span></code></a> for a detailed documentation of the C-QCE <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+This method is able to visualize the C-QCE in terms of multiple univariate distributions if the input is given
+as multiple independent Gaussians.
+This method is also able to visualize the multivariate C-QCE for a multivariate Gaussian if the input is given
+with covariance matrices.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>bins</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 10</em>) – Number of bins used by the C-QCE binning.
+If iterable, use different amount of bins for each dimension (nx1, nx2, … = bins).</p>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([bins])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">plot</span></code>(X, y, q, *[, kind, range_, filename, ...])</p></td>
+<td><p>Visualizes the C-QCE as a bar chart either for multiple univariate data (if standard deviations are given as input) or for a joint multivariate distribution (if covariance matrices are given as input).</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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+  <section id="netcal-presentation-reliabilityregression">
+<h1>netcal.presentation.ReliabilityRegression<a class="headerlink" href="#netcal-presentation-reliabilityregression" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.presentation.ReliabilityRegression">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.presentation.</span></span><span class="sig-name descname"><span class="pre">ReliabilityRegression</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">quantiles</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Iterable</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">ndarray</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">11</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.presentation.ReliabilityRegression" title="Permalink to this definition">¶</a></dt>
+<dd><p>Reliability diagram in the scope of regression calibration for probabilistic regression models.
+This diagram visualizes the quantile coverage frequency for several quantile levels and plots these observed
+coverage scores above the desired quantile levels.
+In this way, it is possible to compare the predicted and the observed quantile levels with each other.</p>
+<p>This method is able to visualize the quantile coverage in terms of multiple univariate distributions if the input
+is given as multiple independent Gaussians.
+This method is also able to visualize the multivariate quantile coverage for a joint multivariate Gaussian if the
+input is given with covariance matrices.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>quantiles</strong> (<em>int</em><em> or </em><em>iterable</em><em>, </em><em>default: 11</em>) – Quantile levels that are used for the visualization of the regression reliability diagram.
+If int, use NumPy’s linspace method to get the quantile levels.
+If iterable, use the specified quantiles for visualization.</p>
+</dd>
+</dl>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([quantiles])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">plot</span></code>(X, y, *[, kind, filename, tikz, ...])</p></td>
+<td><p>Reliability diagram for regression calibration to visualize the predicted quantile levels vs.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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+  <section id="netcal-regression-gpbeta">
+<h1>netcal.regression.GPBeta<a class="headerlink" href="#netcal-regression-gpbeta" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.GPBeta">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.</span></span><span class="sig-name descname"><span class="pre">GPBeta</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_inducing_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_random_samples</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name_prefix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'gpbeta'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.GPBeta" title="Permalink to this definition">¶</a></dt>
+<dd><p>GP-Beta recalibration method for regression uncertainty calibration using the well-known Beta calibration method
+from  classification calibration in combination with a Gaussian process (GP) parameter estimation.
+The basic idea of GP-Beta <a class="footnote-reference brackets" href="#id10" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is to apply recalibration on the uncalibrated cumulative density function (CDF),
+similar as to the Isotonic Regression method <a class="footnote-reference brackets" href="#id11" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+Since the CDF is restricted to the <span class="math notranslate nohighlight">\([0, 1]\)</span> interval, the authors in <a class="footnote-reference brackets" href="#id10" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> propose to use the
+Beta calibration scheme <a class="footnote-reference brackets" href="#id12" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a> known in the scope of confidence calibration.
+Furthermore, the authors use a GP to obtain the recalibration parameters of the Beta function for each
+sample individually, so that it should finally achieve <em>distribution calibration</em> <a class="footnote-reference brackets" href="#id10" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
+<p><strong>Mathematical background:</strong> Let <span class="math notranslate nohighlight">\(f_Y(y)\)</span> denote the uncalibrated probability density function (PDF),
+targeting the probability distribution for <span class="math notranslate nohighlight">\(Y\)</span>.
+Let <span class="math notranslate nohighlight">\(\tau_y \in [0, 1]\)</span> denote a certain quantile on the uncalibrated CDF which
+is denoted by <span class="math notranslate nohighlight">\(\tau_y = F_Y(y)\)</span>.
+Furthermore, let <span class="math notranslate nohighlight">\(g_Y(y)\)</span> and <span class="math notranslate nohighlight">\(G_Y(y)\)</span> denote the recalibrated PDF and CDF, respectively.
+The Beta calibration function <span class="math notranslate nohighlight">\(\mathbf{c}_\beta(\tau_y)\)</span> known from <a class="footnote-reference brackets" href="#id12" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a> is given by</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{c}_\beta(\tau_y) = \phi\big( a \log(\tau_y) - b \log(1-\tau_y) + c \big)\]</div>
+<p>with recalibration parameters <span class="math notranslate nohighlight">\(a,b \in \mathbb{R}_{&gt;0}\)</span> and <span class="math notranslate nohighlight">\(c \in \mathbb{R}\)</span>, and
+<span class="math notranslate nohighlight">\(\phi(\cdot)\)</span> as the sigmoid function <a class="footnote-reference brackets" href="#id12" id="id7" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>.
+This method serves as a mapping from the uncalibrated CDF to the calibrated one, so that</p>
+<div class="math notranslate nohighlight">
+\[G_Y(y) = \mathbf{c}_\beta\big( F_Y(y) \big)\]</div>
+<p>holds. The PDF is the derivative of the CDF, so that the calibrated PDF is given by</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \frac{\partial \mathbf{c}_\beta}{\partial y}
+= \frac{\partial \mathbf{c}_\beta}{\partial \tau_y} \frac{\partial \tau_y}{\partial y}
+= \mathbf{r}_\beta(\tau_y) f_Y(y) ,\]</div>
+<p>with <span class="math notranslate nohighlight">\(\mathbf{r}_\beta(\tau_y)\)</span> as a beta link function <a class="footnote-reference brackets" href="#id10" id="id8" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> given by</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{r}_\beta(\tau_y) = \Bigg(\frac{a}{\tau_y} + \frac{b}{1-\tau_y} \Bigg)
+\mathbf{c}_\beta(\tau_y) \big(1 - \mathbf{c}_\beta(\tau_y)\big) .\]</div>
+<p>Finally, the recalibration parameters <span class="math notranslate nohighlight">\(a, b\)</span> and <span class="math notranslate nohighlight">\(c\)</span> are obtained using a Gaussian process scheme.
+In this way, it is possible to apply non-parametric <em>distribution calibration</em> <a class="footnote-reference brackets" href="#id10" id="id9" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n_inducing_points</strong> (<em>int</em>) – Number of inducing points used to approximate the input space. These inducing points are also optimized.</p></li>
+<li><p><strong>n_random_samples</strong> (<em>int</em>) – Number of random samples used to sample from the parameter distribution during optimization and inference.</p></li>
+<li><p><strong>n_epochs</strong> (<em>int</em><em>, </em><em>default: 200</em>) – Number of optimization epochs.</p></li>
+<li><p><strong>batch_size</strong> (<em>int</em><em>, </em><em>default: 256</em>) – Size of batches during optimization.</p></li>
+<li><p><strong>num_workers</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 0</em>) – Number of workers used for the dataloader.</p></li>
+<li><p><strong>lr</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-2</em>) – Learning rate used for the Adam optimizer.</p></li>
+<li><p><strong>use_cuda</strong> (<em>str</em><em> or </em><em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+You can also pass a string “cuda:0”, “cuda:1”, etc. to specify the CUDA device.
+If False, use CPU for optimization and inference.</p></li>
+<li><p><strong>jitter</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-5</em>) – Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+Gaussian process optimization.</p></li>
+<li><p><strong>name_prefix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;gpbeta&quot;</em>) – Name prefix internally used in Pyro to distinguish between parameter stores.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id10" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id3">2</a>,<a role="doc-backlink" href="#id5">3</a>,<a role="doc-backlink" href="#id8">4</a>,<a role="doc-backlink" href="#id9">5</a>)</span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id11" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+“Accurate uncertainties for deep learning using calibrated regression.”
+International Conference on Machine Learning. PMLR, 2018.
+<a class="reference external" href="http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id12" role="note">
+<span class="label"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id4">1</a>,<a role="doc-backlink" href="#id6">2</a>,<a role="doc-backlink" href="#id7">3</a>)</span>
+<p>Kull, Meelis, Telmo Silva Filho, and Peter Flach:
+“Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers”
+Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
+<a class="reference external" href="http://proceedings.mlr.press/v54/kull17a/kull17a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([n_inducing_points, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Additional information used to print if str(method) is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a GP model to the provided data using Gaussian process optimization.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x)</p></td>
+<td><p>Forward method defines the prior for the GP.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_fantasy_model</span></code>(inputs, targets, **kwargs)</p></td>
+<td><p>Returns a new GP model that incorporates the specified inputs and targets as new training data using online variational conditioning (OVC).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC coefficients, etc.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">guide</span></code>(x, y)</p></td>
+<td><p>Pyro guide that defines the variational distribution for the Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename[, use_cuda])</p></td>
+<td><p>Overwrite base method's load_model function as the parameters for the GP methods are stored differently compared to the remaining methods.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">model</span></code>(x, y)</p></td>
+<td><p>Model function that defines the computation graph.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_guide</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_model</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, t])</p></td>
+<td><p>Transform the given stddev to a distribution-calibrated one using the input mean and stddev as priors for the underlying Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<td><p>Sets gradients of all model parameters to zero.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-regression-gpcauchy">
+<h1>netcal.regression.GPCauchy<a class="headerlink" href="#netcal-regression-gpcauchy" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.GPCauchy">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.</span></span><span class="sig-name descname"><span class="pre">GPCauchy</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_inducing_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_random_samples</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name_prefix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'gpcauchy'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.GPCauchy" title="Permalink to this definition">¶</a></dt>
+<dd><p>GP-Cauchy recalibration method for regression uncertainty calibration that consumes an uncalibrated Gaussian
+distribution but converts it to a calibrated Cauchy distribution.
+This method uses a Gaussian process (GP) for a flexible estimation of the recalibration parameter (cf. <a class="footnote-reference brackets" href="#id6" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>).
+Similar to <a class="reference internal" href="../_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a>, the GP-Cauchy <a class="footnote-reference brackets" href="#id7" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> acts as a kind of temperature scaling for
+the variance of a Gaussian distribution <a class="footnote-reference brackets" href="#id8" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id9" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a>. However, the rescaled variance is interpreted as the
+scaling parameter of a Cauchy distribution. Furthermore, the rescaling parameter is not globally fixed but obtained
+by a GP for each sample individually, so that we are able to convert a Gaussian to a Cauchy distribution <a class="footnote-reference brackets" href="#id7" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+Thus, the GP-Cauchy seeks for <strong>distribution calibration</strong> but for parametric Cauchy distributions.
+Note that this method does not change the mean but only reinterprets the predicted variance as the Cauchy scaling
+parameter. The mode of the Cauchy is assumed to be equal to the input mean.</p>
+<p><strong>Mathematical background:</strong> Let <span class="math notranslate nohighlight">\(f_Y(y)\)</span> denote the uncalibrated probability density function (PDF),
+targeting the probability distribution for <span class="math notranslate nohighlight">\(Y\)</span>. In our case, the uncalibrated PDF is given as a Gaussian, so
+that <span class="math notranslate nohighlight">\(f_Y(y) = \mathcal{N}\big(y; \mu_Y(X), \sigma^2_Y(X)\big)\)</span> with mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and variance
+<span class="math notranslate nohighlight">\(\sigma^2_Y(X)\)</span> obtained by a probabilistic regression model that depends on the input <span class="math notranslate nohighlight">\(X\)</span>.
+The calibrated PDF <span class="math notranslate nohighlight">\(g_Y(y)\)</span> is a rescaled Cauchy distribution with fixed mode <span class="math notranslate nohighlight">\(x_0 \in \mathbb{R}\)</span>
+and rescaled scaling parameter <span class="math notranslate nohighlight">\(\lambda \in \mathbb{R}_{&gt;0}\)</span>, so that</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \text{Cauchy}\Big(y; x_0=\mu_Y(X), \lambda=\big(\theta_y \cdot \sigma_Y(X)\big) \Big) ,\]</div>
+<p>where  <span class="math notranslate nohighlight">\(\theta_y\)</span> is the adaptive rescaling weight for a certain <span class="math notranslate nohighlight">\(y\)</span>.</p>
+<p>The GP-Cauchy utilizes a Gaussian process to obtain <span class="math notranslate nohighlight">\(\theta_y\)</span>, so that</p>
+<div class="math notranslate nohighlight">
+\[\theta_y \sim \text{gp}(0, k) ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(k\)</span> is the kernel function (for a more detailed description of the underlying Gaussian process, see
+documentation of parent class <a class="reference internal" href="../_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.AbstractGP.html#netcal.regression.gp.AbstractGP" title="netcal.regression.gp.AbstractGP"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.AbstractGP</span></code></a>).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n_inducing_points</strong> (<em>int</em>) – Number of inducing points used to approximate the input space. These inducing points are also optimized.</p></li>
+<li><p><strong>n_random_samples</strong> (<em>int</em>) – Number of random samples used to sample from the parameter distribution during optimization and inference.</p></li>
+<li><p><strong>n_epochs</strong> (<em>int</em><em>, </em><em>default: 200</em>) – Number of optimization epochs.</p></li>
+<li><p><strong>batch_size</strong> (<em>int</em><em>, </em><em>default: 256</em>) – Size of batches during optimization.</p></li>
+<li><p><strong>num_workers</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 0</em>) – Number of workers used for the dataloader.</p></li>
+<li><p><strong>lr</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-2</em>) – Learning rate used for the Adam optimizer.</p></li>
+<li><p><strong>use_cuda</strong> (<em>str</em><em> or </em><em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+You can also pass a string “cuda:0”, “cuda:1”, etc. to specify the CUDA device.
+If False, use CPU for optimization and inference.</p></li>
+<li><p><strong>jitter</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-5</em>) – Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+Gaussian process optimization.</p></li>
+<li><p><strong>name_prefix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;gpcauchy&quot;</em>) – Name prefix internally used in Pyro to distinguish between parameter stores.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id5">2</a>)</span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id9" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">4</a><span class="fn-bracket">]</span></span>
+<p>Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([n_inducing_points, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Additional information used to print if str(method) is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a GP model to the provided data using Gaussian process optimization.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x)</p></td>
+<td><p>Forward method defines the prior for the GP.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_fantasy_model</span></code>(inputs, targets, **kwargs)</p></td>
+<td><p>Returns a new GP model that incorporates the specified inputs and targets as new training data using online variational conditioning (OVC).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC coefficients, etc.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">guide</span></code>(x, y)</p></td>
+<td><p>Pyro guide that defines the variational distribution for the Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename[, use_cuda])</p></td>
+<td><p>Overwrite base method's load_model function as the parameters for the GP methods are stored differently compared to the remaining methods.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">model</span></code>(x, y)</p></td>
+<td><p>Model function that defines the computation graph.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_guide</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_model</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<td><p>Transform the given stddev to a distribution-calibrated one using the input mean and stddev as priors for the underlying Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<td><p>Sets gradients of all model parameters to zero.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
+                </div>
+              </div>
+            </div>
+          </div>
+        </div>
+        
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+  <section id="netcal-regression-gpnormal">
+<h1>netcal.regression.GPNormal<a class="headerlink" href="#netcal-regression-gpnormal" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.GPNormal">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.</span></span><span class="sig-name descname"><span class="pre">GPNormal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_inducing_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_random_samples</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">correlations</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name_prefix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'gpnormal'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.GPNormal" title="Permalink to this definition">¶</a></dt>
+<dd><p>GP-Normal recalibration method for regression uncertainty calibration using a temperature scaling for the
+variance of a normal distribution but using the Gaussian process (GP) parameter estimation to adaptively
+obtain the scaling parameter for each input individually.
+The temperature scaling for the variance <a class="footnote-reference brackets" href="#id7" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id8" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> seeks to preserve a parametric Gaussian distribution as
+calibration output and aims to reach <em>variance calibration</em>. That is, matching the predicted variance with the
+observed “error variance” aka mean squared error.
+In contrast to the standard approach, the GP-Normal <a class="footnote-reference brackets" href="#id9" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a> uses a Gaussian process (GP) from <a class="footnote-reference brackets" href="#id10" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a> to flexibly obtain
+a recalibration weight for each sample individually.
+Thus, the GP-Normal seeks for a mixed form of <strong>variance calibration</strong> in a more flexible way towards
+<strong>distribution calibration</strong> for Gaussians.
+Note that this method does not change the mean but only the predicted variance.</p>
+<p><strong>Mathematical background:</strong> Let <span class="math notranslate nohighlight">\(f_Y(y)\)</span> denote the uncalibrated probability density function (PDF),
+targeting the probability distribution for <span class="math notranslate nohighlight">\(Y\)</span>. In our case, the PDF is given as a Gaussian, so that
+<span class="math notranslate nohighlight">\(f_Y(y) = \mathcal{N}\big(y; \mu_Y(X), \sigma^2_Y(X)\big)\)</span> with mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and variance
+<span class="math notranslate nohighlight">\(\sigma^2_Y(X)\)</span> obtained by a probabilistic regression model that depends on the input <span class="math notranslate nohighlight">\(X\)</span>.
+The calibrated PDF <span class="math notranslate nohighlight">\(g_Y(y)\)</span> is the rescaled Gaussian with fixed mean and rescaled variance, so that</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \mathcal{N}\Big(y; \mu_Y(X), \big(\theta_y \cdot \sigma_Y(X)\big)^2\Big) ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\theta_y\)</span> is the adaptive rescaling weight for a certain <span class="math notranslate nohighlight">\(y\)</span>.</p>
+<p>In contrast to the standard temperature scaling approach by <a class="footnote-reference brackets" href="#id7" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id8" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>, the GP-Normal utilizes a Gaussian process
+to obtain <span class="math notranslate nohighlight">\(\theta_y\)</span>, so that</p>
+<div class="math notranslate nohighlight">
+\[\theta_y \sim \text{gp}(0, k) ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(k\)</span> is the kernel function (for a more detailed description of the underlying Gaussian process, see
+documentation of parent class <a class="reference internal" href="../_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.AbstractGP.html#netcal.regression.gp.AbstractGP" title="netcal.regression.gp.AbstractGP"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.AbstractGP</span></code></a>).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n_inducing_points</strong> (<em>int</em>) – Number of inducing points used to approximate the input space. These inducing points are also optimized.</p></li>
+<li><p><strong>n_random_samples</strong> (<em>int</em>) – Number of random samples used to sample from the parameter distribution during optimization and inference.</p></li>
+<li><p><strong>correlations</strong> (<em>bool</em><em>, </em><em>default: False</em><em>,</em>) – If True, perform covariance estimation recalibration if the input during fit/transform is given as multiple
+independent distributions, e.g., by a mean and standard deviation vector for each sample.
+If the input is given as a mean vector and a covariance matrix for each sample, this method applies
+covariance recalibration by learning a recalibration weight for each entry.
+If False, perform standard regression recalibration and output independent probability distributions.</p></li>
+<li><p><strong>n_epochs</strong> (<em>int</em><em>, </em><em>default: 200</em>) – Number of optimization epochs.</p></li>
+<li><p><strong>batch_size</strong> (<em>int</em><em>, </em><em>default: 256</em>) – Size of batches during optimization.</p></li>
+<li><p><strong>num_workers</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 0</em>) – Number of workers used for the dataloader.</p></li>
+<li><p><strong>lr</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-2</em>) – Learning rate used for the Adam optimizer.</p></li>
+<li><p><strong>use_cuda</strong> (<em>str</em><em> or </em><em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+You can also pass a string “cuda:0”, “cuda:1”, etc. to specify the CUDA device.
+If False, use CPU for optimization and inference.</p></li>
+<li><p><strong>jitter</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-5</em>) – Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+Gaussian process optimization.</p></li>
+<li><p><strong>name_prefix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;gpnormal&quot;</em>) – Name prefix internally used in Pyro to distinguish between parameter stores.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id5">2</a>)</span>
+<p>Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id6">2</a>)</span>
+<p>Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id9" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id10" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">4</a><span class="fn-bracket">]</span></span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([n_inducing_points, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Additional information used to print if str(method) is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a GP model to the provided data using Gaussian process optimization.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x)</p></td>
+<td><p>Forward method defines the prior for the GP.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_fantasy_model</span></code>(inputs, targets, **kwargs)</p></td>
+<td><p>Returns a new GP model that incorporates the specified inputs and targets as new training data using online variational conditioning (OVC).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC coefficients, etc.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">guide</span></code>(x, y)</p></td>
+<td><p>Pyro guide that defines the variational distribution for the Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename[, use_cuda])</p></td>
+<td><p>Overwrite base method's load_model function as the parameters for the GP methods are stored differently compared to the remaining methods.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">model</span></code>(x, y)</p></td>
+<td><p>Model function that defines the computation graph.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_guide</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_model</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<td><p>Transform the given stddev to a distribution-calibrated one using the input mean and stddev as priors for the underlying Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<td><p>Sets gradients of all model parameters to zero.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
+                </div>
+              </div>
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+<li><a class="reference internal" href="#netcal.regression.IsotonicRegression"><code class="docutils literal notranslate"><span class="pre">IsotonicRegression</span></code></a></li>
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+<li class="toctree-l4"><a class="reference internal" href="#netcal.regression.IsotonicRegression"><code class="docutils literal notranslate"><span class="pre">IsotonicRegression</span></code></a></li>
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+  <section id="netcal-regression-isotonicregression">
+<h1>netcal.regression.IsotonicRegression<a class="headerlink" href="#netcal-regression-isotonicregression" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.IsotonicRegression">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.</span></span><span class="sig-name descname"><span class="pre">IsotonicRegression</span></span><a class="headerlink" href="#netcal.regression.IsotonicRegression" title="Permalink to this definition">¶</a></dt>
+<dd><p>Isotonic regression calibration for probabilistic regression models with multiple independent
+output dimensions (optionally).
+Isotonic regression is a piecewise constant, monotonically increasing mapping function used to recalibrate
+the estimated cumulative density function (CDF) of a probabilistic forecaster <a class="footnote-reference brackets" href="#id4" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>. The goal of regression
+calibration using Isotonic regression is to achieve quantile calibration.</p>
+<p>On the one hand, this method accepts as input X either a tuple X = (mean, stddev) using two NumPy arrays of
+shape N with N number of samples that express the estimated mean and standard deviation of a probabilistic
+forecaster. On the other hand, a NumPy array of shape (R, N) is also accepted where R denotes the number of
+probabilistic forecasts. For example, if probabilistic outputs are obtained by Monte-Carlo sampling using N samples
+and R stochastic forward passes, it is possible to pass all outputs to the calibration function in a single
+NumPy array.</p>
+<p>This method is capable of multiple independent data dimensions where separate calibration models are fitted for
+each data dimension. This method outputs a tuple consisting of three NumPy arrays:</p>
+<ul class="simple">
+<li><p>1st array: T points where the density/cumulative distribution functions are defined, shape: (T, N, D)</p></li>
+<li><p>2nd array: calibrated probability density function, shape: (T, N, D)</p></li>
+<li><p>3rd array: calibrated cumulative density function, shape: (T, N, D)</p></li>
+</ul>
+<p><strong>Mathematical background:</strong> In <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, regression calibration is defined in terms of <em>quantile calibration</em>.
+A probabilistic forecaster <span class="math notranslate nohighlight">\(h(X)\)</span> outputs for any input <span class="math notranslate nohighlight">\(X \in \mathbb{R}\)</span> a probability density
+distribution <span class="math notranslate nohighlight">\(f_Y(y)\)</span> for the target domain <span class="math notranslate nohighlight">\(Y \in \mathcal{Y} = \mathbb{R}\)</span>. The according
+cumulative density function (CDF) is denoted as <span class="math notranslate nohighlight">\(F_Y(y)\)</span>, the respective (inverse) quantile function
+<span class="math notranslate nohighlight">\(F^{-1}_Y(\tau)\)</span> for a certain confidence level <span class="math notranslate nohighlight">\(\tau \in [0, 1]\)</span>. The quantile function denotes
+the quantile boundaries in <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> given a certain confidence level <span class="math notranslate nohighlight">\(\tau\)</span>.
+Using this notation, <em>quantile calibration</em> <a class="footnote-reference brackets" href="#id4" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined as</p>
+<div class="math notranslate nohighlight">
+\[\mathbb{P}(Y \leq F^{-1}_Y(\tau)) = \tau, \quad \forall \tau \in [0, 1] ,\]</div>
+<p>which is equivalent to</p>
+<div class="math notranslate nohighlight">
+\[\mathbb{P}(F^{-1}_Y(\tau_1) \leq Y \leq F^{-1}_Y(\tau_2)) = \tau_2 - \tau_1,
+\quad \forall \tau_1, \tau_2 \in [0, 1] .\]</div>
+<p>In other words, the estimated quantiles should match the observed quantiles. For example, if we inspect the 90%
+quantiles of a forecaster over multiple samples, we would expect that 90% of all ground-truth estimates fall into
+these quantiles.</p>
+<p>The Isotonic Regression consumes the input cumulative distribution function (CDF) and compares it with the
+empirical data CDF. With this comparison, it is possible to map the uncalibrated CDF estimates to calibrated
+ones using a monotonically increasing step function.</p>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id2">2</a>,<a role="doc-backlink" href="#id3">3</a>)</span>
+<p>Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+“Accurate uncertainties for deep learning using calibrated regression.”
+International Conference on Machine Learning. PMLR, 2018.
+<a class="reference external" href="http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear model parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a isotonic regression calibration method to the provided data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Get parameters for this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename)</p></td>
+<td><p>Load model from saved torch dump.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, t])</p></td>
+<td><p>Transform uncalibrated distributional estimates (mean and stddev or stochastic samples) to calibrated ones by applying isotonic regression calibration of quantiles.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-regression-variancescaling">
+<h1>netcal.regression.VarianceScaling<a class="headerlink" href="#netcal-regression-variancescaling" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.VarianceScaling">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.</span></span><span class="sig-name descname"><span class="pre">VarianceScaling</span></span><a class="headerlink" href="#netcal.regression.VarianceScaling" title="Permalink to this definition">¶</a></dt>
+<dd><p>Variance recalibration using maximum likelihood estimation for multiple independent dimensions (optionally).
+Rescales the input standard deviation by a scalar parameter to achieve <em>variance calibration</em> <a class="footnote-reference brackets" href="#id7" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id8" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+This method uses the negative log likelihood as the loss function to optimize the scalar scaling parameter.
+The distributional mean is fixed during optimization.</p>
+<p>On the one hand, this method accepts as input X either a tuple X = (mean, stddev) using two NumPy arrays of
+shape N with N number of samples that express the estimated mean and standard deviation of a probabilistic
+forecaster. On the other hand, a NumPy array of shape (R, N) is also accepted where R denotes the number of
+probabilistic forecasts. For example, if probabilistic outputs are obtained by Monte-Carlo sampling using N samples
+and R stochastic forward passes, it is possible to pass all outputs to the calibration function in a single
+NumPy array.</p>
+<p>This method is capable of multiple independent data dimensions where separate calibration models are fitted for
+each data dimension. This method outputs the recalibrated standard deviation (stddev) for each dimension D.</p>
+<p><strong>Mathematical background:</strong> In <a class="footnote-reference brackets" href="#id7" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> and <a class="footnote-reference brackets" href="#id8" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>, regression calibration is defined in terms of <em>variance calibration</em>.
+A probabilistic forecaster <span class="math notranslate nohighlight">\(h(X)\)</span> outputs for any input <span class="math notranslate nohighlight">\(X \in \mathbb{R}\)</span> a mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span>
+and a variance <span class="math notranslate nohighlight">\(\sigma_Y^2(X)\)</span> for the target domain <span class="math notranslate nohighlight">\(Y \in \mathcal{Y} = \mathbb{R}\)</span>.
+Using this notation, <em>variance calibration</em> <a class="footnote-reference brackets" href="#id7" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id8" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> is defined as</p>
+<div class="math notranslate nohighlight">
+\[\mathbb{E}_{X,Y}\Big[(\mu_Y(X) - Y)^2 | \sigma^2_Y(X) = \sigma \Big] = \sigma^2,
+\quad \forall \sigma \in \mathbb{R}_{&gt;0},\]</div>
+<p>In other words, the estimated variance should match the observed variance given a certain variance level.
+For example, if a forecaster outputs 100 predictions with a variance of <span class="math notranslate nohighlight">\(\sigma^2=2\)</span>, we would also expect
+a variance (mean squared error) of 2.
+Further definitions for regression calibration are <em>quantile calibration</em> and <em>distribution calibration</em>.</p>
+<p>To achieve <em>variance calibration</em>, the Variance Scaling methods applies a temperature scaling on the
+input variance by a single scalar parameter <span class="math notranslate nohighlight">\(\theta\)</span>. The methods uses the negative log likelihood as the
+loss for the scalar. Since we are working with Gaussians, the loss is given by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathcal{L}(\theta) &amp;= -\sum^N_{n=1} \frac{1}{\sqrt{2\pi} \theta \cdot \sigma_Y(x_n)}
+\exp\Bigg( \frac{y_n - \mu_Y(x_n)}{2 (\theta \cdot \sigma_Y(x_n))^2} \Bigg) \\
+&amp;\propto -N \log(\theta) - \frac{1}{2\theta^2} \sum^N_{n=1} \sigma_Y^{-2}(x_n) ,
+\big(y_n - \mu_Y(x_n)\big)^2\end{split}\]</div>
+<p>which is to be minimized.
+Thus, we seek to get the minimum of the optimization objective which can be analytically determined in this case,
+setting its first derivative to 0 by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}&amp;\frac{\partial \mathcal{L}(\theta)}{\partial \theta} = 0\\
+\leftrightarrow \quad &amp; -N \theta^2 \sum^N_{n=1} \sigma_Y^{-2}(x_n) \big(y_n - \mu_Y(x_n) \big)^2 \\
+\leftrightarrow \quad &amp; \theta \pm \sqrt{\frac{1}{N} \sum^N_{n=1} \sigma_Y^{-2}(x_n) \big(y_n - \mu_Y(x_n) \big)^2} .\end{split}\]</div>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id3">2</a>,<a role="doc-backlink" href="#id5">3</a>)</span>
+<p>Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id4">2</a>,<a role="doc-backlink" href="#id6">3</a>)</span>
+<p>Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>()</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear model parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a variance scaling calibration method to the provided data.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Get parameters for this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename)</p></td>
+<td><p>Load model from saved torch dump.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<td><p>Transform uncalibrated distributional estimates (mean and stddev or stochastic samples) to calibrated ones by applying variance recalibration.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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+              </div>
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+  <section id="netcal-regression-gp-abstractgp">
+<h1>netcal.regression.gp.AbstractGP<a class="headerlink" href="#netcal-regression-gp-abstractgp" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.AbstractGP">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.</span></span><span class="sig-name descname"><span class="pre">AbstractGP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_inducing_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_random_samples</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_parameters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">correlations</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_epochs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">batch_size</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">256</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">num_workers</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lr</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">use_cuda</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">bool</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">jitter</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name_prefix</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'abstractgp'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.AbstractGP" title="Permalink to this definition">¶</a></dt>
+<dd><p>Distribution recalibration of regression models using a Gaussian process parameter estimation.
+The goal of regression calibration using a GP scheme is to achieve <em>distribution calibration</em>,
+i.e., to match the predicted moments (mean, variance) to the true observed ones. In contrast to <em>quantile
+calibration</em> <a href="#id11"><span class="problematic" id="id1">[3]_</span></a>, where only the marginal calibration is of interest, the <em>distribution calibration</em> is more
+restrictive. It requires that the predicted moments should match the observed ones <em>given a certain probability
+distribution</em>. Therefore, the authors in <a class="footnote-reference brackets" href="#id9" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> propose to use Gaussian process to estimate the recalibration
+parameters of a Beta calibration function locally (i.e., matching the observed moments of neighboring samples).</p>
+<p>In this framework, we use the base GP scheme to implement the Beta calibration for regression <a class="footnote-reference brackets" href="#id9" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> as well as
+to derive a novel parametric recalibration that yields a parametric Gaussian or Cauchy distribution as
+calibration output <a class="footnote-reference brackets" href="#id10" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.</p>
+<p>On the one hand, this method accepts as input X either a tuple X = (mean, stddev) using two NumPy arrays of
+shape N with N number of samples that express the estimated mean and standard deviation of a probabilistic
+forecaster. On the other hand, a NumPy array of shape (R, N) is also accepted where R denotes the number of
+probabilistic forecasts. For example, if probabilistic outputs are obtained by Monte-Carlo sampling using N samples
+and R stochastic forward passes, it is possible to pass all outputs to the calibration function in a single
+NumPy array.</p>
+<p>This method is capable of multiple independent data dimensions that are jointly optimized using a single Gaussian
+process. This method outputs a tuple consisting of three NumPy arrays:</p>
+<ul class="simple">
+<li><p>1st array: T points where the density/cumulative distribution functions are defined, shape: (T, N, D)</p></li>
+<li><p>2nd array: calibrated probability density function, shape: (T, N, D)</p></li>
+<li><p>3rd array: calibrated cumulative density function, shape: (T, N, D)</p></li>
+</ul>
+<p><strong>Mathematical background:</strong> In <a class="footnote-reference brackets" href="#id9" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, regression calibration is defined in terms of <em>distribution calibration</em>.
+A probabilistic forecaster <span class="math notranslate nohighlight">\(h(X)\)</span> outputs for any input <span class="math notranslate nohighlight">\(X \in \mathbb{R}\)</span> a probability density
+distribution <span class="math notranslate nohighlight">\(f_Y(y) \in \mathcal{F}_Y\)</span> (where <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> denotes the set of all possible
+probability distributions) for the target domain <span class="math notranslate nohighlight">\(Y \in \mathcal{Y} = \mathbb{R}\)</span>. Furthermore, let
+<span class="math notranslate nohighlight">\(S = h(X)\)</span> denote the random variable of model predictions.
+Using this notation, <em>distribution calibration</em> <a class="footnote-reference brackets" href="#id9" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is defined as</p>
+<div class="math notranslate nohighlight">
+\[f_Y(Y=y | S = s) = s(y), \quad \forall s \in \mathcal{F}_Y, \forall y \in \mathcal{Y} .\]</div>
+<p>In other words, “<em>this definition implies that if a calibrated model predicts a distribution with some mean</em>
+<span class="math notranslate nohighlight">\(\mu\)</span> <em>and variance</em> <span class="math notranslate nohighlight">\(\sigma^2\)</span> <em>, then it means that on average over all cases with the same
+prediction the mean of the target is</em> <span class="math notranslate nohighlight">\(\mu\)</span> <em>and variance is</em> <span class="math notranslate nohighlight">\(\sigma^2\)</span>” (cf. <a class="footnote-reference brackets" href="#id9" id="id7" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, p. 4 ll. 25-28).</p>
+<p>For uncertainty recalibration, a standard calibration function can be used, e. g., Variance Scaling.
+In contrast to the standard methods, we can use a Gaussian process to estimate the rescaling parameter of the
+scaling method. This offers more flexibility and a more “local” or focused recalibration of a single sample.</p>
+<p>Since not all calibration methods yield an analytically tractable likelihood (e.g., the GP-Beta uses a non-standard
+likelihood), the current GP scheme is a sampling based variational one.
+Furthermore, as the amount of training data might grow very large, we use an approximate GP with so called
+inducing points that are learnt from the data and used during inference to obtain the calibration parameters.
+Therefore, we the computational complexity keeps fixed during inference.
+For a detailed derivation of the GP scheme, cf. <a class="footnote-reference brackets" href="#id9" id="id8" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+For a detailed description of the kernel function, cf. <a class="reference internal" href="../_autosummary_regression_gp_submodules/_autosummary_regression_gp_kernel/netcal.regression.gp.kernel.GaussianRBFKernel.html#netcal.regression.gp.kernel.GaussianRBFKernel" title="netcal.regression.gp.kernel.GaussianRBFKernel"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.kernel.GaussianRBFKernel</span></code></a>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n_inducing_points</strong> (<em>int</em>) – Number of inducing points used to approximate the input space. These inducing points are also optimized.</p></li>
+<li><p><strong>n_random_samples</strong> (<em>int</em>) – Number of random samples used to sample from the parameter distribution during optimization and inference.</p></li>
+<li><p><strong>n_parameters</strong> (<em>int</em>) – Number of parameters that are required for a dedicated implementation of the GP method (mainly used internally).</p></li>
+<li><p><strong>correlations</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If True, perform covariance estimation or covariance recalibration on multivariate input data.
+Only works for GPNormal.</p></li>
+<li><p><strong>n_epochs</strong> (<em>int</em><em>, </em><em>default: 200</em>) – Number of optimization epochs.</p></li>
+<li><p><strong>batch_size</strong> (<em>int</em><em>, </em><em>default: 256</em>) – Size of batches during optimization.</p></li>
+<li><p><strong>num_workers</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 0</em>) – Number of workers used for the dataloader.</p></li>
+<li><p><strong>lr</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-2</em>) – Learning rate used for the Adam optimizer.</p></li>
+<li><p><strong>use_cuda</strong> (<em>str</em><em> or </em><em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+You can also pass a string “cuda:0”, “cuda:1”, etc. to specify the CUDA device.
+If False, use CPU for optimization and inference.</p></li>
+<li><p><strong>jitter</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-5</em>) – Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+Gaussian process optimization.</p></li>
+<li><p><strong>name_prefix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;abstractgp&quot;</em>) – Name prefix internally used in Pyro to distinguish between parameter stores.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id9" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id3">2</a>,<a role="doc-backlink" href="#id5">3</a>,<a role="doc-backlink" href="#id6">4</a>,<a role="doc-backlink" href="#id7">5</a>,<a role="doc-backlink" href="#id8">6</a>)</span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning (pp. 5897-5906), 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id10" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">2</a><span class="fn-bracket">]</span></span>
+<p>Song, L., Zhang, X., Smola, A., Gretton, A., &amp; Schölkopf, B.:
+“Tailoring density estimation via reproducing kernel moment matching.”
+In Proceedings of the 25th international conference on Machine learning (pp. 992-999), July 2008.
+<a class="reference external" href="https://www.cs.uic.edu/~zhangx/pubDoc/xinhua_icml08.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(n_inducing_points, ...[, ...])</p></td>
+<td><p>Create an instance of <cite>AbstractCalibration</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Additional information used to print if str(method) is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a GP model to the provided data using Gaussian process optimization.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x)</p></td>
+<td><p>Forward method defines the prior for the GP.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_fantasy_model</span></code>(inputs, targets, **kwargs)</p></td>
+<td><p>Returns a new GP model that incorporates the specified inputs and targets as new training data using online variational conditioning (OVC).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC coefficients, etc.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">guide</span></code>(x, y)</p></td>
+<td><p>Pyro guide that defines the variational distribution for the Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename[, use_cuda])</p></td>
+<td><p>Overwrite base method's load_model function as the parameters for the GP methods are stored differently compared to the remaining methods.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">model</span></code>(x, y)</p></td>
+<td><p>Model function that defines the computation graph.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_guide</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_model</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<td><p>Transform the given stddev to a distribution-calibrated one using the input mean and stddev as priors for the underlying Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<td><p>Sets gradients of all model parameters to zero.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-regression-gp-gpbeta">
+<h1>netcal.regression.gp.GPBeta<a class="headerlink" href="#netcal-regression-gp-gpbeta" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.GPBeta">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.</span></span><span class="sig-name descname"><span class="pre">GPBeta</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_inducing_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_random_samples</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name_prefix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'gpbeta'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.GPBeta" title="Permalink to this definition">¶</a></dt>
+<dd><p>GP-Beta recalibration method for regression uncertainty calibration using the well-known Beta calibration method
+from  classification calibration in combination with a Gaussian process (GP) parameter estimation.
+The basic idea of GP-Beta <a class="footnote-reference brackets" href="#id10" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> is to apply recalibration on the uncalibrated cumulative density function (CDF),
+similar as to the Isotonic Regression method <a class="footnote-reference brackets" href="#id11" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+Since the CDF is restricted to the <span class="math notranslate nohighlight">\([0, 1]\)</span> interval, the authors in <a class="footnote-reference brackets" href="#id10" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> propose to use the
+Beta calibration scheme <a class="footnote-reference brackets" href="#id12" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a> known in the scope of confidence calibration.
+Furthermore, the authors use a GP to obtain the recalibration parameters of the Beta function for each
+sample individually, so that it should finally achieve <em>distribution calibration</em> <a class="footnote-reference brackets" href="#id10" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
+<p><strong>Mathematical background:</strong> Let <span class="math notranslate nohighlight">\(f_Y(y)\)</span> denote the uncalibrated probability density function (PDF),
+targeting the probability distribution for <span class="math notranslate nohighlight">\(Y\)</span>.
+Let <span class="math notranslate nohighlight">\(\tau_y \in [0, 1]\)</span> denote a certain quantile on the uncalibrated CDF which
+is denoted by <span class="math notranslate nohighlight">\(\tau_y = F_Y(y)\)</span>.
+Furthermore, let <span class="math notranslate nohighlight">\(g_Y(y)\)</span> and <span class="math notranslate nohighlight">\(G_Y(y)\)</span> denote the recalibrated PDF and CDF, respectively.
+The Beta calibration function <span class="math notranslate nohighlight">\(\mathbf{c}_\beta(\tau_y)\)</span> known from <a class="footnote-reference brackets" href="#id12" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a> is given by</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{c}_\beta(\tau_y) = \phi\big( a \log(\tau_y) - b \log(1-\tau_y) + c \big)\]</div>
+<p>with recalibration parameters <span class="math notranslate nohighlight">\(a,b \in \mathbb{R}_{&gt;0}\)</span> and <span class="math notranslate nohighlight">\(c \in \mathbb{R}\)</span>, and
+<span class="math notranslate nohighlight">\(\phi(\cdot)\)</span> as the sigmoid function <a class="footnote-reference brackets" href="#id12" id="id7" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>.
+This method serves as a mapping from the uncalibrated CDF to the calibrated one, so that</p>
+<div class="math notranslate nohighlight">
+\[G_Y(y) = \mathbf{c}_\beta\big( F_Y(y) \big)\]</div>
+<p>holds. The PDF is the derivative of the CDF, so that the calibrated PDF is given by</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \frac{\partial \mathbf{c}_\beta}{\partial y}
+= \frac{\partial \mathbf{c}_\beta}{\partial \tau_y} \frac{\partial \tau_y}{\partial y}
+= \mathbf{r}_\beta(\tau_y) f_Y(y) ,\]</div>
+<p>with <span class="math notranslate nohighlight">\(\mathbf{r}_\beta(\tau_y)\)</span> as a beta link function <a class="footnote-reference brackets" href="#id10" id="id8" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> given by</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{r}_\beta(\tau_y) = \Bigg(\frac{a}{\tau_y} + \frac{b}{1-\tau_y} \Bigg)
+\mathbf{c}_\beta(\tau_y) \big(1 - \mathbf{c}_\beta(\tau_y)\big) .\]</div>
+<p>Finally, the recalibration parameters <span class="math notranslate nohighlight">\(a, b\)</span> and <span class="math notranslate nohighlight">\(c\)</span> are obtained using a Gaussian process scheme.
+In this way, it is possible to apply non-parametric <em>distribution calibration</em> <a class="footnote-reference brackets" href="#id10" id="id9" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n_inducing_points</strong> (<em>int</em>) – Number of inducing points used to approximate the input space. These inducing points are also optimized.</p></li>
+<li><p><strong>n_random_samples</strong> (<em>int</em>) – Number of random samples used to sample from the parameter distribution during optimization and inference.</p></li>
+<li><p><strong>n_epochs</strong> (<em>int</em><em>, </em><em>default: 200</em>) – Number of optimization epochs.</p></li>
+<li><p><strong>batch_size</strong> (<em>int</em><em>, </em><em>default: 256</em>) – Size of batches during optimization.</p></li>
+<li><p><strong>num_workers</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 0</em>) – Number of workers used for the dataloader.</p></li>
+<li><p><strong>lr</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-2</em>) – Learning rate used for the Adam optimizer.</p></li>
+<li><p><strong>use_cuda</strong> (<em>str</em><em> or </em><em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+You can also pass a string “cuda:0”, “cuda:1”, etc. to specify the CUDA device.
+If False, use CPU for optimization and inference.</p></li>
+<li><p><strong>jitter</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-5</em>) – Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+Gaussian process optimization.</p></li>
+<li><p><strong>name_prefix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;gpbeta&quot;</em>) – Name prefix internally used in Pyro to distinguish between parameter stores.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id10" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id3">2</a>,<a role="doc-backlink" href="#id5">3</a>,<a role="doc-backlink" href="#id8">4</a>,<a role="doc-backlink" href="#id9">5</a>)</span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id11" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+“Accurate uncertainties for deep learning using calibrated regression.”
+International Conference on Machine Learning. PMLR, 2018.
+<a class="reference external" href="http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id12" role="note">
+<span class="label"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id4">1</a>,<a role="doc-backlink" href="#id6">2</a>,<a role="doc-backlink" href="#id7">3</a>)</span>
+<p>Kull, Meelis, Telmo Silva Filho, and Peter Flach:
+“Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers”
+Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
+<a class="reference external" href="http://proceedings.mlr.press/v54/kull17a/kull17a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([n_inducing_points, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Additional information used to print if str(method) is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a GP model to the provided data using Gaussian process optimization.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x)</p></td>
+<td><p>Forward method defines the prior for the GP.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_fantasy_model</span></code>(inputs, targets, **kwargs)</p></td>
+<td><p>Returns a new GP model that incorporates the specified inputs and targets as new training data using online variational conditioning (OVC).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC coefficients, etc.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">guide</span></code>(x, y)</p></td>
+<td><p>Pyro guide that defines the variational distribution for the Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename[, use_cuda])</p></td>
+<td><p>Overwrite base method's load_model function as the parameters for the GP methods are stored differently compared to the remaining methods.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">model</span></code>(x, y)</p></td>
+<td><p>Model function that defines the computation graph.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_guide</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_model</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, t])</p></td>
+<td><p>Transform the given stddev to a distribution-calibrated one using the input mean and stddev as priors for the underlying Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
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+  <section id="netcal-regression-gp-gpcauchy">
+<h1>netcal.regression.gp.GPCauchy<a class="headerlink" href="#netcal-regression-gp-gpcauchy" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.GPCauchy">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.</span></span><span class="sig-name descname"><span class="pre">GPCauchy</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_inducing_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_random_samples</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name_prefix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'gpcauchy'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.GPCauchy" title="Permalink to this definition">¶</a></dt>
+<dd><p>GP-Cauchy recalibration method for regression uncertainty calibration that consumes an uncalibrated Gaussian
+distribution but converts it to a calibrated Cauchy distribution.
+This method uses a Gaussian process (GP) for a flexible estimation of the recalibration parameter (cf. <a class="footnote-reference brackets" href="#id6" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>).
+Similar to <a class="reference internal" href="netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a>, the GP-Cauchy <a class="footnote-reference brackets" href="#id7" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> acts as a kind of temperature scaling for
+the variance of a Gaussian distribution <a class="footnote-reference brackets" href="#id8" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id9" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a>. However, the rescaled variance is interpreted as the
+scaling parameter of a Cauchy distribution. Furthermore, the rescaling parameter is not globally fixed but obtained
+by a GP for each sample individually, so that we are able to convert a Gaussian to a Cauchy distribution <a class="footnote-reference brackets" href="#id7" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+Thus, the GP-Cauchy seeks for <strong>distribution calibration</strong> but for parametric Cauchy distributions.
+Note that this method does not change the mean but only reinterprets the predicted variance as the Cauchy scaling
+parameter. The mode of the Cauchy is assumed to be equal to the input mean.</p>
+<p><strong>Mathematical background:</strong> Let <span class="math notranslate nohighlight">\(f_Y(y)\)</span> denote the uncalibrated probability density function (PDF),
+targeting the probability distribution for <span class="math notranslate nohighlight">\(Y\)</span>. In our case, the uncalibrated PDF is given as a Gaussian, so
+that <span class="math notranslate nohighlight">\(f_Y(y) = \mathcal{N}\big(y; \mu_Y(X), \sigma^2_Y(X)\big)\)</span> with mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and variance
+<span class="math notranslate nohighlight">\(\sigma^2_Y(X)\)</span> obtained by a probabilistic regression model that depends on the input <span class="math notranslate nohighlight">\(X\)</span>.
+The calibrated PDF <span class="math notranslate nohighlight">\(g_Y(y)\)</span> is a rescaled Cauchy distribution with fixed mode <span class="math notranslate nohighlight">\(x_0 \in \mathbb{R}\)</span>
+and rescaled scaling parameter <span class="math notranslate nohighlight">\(\lambda \in \mathbb{R}_{&gt;0}\)</span>, so that</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \text{Cauchy}\Big(y; x_0=\mu_Y(X), \lambda=\big(\theta_y \cdot \sigma_Y(X)\big) \Big) ,\]</div>
+<p>where  <span class="math notranslate nohighlight">\(\theta_y\)</span> is the adaptive rescaling weight for a certain <span class="math notranslate nohighlight">\(y\)</span>.</p>
+<p>The GP-Cauchy utilizes a Gaussian process to obtain <span class="math notranslate nohighlight">\(\theta_y\)</span>, so that</p>
+<div class="math notranslate nohighlight">
+\[\theta_y \sim \text{gp}(0, k) ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(k\)</span> is the kernel function (for a more detailed description of the underlying Gaussian process, see
+documentation of parent class <a class="reference internal" href="netcal.regression.gp.AbstractGP.html#netcal.regression.gp.AbstractGP" title="netcal.regression.gp.AbstractGP"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.AbstractGP</span></code></a>).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n_inducing_points</strong> (<em>int</em>) – Number of inducing points used to approximate the input space. These inducing points are also optimized.</p></li>
+<li><p><strong>n_random_samples</strong> (<em>int</em>) – Number of random samples used to sample from the parameter distribution during optimization and inference.</p></li>
+<li><p><strong>n_epochs</strong> (<em>int</em><em>, </em><em>default: 200</em>) – Number of optimization epochs.</p></li>
+<li><p><strong>batch_size</strong> (<em>int</em><em>, </em><em>default: 256</em>) – Size of batches during optimization.</p></li>
+<li><p><strong>num_workers</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 0</em>) – Number of workers used for the dataloader.</p></li>
+<li><p><strong>lr</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-2</em>) – Learning rate used for the Adam optimizer.</p></li>
+<li><p><strong>use_cuda</strong> (<em>str</em><em> or </em><em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+You can also pass a string “cuda:0”, “cuda:1”, etc. to specify the CUDA device.
+If False, use CPU for optimization and inference.</p></li>
+<li><p><strong>jitter</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-5</em>) – Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+Gaussian process optimization.</p></li>
+<li><p><strong>name_prefix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;gpcauchy&quot;</em>) – Name prefix internally used in Pyro to distinguish between parameter stores.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id5">2</a>)</span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id9" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">4</a><span class="fn-bracket">]</span></span>
+<p>Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([n_inducing_points, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Additional information used to print if str(method) is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a GP model to the provided data using Gaussian process optimization.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x)</p></td>
+<td><p>Forward method defines the prior for the GP.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_fantasy_model</span></code>(inputs, targets, **kwargs)</p></td>
+<td><p>Returns a new GP model that incorporates the specified inputs and targets as new training data using online variational conditioning (OVC).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC coefficients, etc.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">guide</span></code>(x, y)</p></td>
+<td><p>Pyro guide that defines the variational distribution for the Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename[, use_cuda])</p></td>
+<td><p>Overwrite base method's load_model function as the parameters for the GP methods are stored differently compared to the remaining methods.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">model</span></code>(x, y)</p></td>
+<td><p>Model function that defines the computation graph.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_guide</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_model</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<td><p>Transform the given stddev to a distribution-calibrated one using the input mean and stddev as priors for the underlying Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<td><p>Sets gradients of all model parameters to zero.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
+                </div>
+              </div>
+            </div>
+          </div>
+        </div>
+        
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new file mode 100644
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+  <section id="netcal-regression-gp-gpnormal">
+<h1>netcal.regression.gp.GPNormal<a class="headerlink" href="#netcal-regression-gp-gpnormal" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.GPNormal">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.</span></span><span class="sig-name descname"><span class="pre">GPNormal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_inducing_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">12</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_random_samples</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">128</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">correlations</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name_prefix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'gpnormal'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.GPNormal" title="Permalink to this definition">¶</a></dt>
+<dd><p>GP-Normal recalibration method for regression uncertainty calibration using a temperature scaling for the
+variance of a normal distribution but using the Gaussian process (GP) parameter estimation to adaptively
+obtain the scaling parameter for each input individually.
+The temperature scaling for the variance <a class="footnote-reference brackets" href="#id7" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id8" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> seeks to preserve a parametric Gaussian distribution as
+calibration output and aims to reach <em>variance calibration</em>. That is, matching the predicted variance with the
+observed “error variance” aka mean squared error.
+In contrast to the standard approach, the GP-Normal <a class="footnote-reference brackets" href="#id9" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a> uses a Gaussian process (GP) from <a class="footnote-reference brackets" href="#id10" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a> to flexibly obtain
+a recalibration weight for each sample individually.
+Thus, the GP-Normal seeks for a mixed form of <strong>variance calibration</strong> in a more flexible way towards
+<strong>distribution calibration</strong> for Gaussians.
+Note that this method does not change the mean but only the predicted variance.</p>
+<p><strong>Mathematical background:</strong> Let <span class="math notranslate nohighlight">\(f_Y(y)\)</span> denote the uncalibrated probability density function (PDF),
+targeting the probability distribution for <span class="math notranslate nohighlight">\(Y\)</span>. In our case, the PDF is given as a Gaussian, so that
+<span class="math notranslate nohighlight">\(f_Y(y) = \mathcal{N}\big(y; \mu_Y(X), \sigma^2_Y(X)\big)\)</span> with mean <span class="math notranslate nohighlight">\(\mu_Y(X)\)</span> and variance
+<span class="math notranslate nohighlight">\(\sigma^2_Y(X)\)</span> obtained by a probabilistic regression model that depends on the input <span class="math notranslate nohighlight">\(X\)</span>.
+The calibrated PDF <span class="math notranslate nohighlight">\(g_Y(y)\)</span> is the rescaled Gaussian with fixed mean and rescaled variance, so that</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \mathcal{N}\Big(y; \mu_Y(X), \big(\theta_y \cdot \sigma_Y(X)\big)^2\Big) ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\theta_y\)</span> is the adaptive rescaling weight for a certain <span class="math notranslate nohighlight">\(y\)</span>.</p>
+<p>In contrast to the standard temperature scaling approach by <a class="footnote-reference brackets" href="#id7" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, <a class="footnote-reference brackets" href="#id8" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>, the GP-Normal utilizes a Gaussian process
+to obtain <span class="math notranslate nohighlight">\(\theta_y\)</span>, so that</p>
+<div class="math notranslate nohighlight">
+\[\theta_y \sim \text{gp}(0, k) ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(k\)</span> is the kernel function (for a more detailed description of the underlying Gaussian process, see
+documentation of parent class <a class="reference internal" href="netcal.regression.gp.AbstractGP.html#netcal.regression.gp.AbstractGP" title="netcal.regression.gp.AbstractGP"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.AbstractGP</span></code></a>).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>n_inducing_points</strong> (<em>int</em>) – Number of inducing points used to approximate the input space. These inducing points are also optimized.</p></li>
+<li><p><strong>n_random_samples</strong> (<em>int</em>) – Number of random samples used to sample from the parameter distribution during optimization and inference.</p></li>
+<li><p><strong>correlations</strong> (<em>bool</em><em>, </em><em>default: False</em><em>,</em>) – If True, perform covariance estimation recalibration if the input during fit/transform is given as multiple
+independent distributions, e.g., by a mean and standard deviation vector for each sample.
+If the input is given as a mean vector and a covariance matrix for each sample, this method applies
+covariance recalibration by learning a recalibration weight for each entry.
+If False, perform standard regression recalibration and output independent probability distributions.</p></li>
+<li><p><strong>n_epochs</strong> (<em>int</em><em>, </em><em>default: 200</em>) – Number of optimization epochs.</p></li>
+<li><p><strong>batch_size</strong> (<em>int</em><em>, </em><em>default: 256</em>) – Size of batches during optimization.</p></li>
+<li><p><strong>num_workers</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 0</em>) – Number of workers used for the dataloader.</p></li>
+<li><p><strong>lr</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-2</em>) – Learning rate used for the Adam optimizer.</p></li>
+<li><p><strong>use_cuda</strong> (<em>str</em><em> or </em><em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – The optimization and inference might also run on a CUDA device. If True, use the first available CUDA device.
+You can also pass a string “cuda:0”, “cuda:1”, etc. to specify the CUDA device.
+If False, use CPU for optimization and inference.</p></li>
+<li><p><strong>jitter</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: 1e-5</em>) – Small digit that is added to the diagonal of a covariance matrix to stabilize Cholesky decomposition during
+Gaussian process optimization.</p></li>
+<li><p><strong>name_prefix</strong> (<em>str</em><em>, </em><em>optional</em><em>, </em><em>default: &quot;gpnormal&quot;</em>) – Name prefix internally used in Pyro to distinguish between parameter stores.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id5">2</a>)</span>
+<p>Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id6">2</a>)</span>
+<p>Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id9" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id10" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">4</a><span class="fn-bracket">]</span></span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([n_inducing_points, ...])</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
+<td><p>Clear module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Additional information used to print if str(method) is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code>(X, y[, tensorboard])</p></td>
+<td><p>Fit a GP model to the provided data using Gaussian process optimization.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code>(X[, y])</p></td>
+<td><p>Fit to data, then transform it.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x)</p></td>
+<td><p>Forward method defines the prior for the GP.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_fantasy_model</span></code>(inputs, targets, **kwargs)</p></td>
+<td><p>Returns a new GP model that incorporates the specified inputs and targets as new training data using online variational conditioning (OVC).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code>([deep])</p></td>
+<td><p>Overwrite base method's get_params function to also capture child parameters as variational strategy, LMC coefficients, etc.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">guide</span></code>(x, y)</p></td>
+<td><p>Pyro guide that defines the variational distribution for the Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_model</span></code>(filename[, use_cuda])</p></td>
+<td><p>Overwrite base method's load_model function as the parameters for the GP methods are stored differently compared to the remaining methods.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">model</span></code>(x, y)</p></td>
+<td><p>Model function that defines the computation graph.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_guide</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_model</span></code>(input[, beta, name_prefix])</p></td>
+<td><p>(For Pyro integration only).</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
+<td><p>Set the parameters of this estimator.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<td><p>Transform the given stddev to a distribution-calibrated one using the input mean and stddev as priors for the underlying Gaussian process.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<td><p>Sets gradients of all model parameters to zero.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
+                </div>
+              </div>
+            </div>
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+  <section id="netcal-regression-gp-kernel-gaussianrbfkernel">
+<h1>netcal.regression.gp.kernel.GaussianRBFKernel<a class="headerlink" href="#netcal-regression-gp-kernel-gaussianrbfkernel" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.kernel.GaussianRBFKernel">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.kernel.</span></span><span class="sig-name descname"><span class="pre">GaussianRBFKernel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cov</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.kernel.GaussianRBFKernel" title="Permalink to this definition">¶</a></dt>
+<dd><p>Computes the Gaussian RBF kernel using input points defined as Gaussians.
+This kernel has been proposed by <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+Given input samples <span class="math notranslate nohighlight">\(\mathbf{x}_i, \mathbf{x}_j \in \mathbb{R}^d\)</span> of dimension <span class="math notranslate nohighlight">\(d\)</span> with
+according covariances <span class="math notranslate nohighlight">\(\Sigma_i, \Sigma_j \in \mathbb{R}^{d \times d}\)</span> that define a
+Gaussian for each input point. The kernel function is defined as</p>
+<div class="math notranslate nohighlight">
+\[k\Big((\mathbf{x}_i, \Sigma_i), (\mathbf{x}_j, \Sigma_j)\Big) = \theta^d |\Sigma_{ij}|^{-\frac{1}{2}} \exp \Bigg( -\frac{1}{2} (\mathbf{x}_i-\mathbf{x}_j)^\top
+\Sigma_{ij}^{-1}(\mathbf{x}_i-\mathbf{x}_j)  \Bigg) ,\]</div>
+<p>with</p>
+<div class="math notranslate nohighlight">
+\[\Sigma_{ij} = \Sigma_i + \Sigma_j + \theta^2 \mathbf{I} ,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\theta \in \mathbb{R}\)</span> is a lengthscale parameter. Since we’re only using
+independent normal distributions for each dimension, we only have diagonal covariance matrices.</p>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Song, L., Zhang, X., Smola, A., Gretton, A., &amp; Schölkopf, B.:
+“Tailoring density estimation via reproducing kernel moment matching.”
+In Proceedings of the 25th international conference on Machine learning (pp. 992-999), July 2008.
+<a class="reference external" href="https://www.cs.uic.edu/~zhangx/pubDoc/xinhua_icml08.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(*args, cov, **kwargs)</p></td>
+<td><p>Initializes internal Module state, shared by both nn.Module and ScriptModule.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_module</span></code>(name, module)</p></td>
+<td><p>Adds a child module to the current module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">added_loss_terms</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply</span></code>(fn)</p></td>
+<td><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>) as well as self.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">bfloat16</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">buffers</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module buffers.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraint_for_parameter_name</span></code>(param_name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">covar_dist</span></code>(x1, x2[, diag, ...])</p></td>
+<td><p>This is a helper method for computing the Euclidean distance between all pairs of points in x1 and x2.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cpu</span></code>()</p></td>
+<td><p>Moves all model parameters and buffers to the CPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cuda</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the GPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<td><p>Sets the module in evaluation mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<td><p>Set the extra representation of the module</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(x1, x2[, diag])</p></td>
+<td><p>Computes the Gaussian moment-matching RBF kernel.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">initialize</span></code>(**kwargs)</p></td>
+<td><p>Set a value for a parameter</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_strict_shapes</span></code>(value)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">local_load_samples</span></code>(samples_dict, memo, prefix)</p></td>
+<td><p>Defines local behavior of this Module when loading parameters from a samples_dict generated by a Pyro sampling mechanism.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<td><p>Returns an iterator over all modules in the network.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_added_loss_terms</span></code>()</p></td>
+<td><p>Returns an iterator over module variational strategies, yielding both the name of the variational strategy as well as the strategy itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_constraints</span></code>([memo, prefix])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_hyperparameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters_and_constraints</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_priors</span></code>([memo, prefix])</p></td>
+<td><p>Returns an iterator over the module's priors, yielding the name of the prior, the prior, the associated parameter names, and the transformation callable.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_sub_kernels</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">num_outputs_per_input</span></code>(x1, x2)</p></td>
+<td><p>How many outputs are produced per input (default 1) if x1 is size <cite>n x d</cite> and x2 is size <cite>m x d</cite>, then the size of the kernel will be <cite>(n * num_outputs_per_input) x (m * num_outputs_per_input)</cite> Default: 1</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<td><p>Returns an iterator over module parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prediction_strategy</span></code>(train_inputs, ...)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_load_from_samples</span></code>(samples_dict)</p></td>
+<td><p>Convert this Module in to a batch Module by loading parameters from the given <cite>samples_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyro_sample_from_prior</span></code>()</p></td>
+<td><p>For each parameter in this Module and submodule that have defined priors, sample a value for that parameter from its corresponding prior with a pyro.sample primitive and load the resulting value in to the parameter.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_added_loss_term</span></code>(name)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<td><p>Adds a buffer to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_constraint</span></code>(param_name, constraint)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<td><p>Registers a forward pre-hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, parameter)</p></td>
+<td><p>Adds a parameter to the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_prior</span></code>(name, prior, param_or_closure)</p></td>
+<td><p>Adds a prior to the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<td><p>Change if autograd should record operations on parameters in this module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_from_prior</span></code>(prior_name)</p></td>
+<td><p>Sample parameter values from prior.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
+<td><p>Returns a dictionary containing a whole state of the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sub_kernels</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<td><p>Moves and/or casts the parameters and buffers.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_pyro_random_module</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<td><p>Sets the module in training mode.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">update_added_loss_term</span></code>(name, added_loss_term)</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational_parameters</span></code>()</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<td><p>Sets gradients of all model parameters to zero.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
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+  <section id="netcal-regression-gp-likelihood-betalikelihood">
+<h1>netcal.regression.gp.likelihood.BetaLikelihood<a class="headerlink" href="#netcal-regression-gp-likelihood-betalikelihood" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.likelihood.BetaLikelihood">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.likelihood.</span></span><span class="sig-name descname"><span class="pre">BetaLikelihood</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">loc</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">logvar</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parameters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.likelihood.BetaLikelihood" title="Permalink to this definition">¶</a></dt>
+<dd><p>Beta likelihood used to implement the basic functionality of the <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPBeta.html#netcal.regression.gp.GPBeta" title="netcal.regression.gp.GPBeta"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPBeta</span></code></a>
+recalibration method.
+This function serves the standard beta calibration mapping for the cumulative distribution function (CDF) as well
+as the derived beta link function for the recalibration of the probability density function (PDF).
+Since the likelihood of the Gaussian process is calculated during model training using the PDF, this method
+is required not only for the inference but also for the training of the <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPBeta.html#netcal.regression.gp.GPBeta" title="netcal.regression.gp.GPBeta"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPBeta</span></code></a> method
+<a class="footnote-reference brackets" href="#id6" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
+<p><strong>Mathematical background:</strong> From the docstring of <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPBeta.html#netcal.regression.gp.GPBeta" title="netcal.regression.gp.GPBeta"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPBeta</span></code></a>, we know that the GP-Beta
+utilizes the beta calibration method <a class="footnote-reference brackets" href="#id7" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> from confidence calibration (cf. <a class="reference internal" href="../../../_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration" title="netcal.scaling.BetaCalibration"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.scaling.BetaCalibration</span></code></a>)
+for the recalibration of the CDF.
+Let <span class="math notranslate nohighlight">\(f_Y(y)\)</span> denote the uncalibrated probability density function (PDF), targeting the probability
+distribution for <span class="math notranslate nohighlight">\(Y\)</span>. Let <span class="math notranslate nohighlight">\(\tau_y \in [0, 1]\)</span> denote a certain quantile on the uncalibrated CDF which
+is denoted by <span class="math notranslate nohighlight">\(\tau_y = F_Y(y)\)</span>.
+Furthermore, let <span class="math notranslate nohighlight">\(g_Y(y)\)</span> and <span class="math notranslate nohighlight">\(G_Y(y)\)</span> denote the recalibrated PDF and CDF, respectively.
+The Beta calibration function <span class="math notranslate nohighlight">\(\mathbf{c}_\beta(\tau_y)\)</span> known from <a class="footnote-reference brackets" href="#id7" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> is given by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{c}_\beta(\tau_y) &amp;= \phi\big( a \log(\tau_y) - b \log(1-\tau_y) + c \big) \\
+&amp;= \phi\big( z(\tau_y) \big) ,\end{split}\]</div>
+<p>with recalibration parameters <span class="math notranslate nohighlight">\(a,b \in \mathbb{R}_{&gt;0}\)</span> and <span class="math notranslate nohighlight">\(c \in \mathbb{R}\)</span>, and
+<span class="math notranslate nohighlight">\(\phi(\cdot)\)</span> as the sigmoid function <a class="footnote-reference brackets" href="#id7" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
+In this case, we denote the logit of the beta calibration function <span class="math notranslate nohighlight">\(\mathbf{c}_\beta(\tau_y)\)</span> by</p>
+<div class="math notranslate nohighlight">
+\[z(\tau_y) = a \log(\tau_y) - b \log(1-\tau_y) + c .\]</div>
+<p>The beta calibration method serves as a mapping from the uncalibrated CDF to the calibrated one, so that</p>
+<div class="math notranslate nohighlight">
+\[G_Y(y) = \mathbf{c}_\beta\big( F_Y(y) \big)\]</div>
+<p>holds. The PDF is recalibrated using the beta link function <span class="math notranslate nohighlight">\(\mathbf{r}_\beta(\tau_y)\)</span> <a class="footnote-reference brackets" href="#id6" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> by</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \frac{\partial \mathbf{c}_\beta}{\partial y}
+= \frac{\partial \mathbf{c}_\beta}{\partial \tau_y} \frac{\partial \tau_y}{\partial y}
+= \mathbf{r}_\beta(\tau_y) f_Y(y) ,\]</div>
+<p>where the beta link function is given by</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{r}_\beta(\tau_y) = \Bigg(\frac{a}{\tau_y} + \frac{b}{1-\tau_y} \Bigg)
+\mathbf{c}_\beta(\tau_y) \big(1 - \mathbf{c}_\beta(\tau_y)\big) .\]</div>
+<p>The recalibration parameters <span class="math notranslate nohighlight">\(a,b\)</span> and <span class="math notranslate nohighlight">\(c\)</span> are not directly infered by the GP but rather use the
+underlying function parameters <span class="math notranslate nohighlight">\(w_a, w_b, w_c \in \mathbb{R}\)</span>, so that</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}a &amp;= \exp(\gamma_a^{-1} w_a + \delta_a) \\
+b &amp;= \exp(\gamma_b^{-1} w_b + \delta_b) \\
+c &amp;= \gamma_c^{-1} w_c + \delta_c\end{split}\]</div>
+<p>are given as the beta distribution parameters to guarantee <span class="math notranslate nohighlight">\(a, b &gt; 0\)</span>.
+During optimization, we need the log of the link function. We use a numerical more stable version:</p>
+<div class="math notranslate nohighlight">
+\[\log\big(\mathbf{r}_\beta(\tau_y)\big) = \log \Bigg(\frac{a}{\tau_y} + \frac{b}{1-\tau_y} \Bigg) +
+\log \Big( \mathbf{c}_\beta(\tau_y) \big(1 - \mathbf{c}_\beta(\tau_y)\big) \Big)\]</div>
+<p>The first part can be rewritten as:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}&amp; \log \Bigg(\frac{a}{\tau_y} + \frac{b}{1-\tau_y} \Bigg) \\
+&amp;= \log \Bigg( \exp \Big( \log(a) - \log(\tau_y) \Big) + \exp \Big( \log(b) - \log(1-\tau_y) \Big) \Bigg) \\
+&amp;= \log \Bigg( \exp \Big( \gamma_a^{-1} w_a + \delta_a - \log(\tau_y) \Big) + \exp \Big( \gamma_b^{-1} w_b + \delta_b - \log(1-\tau_y) \Big) \Bigg) \\
+&amp;= \text{logsumexp} \Bigg[ \Big( \gamma_a^{-1} w_a + \delta_a - \log(\tau_y) \Big), \Big( \gamma_b^{-1} w_b + \delta_b - \log(1-\tau_y) \Big) \Bigg]\end{split}\]</div>
+<p>where <span class="math notranslate nohighlight">\(\text{logsumexp}\)</span> is a numerical stable version of <span class="math notranslate nohighlight">\(\log \Big( \sum_x \exp(x) \Big)\)</span> in PyTorch.
+In addition, we can also simplify the expression for the log of the sigmoid functions that are used within
+the computation of <span class="math notranslate nohighlight">\(\mathbf{c}_\beta(\tau_y)\)</span> by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\log(\phi(x)) &amp;= -\log \Big( \exp(-x) + 1 \Big), \\
+\log(1-\phi(x)) &amp;= -\log \Big( \exp(x) + 1 \Big)\end{split}\]</div>
+<p>which can also be expressed in terms of PyTorch’s numerical more stable <span class="math notranslate nohighlight">\(\text{softplus}\)</span>
+function <span class="math notranslate nohighlight">\(\log \Big( \exp(x) + 1 \Big)\)</span>. Thus, the log of the link function can be expressed as</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\log(r_\beta(\tau_y)) = &amp;\text{logsumexp} \Bigg[ \Big( \gamma_a^{-1} w_a + \delta_a - \log(\tau_y) \Big),
+\Big( \gamma_b^{-1} w_b + \delta_b - \log(1-\tau_y) \Big) \Bigg] \\
+&amp;- \Big(\text{softplus}\big(-z(x)\big) + \text{softplus}\big(z(x)\big)\Big)\end{split}\]</div>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>loc</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>[</em><em>1</em><em>]</em><em>, </em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+This class also supports broadcasting of the calculations to t sampling points (defining the non-parametric
+PDF/CDF, first dim) and r random samples (second dim).</p></li>
+<li><p><strong>logvar</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>[</em><em>1</em><em>]</em><em>, </em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Log of the variance vector of the uncalibrated (Gaussian) probability distribution with n samples and d
+dimensions. This class also supports broadcasting of the calculations to t sampling points (defining the
+non-parametric PDF/CDF, first dim) and r random samples (second dim).</p></li>
+<li><p><strong>parameters</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>[</em><em>1</em><em>]</em><em>, </em><em>r</em><em>]</em><em>, </em><em>n</em><em>, </em><em>p*d</em><em>)</em>) – Rescaling parameters of the beta link function <strong>before applying the exponential</strong> (for parameters <span class="math notranslate nohighlight">\(a, b\)</span>)
+with n samples d dimensions, r random samples and p as the number of parameters (p=3 in this case).</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id5">2</a>)</span>
+<p>Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning (pp. 5897-5906), 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+</aside>
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id3">2</a>,<a role="doc-backlink" href="#id4">3</a>)</span>
+<p>Kull, Meelis, Telmo Silva Filho, and Peter Flach:
+“Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers”
+Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
+<a class="reference external" href="http://proceedings.mlr.press/v54/kull17a/kull17a.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(loc, logvar, parameters)</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cdf</span></code>(t)</p></td>
+<td><p>Calculate cumulative distribution function (CDF) at the points given by 't' using the underlying uncalibrated cumulative <span class="math notranslate nohighlight">\(F_Y(y)\)</span> that is rescaled by the calibration parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">conjugate_update</span></code>(other)</p></td>
+<td><p>EXPERIMENTAL Creates an updated distribution fusing information from another compatible distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">entropy</span></code>()</p></td>
+<td><p>Returns entropy of distribution, batched over batch_shape.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">enumerate_support</span></code>([expand])</p></td>
+<td><p>Returns tensor containing all values supported by a discrete distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand</span></code>(batch_shape[, _instance])</p></td>
+<td><p>Returns a new <code class="xref py py-class docutils literal notranslate"><span class="pre">ExpandedDistribution</span></code> instance with batch dimensions expanded to <cite>batch_shape</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand_by</span></code>(sample_shape)</p></td>
+<td><p>Expands a distribution by adding <code class="docutils literal notranslate"><span class="pre">sample_shape</span></code> to the left side of its <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_rsample_</span></code>(value)</p></td>
+<td><p>Force reparameterized or detached sampling on a single distribution instance.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">icdf</span></code>(value)</p></td>
+<td><p>Returns the inverse cumulative density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">independent</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_shapes</span></code>(**arg_shapes)</p></td>
+<td><p>Infers <code class="docutils literal notranslate"><span class="pre">batch_shape</span></code> and <code class="docutils literal notranslate"><span class="pre">event_shape</span></code> given shapes of args to <code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">log_prob</span></code>(value)</p></td>
+<td><p>Calculate the log-density at the points given by 'value' using the underlying uncalibrated distribution <span class="math notranslate nohighlight">\(f_Y(y)\)</span> that is rescaled by the calibration parameters.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">mask</span></code>(mask)</p></td>
+<td><p>Masks a distribution by a boolean or boolean-valued tensor that is broadcastable to the distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> .</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">perplexity</span></code>()</p></td>
+<td><p>Returns perplexity of distribution, batched over batch_shape.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reshape</span></code>([sample_shape, extra_event_dims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">rsample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped reparameterized sample or sample_shape shaped batch of reparameterized samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped sample or sample_shape shaped batch of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_n</span></code>(n)</p></td>
+<td><p>Generates n samples or n batches of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">score_parts</span></code>(x, *args, **kwargs)</p></td>
+<td><p>Computes ingredients for stochastic gradient estimators of ELBO.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_default_validate_args</span></code>(value)</p></td>
+<td><p>Sets whether validation is enabled or disabled.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">shape</span></code>([sample_shape])</p></td>
+<td><p>The tensor shape of samples from this distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_event</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p>Reinterprets the <code class="docutils literal notranslate"><span class="pre">n</span></code> rightmost dimensions of this distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> as event dims, adding them to the left side of <code class="xref py py-attr docutils literal notranslate"><span class="pre">event_shape</span></code>.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
+
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+<li class="toctree-l7"><a class="reference internal" href="netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood.html">netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood</a></li>
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+<li class="toctree-l7 current"><a class="current reference internal" href="#">netcal.regression.gp.likelihood.CauchyLikelihood</a><ul>
+<li class="toctree-l8"><a class="reference internal" href="#netcal.regression.gp.likelihood.CauchyLikelihood"><code class="docutils literal notranslate"><span class="pre">CauchyLikelihood</span></code></a></li>
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+  <section id="netcal-regression-gp-likelihood-cauchylikelihood">
+<h1>netcal.regression.gp.likelihood.CauchyLikelihood<a class="headerlink" href="#netcal-regression-gp-likelihood-cauchylikelihood" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.likelihood.CauchyLikelihood">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.likelihood.</span></span><span class="sig-name descname"><span class="pre">CauchyLikelihood</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">loc</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">logvar</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parameters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.likelihood.CauchyLikelihood" title="Permalink to this definition">¶</a></dt>
+<dd><p>Standard likelihood of a Cauchy distribution used within <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPCauchy.html#netcal.regression.gp.GPCauchy" title="netcal.regression.gp.GPCauchy"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPCauchy</span></code></a>
+where the scaling parameter <span class="math notranslate nohighlight">\(\lambda\)</span> is obtained by
+combining the uncalibrated standard deviation with a rescaling parameter obtained by a Gaussian process.
+This method provides the likelihood for the <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPCauchy.html#netcal.regression.gp.GPCauchy" title="netcal.regression.gp.GPCauchy"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPCauchy</span></code></a> by applying a rescaling
+of the uncalibrated input standard deviation by a recalibration parameter <span class="math notranslate nohighlight">\(\theta_y\)</span> <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, so that the
+recalibrated probability density function (PDF) <span class="math notranslate nohighlight">\(g_Y(y)\)</span> is given by</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \text{Cauchy}\Big(y; x_0=\mu_Y(X), \lambda=\big(\theta_y \cdot \sigma_Y(X)\big)\Big)\]</div>
+<p>with <span class="math notranslate nohighlight">\(\mu_Y(X) \in \mathbb{R}\)</span> and <span class="math notranslate nohighlight">\(\sigma_Y(X) \in \mathbb{R}_{&gt;0}\)</span> as the uncalibrated
+mean and standard deviation, respectively, and <span class="math notranslate nohighlight">\(x_0\)</span> as the mode of the Cauchy which is approximated by
+the uncalibrated mean estimate.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>loc</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+This class also supports broadcasting of the calculations to r random samples (first dim).</p></li>
+<li><p><strong>logvar</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Log of the variance vector of the uncalibrated (Gaussian) probability distribution with n samples and d
+dimensions. This class also supports broadcasting of the calculations to r random samples (first dim).</p></li>
+<li><p><strong>parameters</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>r</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Rescaling parameter of the GP-Cauchy with n samples d dimensions and r random samples.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(loc, logvar, parameters)</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cdf</span></code>(value)</p></td>
+<td><p>Returns the cumulative density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">conjugate_update</span></code>(other)</p></td>
+<td><p>EXPERIMENTAL Creates an updated distribution fusing information from another compatible distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">entropy</span></code>()</p></td>
+<td><p>Returns entropy of distribution, batched over batch_shape.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">enumerate_support</span></code>([expand])</p></td>
+<td><p>Returns tensor containing all values supported by a discrete distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand</span></code>(batch_shape[, _instance])</p></td>
+<td><p>Expand-method.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand_by</span></code>(sample_shape)</p></td>
+<td><p>Expands a distribution by adding <code class="docutils literal notranslate"><span class="pre">sample_shape</span></code> to the left side of its <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_rsample_</span></code>(value)</p></td>
+<td><p>Force reparameterized or detached sampling on a single distribution instance.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">icdf</span></code>(value)</p></td>
+<td><p>Returns the inverse cumulative density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">independent</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_shapes</span></code>(**arg_shapes)</p></td>
+<td><p>Infers <code class="docutils literal notranslate"><span class="pre">batch_shape</span></code> and <code class="docutils literal notranslate"><span class="pre">event_shape</span></code> given shapes of args to <code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">log_prob</span></code>(value)</p></td>
+<td><p>Returns the log of the probability density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">mask</span></code>(mask)</p></td>
+<td><p>Masks a distribution by a boolean or boolean-valued tensor that is broadcastable to the distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> .</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">perplexity</span></code>()</p></td>
+<td><p>Returns perplexity of distribution, batched over batch_shape.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reshape</span></code>([sample_shape, extra_event_dims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">rsample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped reparameterized sample or sample_shape shaped batch of reparameterized samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped sample or sample_shape shaped batch of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_n</span></code>(n)</p></td>
+<td><p>Generates n samples or n batches of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">score_parts</span></code>(x, *args, **kwargs)</p></td>
+<td><p>Computes ingredients for stochastic gradient estimators of ELBO.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_default_validate_args</span></code>(value)</p></td>
+<td><p>Sets whether validation is enabled or disabled.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">shape</span></code>([sample_shape])</p></td>
+<td><p>The tensor shape of samples from this distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_event</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p>Reinterprets the <code class="docutils literal notranslate"><span class="pre">n</span></code> rightmost dimensions of this distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> as event dims, adding them to the left side of <code class="xref py py-attr docutils literal notranslate"><span class="pre">event_shape</span></code>.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+  <section id="netcal-regression-gp-likelihood-scaledmultivariatenormallikelihood">
+<h1>netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood<a class="headerlink" href="#netcal-regression-gp-likelihood-scaledmultivariatenormallikelihood" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.likelihood.</span></span><span class="sig-name descname"><span class="pre">ScaledMultivariateNormalLikelihood</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">loc</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parameters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood" title="Permalink to this definition">¶</a></dt>
+<dd><p>Standard likelihood of a <strong>multivariate</strong> normal distribution used within <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a>
+for <em>covariance estimation</em> and <em>covariance recalibration</em>.
+This method provides the multivariate likelihood for the <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a> when
+“correlations=True”.
+The input to this class is given as the LDL* decomposed (uncalibrated) covariance matrix
+<span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}_{\mathbf{Y}}(X) = \mathbf{L}\mathbf{D}\mathbf{L}^{\top}\)</span>.
+Afterwards, this method applies a rescaling of the uncalibrated <span class="math notranslate nohighlight">\(\mathbf{L} \in \mathbb{R}^{d \times d}\)</span>
+and <span class="math notranslate nohighlight">\(\mathbf{D} \in \mathbb{R}^{d \times d}\)</span> matrices by the
+recalibration parameters <span class="math notranslate nohighlight">\(\theta_L \in \mathbb{R}^{d \times d}\)</span> and
+<span class="math notranslate nohighlight">\(\theta_D \in \mathbb{R}^{d \times d}_{&gt;0}\)</span> <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, so that the recalibrated
+probability density function (PDF) <span class="math notranslate nohighlight">\(g_{\mathbf{Y}}(\mathbf{y})\)</span> is given by</p>
+<div class="math notranslate nohighlight">
+\[g_{\mathbf{Y}}(\mathbf{y}) = \mathcal{N}\Big(\mathbf{y}; \boldsymbol{\mu}_{\mathbf{Y}}(X),
+(\theta_L \odot \mathbf{L})(\theta_D \odot \mathbf{D})(\theta_L \odot \mathbf{L})^{\top} \big) \Big)\]</div>
+<p>with <span class="math notranslate nohighlight">\(\boldsymbol{\mu}_{\mathbf{Y}}(X) \in \mathbb{R}\)</span> as the uncalibrated mean and <span class="math notranslate nohighlight">\(\odot\)</span> as
+the element-wise matrix multiplication operator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>loc</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+This class also supports broadcasting of the calculations to r random samples (first dim).</p></li>
+<li><p><strong>var</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>(</em><em>d^2+d</em><em>) </em><em>// 2</em><em>)</em>) – LDL* decomposed covariance matrix (compressed form) of the uncalibrated (Gaussian) probability distribution
+with n samples and d dimensions. This class also supports broadcasting of the calculations to r random samples
+(first dim).</p></li>
+<li><p><strong>parameters</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>r</em><em>]</em><em>, </em><em>n</em><em>, </em><em>(</em><em>d+d^2</em><em>) </em><em>// 2</em><em>)</em>) – Rescaling parameter of the GP-Normal for the decomposed covariance matrices with n samples d dimensions
+and r random samples.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(loc, var, parameters)</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cdf</span></code>(value)</p></td>
+<td><p>Returns the cumulative density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">conjugate_update</span></code>(other)</p></td>
+<td><p>EXPERIMENTAL Creates an updated distribution fusing information from another compatible distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">entropy</span></code>()</p></td>
+<td><p>Returns entropy of distribution, batched over batch_shape.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">enumerate_support</span></code>([expand])</p></td>
+<td><p>Returns tensor containing all values supported by a discrete distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand</span></code>(batch_shape[, _instance])</p></td>
+<td><p>Expand-method.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand_by</span></code>(sample_shape)</p></td>
+<td><p>Expands a distribution by adding <code class="docutils literal notranslate"><span class="pre">sample_shape</span></code> to the left side of its <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_rsample_</span></code>(value)</p></td>
+<td><p>Force reparameterized or detached sampling on a single distribution instance.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">icdf</span></code>(value)</p></td>
+<td><p>Returns the inverse cumulative density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">independent</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_shapes</span></code>(loc[, covariance_matrix, ...])</p></td>
+<td><p>Infers <code class="docutils literal notranslate"><span class="pre">batch_shape</span></code> and <code class="docutils literal notranslate"><span class="pre">event_shape</span></code> given shapes of args to <code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">log_prob</span></code>(value)</p></td>
+<td><p>Returns the log of the probability density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">mask</span></code>(mask)</p></td>
+<td><p>Masks a distribution by a boolean or boolean-valued tensor that is broadcastable to the distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> .</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">perplexity</span></code>()</p></td>
+<td><p>Returns perplexity of distribution, batched over batch_shape.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reconstruct</span></code>(decomposed)</p></td>
+<td><p>Reconstruct the lower <span class="math notranslate nohighlight">\(\mathbf{L}\)</span> and diagonal <span class="math notranslate nohighlight">\(\mathbf{D}\)</span> matrices from the flat input vector given by &quot;decomposed&quot; since Pyro does not support an additional dimension internally.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">rescale</span></code>(var, parameters)</p></td>
+<td><p>This method applies the rescaling of the LDL* decomposed covariance matrices by computing <span class="math notranslate nohighlight">\(\theta_L \odot \mathbf{L}\)</span> and <span class="math notranslate nohighlight">\(\theta_D \odot \mathbf{D}\)</span>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reshape</span></code>([sample_shape, extra_event_dims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">rsample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped reparameterized sample or sample_shape shaped batch of reparameterized samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped sample or sample_shape shaped batch of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_n</span></code>(n)</p></td>
+<td><p>Generates n samples or n batches of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">score_parts</span></code>(x, *args, **kwargs)</p></td>
+<td><p>Computes ingredients for stochastic gradient estimators of ELBO.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_default_validate_args</span></code>(value)</p></td>
+<td><p>Sets whether validation is enabled or disabled.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">shape</span></code>([sample_shape])</p></td>
+<td><p>The tensor shape of samples from this distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_event</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p>Reinterprets the <code class="docutils literal notranslate"><span class="pre">n</span></code> rightmost dimensions of this distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> as event dims, adding them to the left side of <code class="xref py py-attr docutils literal notranslate"><span class="pre">event_shape</span></code>.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
+</section>
+
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+<li><a class="reference internal" href="#netcal.regression.gp.likelihood.ScaledNormalLikelihood"><code class="docutils literal notranslate"><span class="pre">ScaledNormalLikelihood</span></code></a></li>
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+<li class="toctree-l8"><a class="reference internal" href="#netcal.regression.gp.likelihood.ScaledNormalLikelihood"><code class="docutils literal notranslate"><span class="pre">ScaledNormalLikelihood</span></code></a></li>
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+  <section id="netcal-regression-gp-likelihood-scalednormallikelihood">
+<h1>netcal.regression.gp.likelihood.ScaledNormalLikelihood<a class="headerlink" href="#netcal-regression-gp-likelihood-scalednormallikelihood" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regression.gp.likelihood.ScaledNormalLikelihood">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regression.gp.likelihood.</span></span><span class="sig-name descname"><span class="pre">ScaledNormalLikelihood</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">loc</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">logvar</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parameters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Tensor</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regression.gp.likelihood.ScaledNormalLikelihood" title="Permalink to this definition">¶</a></dt>
+<dd><p>Standard likelihood of a normal distribution used within <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a>
+with additional rescaling parameters for the variance.
+This method provides the likelihood for the <a class="reference internal" href="../../_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a> by applying a rescaling
+of the uncalibrated input variance by a recalibration parameter <span class="math notranslate nohighlight">\(\theta_y\)</span> <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, so that the recalibrated
+probability density function (PDF) <span class="math notranslate nohighlight">\(g_Y(y)\)</span> is given by</p>
+<div class="math notranslate nohighlight">
+\[g_Y(y) = \mathcal{N}\Big(y; \mu_Y(X), \big(\theta_y \cdot \sigma_Y(X)\big)^2\Big)\]</div>
+<p>with <span class="math notranslate nohighlight">\(\mu_Y(X) \in \mathbb{R}\)</span> and <span class="math notranslate nohighlight">\(\sigma_Y(X) \in \mathbb{R}_{&gt;0}\)</span> as the uncalibrated
+mean and standard deviation, respectively.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>loc</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Mean vector of the uncalibrated (Gaussian) probability distribution with n samples and d dimensions.
+This class also supports broadcasting of the calculations to r random samples (first dim).</p></li>
+<li><p><strong>logvar</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>1</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Log of the variance vector of the uncalibrated (Gaussian) probability distribution with n samples and d
+dimensions. This class also supports broadcasting of the calculations to r random samples (first dim).</p></li>
+<li><p><strong>parameters</strong> (<em>torch.Tensor</em><em>, </em><em>shape:</em><em> (</em><em>[</em><em>r</em><em>]</em><em>, </em><em>n</em><em>, </em><em>d</em><em>)</em>) – Rescaling parameter of the GP-Normal with n samples d dimensions and r random samples.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">References</p>
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+European Conference on Computer Vision (ECCV) Workshops, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</aside>
+</aside>
+<p class="rubric">Methods</p>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(loc, logvar, parameters)</p></td>
+<td><p>Constructor.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">cdf</span></code>(value)</p></td>
+<td><p>Returns the cumulative density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">conjugate_update</span></code>(other)</p></td>
+<td><p>EXPERIMENTAL Creates an updated distribution fusing information from another compatible distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">entropy</span></code>()</p></td>
+<td><p>Method to compute the entropy using Bregman divergence of the log normalizer.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">enumerate_support</span></code>([expand])</p></td>
+<td><p>Returns tensor containing all values supported by a discrete distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand</span></code>(batch_shape[, _instance])</p></td>
+<td><p>Expand-method.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">expand_by</span></code>(sample_shape)</p></td>
+<td><p>Expands a distribution by adding <code class="docutils literal notranslate"><span class="pre">sample_shape</span></code> to the left side of its <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">has_rsample_</span></code>(value)</p></td>
+<td><p>Force reparameterized or detached sampling on a single distribution instance.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">icdf</span></code>(value)</p></td>
+<td><p>Returns the inverse cumulative density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">independent</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_shapes</span></code>(**arg_shapes)</p></td>
+<td><p>Infers <code class="docutils literal notranslate"><span class="pre">batch_shape</span></code> and <code class="docutils literal notranslate"><span class="pre">event_shape</span></code> given shapes of args to <code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">log_prob</span></code>(value)</p></td>
+<td><p>Returns the log of the probability density/mass function evaluated at <cite>value</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">mask</span></code>(mask)</p></td>
+<td><p>Masks a distribution by a boolean or boolean-valued tensor that is broadcastable to the distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> .</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">perplexity</span></code>()</p></td>
+<td><p>Returns perplexity of distribution, batched over batch_shape.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">reshape</span></code>([sample_shape, extra_event_dims])</p></td>
+<td><p></p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">rsample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped reparameterized sample or sample_shape shaped batch of reparameterized samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample</span></code>([sample_shape])</p></td>
+<td><p>Generates a sample_shape shaped sample or sample_shape shaped batch of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">sample_n</span></code>(n)</p></td>
+<td><p>Generates n samples or n batches of samples if the distribution parameters are batched.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">score_parts</span></code>(x, *args, **kwargs)</p></td>
+<td><p>Computes ingredients for stochastic gradient estimators of ELBO.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_default_validate_args</span></code>(value)</p></td>
+<td><p>Sets whether validation is enabled or disabled.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">shape</span></code>([sample_shape])</p></td>
+<td><p>The tensor shape of samples from this distribution.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_event</span></code>([reinterpreted_batch_ndims])</p></td>
+<td><p>Reinterprets the <code class="docutils literal notranslate"><span class="pre">n</span></code> rightmost dimensions of this distributions <code class="xref py py-attr docutils literal notranslate"><span class="pre">batch_shape</span></code> as event dims, adding them to the left side of <code class="xref py py-attr docutils literal notranslate"><span class="pre">event_shape</span></code>.</p></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
+
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+<span id="netcal-regression-gp-kernel"></span><h1>netcal.regression.gp.kernel<a class="headerlink" href="#module-netcal.regression.gp.kernel" title="Permalink to this heading">¶</a></h1>
+<section id="kernels-for-gp">
+<h2>Kernels for GP<a class="headerlink" href="#kernels-for-gp" title="Permalink to this heading">¶</a></h2>
+<p>Package with all custom definitions for the kernel functions that are used by the Gaussian process (GP) framework.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
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+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression_gp_kernel/netcal.regression.gp.kernel.GaussianRBFKernel.html#netcal.regression.gp.kernel.GaussianRBFKernel" title="netcal.regression.gp.kernel.GaussianRBFKernel"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GaussianRBFKernel</span></code></a>(*args, cov, **kwargs)</p></td>
+<td><p>Computes the Gaussian RBF kernel using input points defined as Gaussians.</p></td>
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+  <section id="module-netcal.regression.gp.likelihood">
+<span id="netcal-regression-gp-likelihood"></span><h1>netcal.regression.gp.likelihood<a class="headerlink" href="#module-netcal.regression.gp.likelihood" title="Permalink to this heading">¶</a></h1>
+<section id="likelihoods-for-gp">
+<h2>Likelihoods for GP<a class="headerlink" href="#likelihoods-for-gp" title="Permalink to this heading">¶</a></h2>
+<p>Package with all custom definitions for the likelihood functions that are used by the Gaussian process (GP) framework
+during training and inference.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledNormalLikelihood.html#netcal.regression.gp.likelihood.ScaledNormalLikelihood" title="netcal.regression.gp.likelihood.ScaledNormalLikelihood"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ScaledNormalLikelihood</span></code></a>(loc, logvar, parameters)</p></td>
+<td><p>Standard likelihood of a normal distribution used within <a class="reference internal" href="../_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a> with additional rescaling parameters for the variance.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood.html#netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood" title="netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ScaledMultivariateNormalLikelihood</span></code></a>(loc, var, ...)</p></td>
+<td><p>Standard likelihood of a <strong>multivariate</strong> normal distribution used within <a class="reference internal" href="../_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPNormal</span></code></a> for <em>covariance estimation</em> and <em>covariance recalibration</em>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.BetaLikelihood.html#netcal.regression.gp.likelihood.BetaLikelihood" title="netcal.regression.gp.likelihood.BetaLikelihood"><code class="xref py py-obj docutils literal notranslate"><span class="pre">BetaLikelihood</span></code></a>(loc, logvar, parameters)</p></td>
+<td><p>Beta likelihood used to implement the basic functionality of the <a class="reference internal" href="../_autosummary_regression_gp/netcal.regression.gp.GPBeta.html#netcal.regression.gp.GPBeta" title="netcal.regression.gp.GPBeta"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPBeta</span></code></a> recalibration method.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.CauchyLikelihood.html#netcal.regression.gp.likelihood.CauchyLikelihood" title="netcal.regression.gp.likelihood.CauchyLikelihood"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CauchyLikelihood</span></code></a>(loc, logvar, parameters)</p></td>
+<td><p>Standard likelihood of a Cauchy distribution used within <a class="reference internal" href="../_autosummary_regression_gp/netcal.regression.gp.GPCauchy.html#netcal.regression.gp.GPCauchy" title="netcal.regression.gp.GPCauchy"><code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.regression.gp.GPCauchy</span></code></a> where the scaling parameter <span class="math notranslate nohighlight">\(\lambda\)</span> is obtained by combining the uncalibrated standard deviation with a rescaling parameter obtained by a Gaussian process.</p></td>
+</tr>
+</tbody>
+</table>
+</section>
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+<li class="toctree-l5"><a class="reference internal" href="_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.html">netcal.regression.gp.kernel</a></li>
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+  <section id="module-netcal.regression.gp">
+<span id="netcal-regression-gp"></span><h1>netcal.regression.gp<a class="headerlink" href="#module-netcal.regression.gp" title="Permalink to this heading">¶</a></h1>
+<section id="regression-gp-calibration-package">
+<h2>Regression GP Calibration Package<a class="headerlink" href="#regression-gp-calibration-package" title="Permalink to this heading">¶</a></h2>
+<p>This package provides the framework for all Gaussian Process (GP) recalibration schemes.
+These are <em>GP-Beta</em> [2], GP-Normal [3], and GP-Cauchy [3]. The goal of regression calibration using a GP scheme is to achieve
+<em>distribution calibration</em>, i.e., to match the predicted moments (mean, variance) to the true observed ones.
+In contrast to <em>quantile calibration</em> [1], where only the marginal calibration is of interest, the <em>distribution calibration</em> [2] is more
+restrictive. It requires that the predicted moments should match the observed ones <em>given a certain probability
+distribution</em>. Therefore, the authors in [2] propose to use Gaussian process to estimate the recalibration
+parameters of a Beta calibration function locally (i.e., matching the observed moments of neighboring samples).
+The <em>GP-Normal</em> and the <em>GP-Cauchy</em> follow the same principle but return parametric output distributions after calibration.</p>
+<section id="references">
+<h3>References<a class="headerlink" href="#references" title="Permalink to this heading">¶</a></h3>
+<p>[1] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+“Accurate uncertainties for deep learning using calibrated regression.”
+International Conference on Machine Learning. PMLR, 2018.
+<a class="reference external" href="http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf">Get source online</a></p>
+<p>[2] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+<p>[3] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+ArXiv preprint arXiv:2207.01242, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</section>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression_gp/netcal.regression.gp.AbstractGP.html#netcal.regression.gp.AbstractGP" title="netcal.regression.gp.AbstractGP"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AbstractGP</span></code></a>(n_inducing_points, ...[, ...])</p></td>
+<td><p>Distribution recalibration of regression models using a Gaussian process parameter estimation.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regression_gp/netcal.regression.gp.GPBeta.html#netcal.regression.gp.GPBeta" title="netcal.regression.gp.GPBeta"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GPBeta</span></code></a>([n_inducing_points, ...])</p></td>
+<td><p>GP-Beta recalibration method for regression uncertainty calibration using the well-known Beta calibration method from  classification calibration in combination with a Gaussian process (GP) parameter estimation.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal" title="netcal.regression.gp.GPNormal"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GPNormal</span></code></a>([n_inducing_points, ...])</p></td>
+<td><p>GP-Normal recalibration method for regression uncertainty calibration using a temperature scaling for the variance of a normal distribution but using the Gaussian process (GP) parameter estimation to adaptively obtain the scaling parameter for each input individually.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regression_gp/netcal.regression.gp.GPCauchy.html#netcal.regression.gp.GPCauchy" title="netcal.regression.gp.GPCauchy"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GPCauchy</span></code></a>([n_inducing_points, ...])</p></td>
+<td><p>GP-Cauchy recalibration method for regression uncertainty calibration that consumes an uncalibrated Gaussian distribution but converts it to a calibrated Cauchy distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+<section id="packages">
+<h2>Packages<a class="headerlink" href="#packages" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.html#module-netcal.regression.gp.kernel" title="netcal.regression.gp.kernel"><code class="xref py py-obj docutils literal notranslate"><span class="pre">kernel</span></code></a></p></td>
+<td><p>Kernels for GP
+
+Package with all custom definitions for the kernel functions that are used by the Gaussian process (GP) framework.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regression_gp_submodules/netcal.regression.gp.likelihood.html#module-netcal.regression.gp.likelihood" title="netcal.regression.gp.likelihood"><code class="xref py py-obj docutils literal notranslate"><span class="pre">likelihood</span></code></a></p></td>
+<td><p>Likelihoods for GP
+
+Package with all custom definitions for the likelihood functions that are used by the Gaussian process (GP) framework
+during training and inference.</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+</section>
+
+
+                </div>
+              </div>
+            </div>
+          </div>
+        </div>
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index 22e890e..1c6ef0b 100644
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+<li><a class="reference internal" href="#netcal.regularization.ConfidencePenalty"><code class="docutils literal notranslate"><span class="pre">ConfidencePenalty</span></code></a><ul>
+<li><a class="reference internal" href="#netcal.regularization.ConfidencePenalty.__init__"><code class="docutils literal notranslate"><span class="pre">ConfidencePenalty.__init__()</span></code></a></li>
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-  <div class="section" id="netcal-regularization-confidencepenalty">
-<h1>netcal.regularization.ConfidencePenalty<a class="headerlink" href="#netcal-regularization-confidencepenalty" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.regularization.ConfidencePenalty">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.regularization.</code><code class="sig-name descname">ConfidencePenalty</code><span class="sig-paren">(</span><em class="sig-param">weight: float = 1.0</em>, <em class="sig-param">threshold: float = -1.0</em>, <em class="sig-param">reduction='mean'</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.modules.loss._Loss</span></code></p>
-<p>Confidence penalty regularization implementation for PyTorch.
-This penalty term can be applied to any loss function as a regularizer <a class="footnote-reference brackets" href="#id2" id="id1">1</a>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.regularization.html#regularization-methods-for-confidence-calibration">Regularization Methods for Confidence Calibration</a></li>
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+  <section id="netcal-regularization-confidencepenalty">
+<h1>netcal.regularization.ConfidencePenalty<a class="headerlink" href="#netcal-regularization-confidencepenalty" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regularization.ConfidencePenalty">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regularization.</span></span><span class="sig-name descname"><span class="pre">ConfidencePenalty</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reduction</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'mean'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty" title="Permalink to this definition">¶</a></dt>
+<dd><p>Confidence penalty regularization implementation for PyTorch.
+This penalty term can be applied to any loss function as a regularizer <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>weight</strong> (<em>float</em>) – Weight of entropy.</p></li>
 <li><p><strong>threshold</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Entropy threshold (no penalty is assigned above threshold).</p></li>
@@ -63,26 +204,23 @@ <h1>netcal.regularization.ConfidencePenalty<a class="headerlink" href="#netcal-r
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>G. Pereyra, G. Tucker, J. Chorowski, Lukasz Kaiser, and G. Hinton:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>G. Pereyra, G. Tucker, J. Chorowski, Lukasz Kaiser, and G. Hinton:
 “Regularizing neural networks by penalizing confident output distributions.”
 CoRR, 2017.
 <a class="reference external" href="https://arxiv.org/pdf/1701.06548">Get source online</a></p>
-</dd>
-</dl>
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.__init__">
-<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">weight: float = 1.0</em>, <em class="sig-param">threshold: float = -1.0</em>, <em class="sig-param">reduction='mean'</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty.__init__" title="Permalink to this definition">¶</a></dt>
+</aside>
+</aside>
+<dl class="py method">
+<dt class="sig sig-object py" id="netcal.regularization.ConfidencePenalty.__init__">
+<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">reduction</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'mean'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty.__init__" title="Permalink to this definition">¶</a></dt>
 <dd><p>Constructor. For parameter description, see class docstring.</p>
 </dd></dl>
 
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([weight, threshold, reduction])</p></td>
 <td><p>Constructor.</p></td>
@@ -111,23 +249,41 @@ <h1>netcal.regularization.ConfidencePenalty<a class="headerlink" href="#netcal-r
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">double</span></code>()</p></td>
 <td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">entropy</span></code>(input, calibrated)</p></td>
+<td><p>Cross entropy between input tensor and calibrated counter part</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">eval</span></code>()</p></td>
 <td><p>Sets the module in evaluation mode.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">extra_repr</span></code>()</p></td>
 <td><p>Set the extra representation of the module</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
 <td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(input)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(input, *ig_args, **ig_kwargs)</p></td>
 <td><p>Forward call.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
 <td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
 </tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
-<td><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into this module and its descendants.</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
 <td><p>Returns an iterator over all modules in the network.</p></td>
@@ -159,1128 +315,106 @@ <h1>netcal.regularization.ConfidencePenalty<a class="headerlink" href="#netcal-r
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
 <td><p>Registers a forward pre-hook on the module.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, param)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, param)</p></td>
 <td><p>Adds a parameter to the module.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
 <td><p>Change if autograd should record operations on parameters in this module.</p></td>
 </tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
 <td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>([destination, prefix, keep_vars])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
 <td><p>Returns a dictionary containing a whole state of the module.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
 <td><p>Moves and/or casts the parameters and buffers.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
 <td><p>Sets the module in training mode.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
 <td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
 </tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
 <td><p>Sets gradients of all model parameters to zero.</p></td>
 </tr>
 </tbody>
 </table>
 <p class="rubric">Attributes</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">dump_patches</span></code></p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">T_destination</span></code></p></td>
+<td><p>alias of TypeVar('T_destination', bound=<code class="xref py py-class docutils literal notranslate"><span class="pre">Dict</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code>])</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">dump_patches</span></code></p></td>
 <td><p></p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">epsilon</span></code></p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">epsilon</span></code></p></td>
 <td><p></p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty._get_backward_hooks">
-<code class="sig-name descname">_get_backward_hooks</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty._get_backward_hooks" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the backward hooks for use in the call function.
-It returns two lists, one with the full backward hooks and one with the non-full
-backward hooks.</p>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty._load_from_state_dict">
-<code class="sig-name descname">_load_from_state_dict</code><span class="sig-paren">(</span><em class="sig-param">state_dict</em>, <em class="sig-param">prefix</em>, <em class="sig-param">local_metadata</em>, <em class="sig-param">strict</em>, <em class="sig-param">missing_keys</em>, <em class="sig-param">unexpected_keys</em>, <em class="sig-param">error_msgs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty._load_from_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into only
-this module, but not its descendants. This is called on every submodule
-in <code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code>. Metadata saved for this
-module in input <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> is provided as <code class="xref py py-attr docutils literal notranslate"><span class="pre">local_metadata</span></code>.
-For state dicts without metadata, <code class="xref py py-attr docutils literal notranslate"><span class="pre">local_metadata</span></code> is empty.
-Subclasses can achieve class-specific backward compatible loading using
-the version number at <cite>local_metadata.get(“version”, None)</cite>.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p><a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> is not the same object as the input
-<a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> to <code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code>. So
-it can be modified.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>state_dict</strong> (<em>dict</em>) – a dict containing parameters and
-persistent buffers.</p></li>
-<li><p><strong>prefix</strong> (<em>str</em>) – the prefix for parameters and buffers used in this
-module</p></li>
-<li><p><strong>local_metadata</strong> (<em>dict</em>) – a dict containing the metadata for this module.
-See</p></li>
-<li><p><strong>strict</strong> (<em>bool</em>) – whether to strictly enforce that the keys in
-<a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> with <code class="xref py py-attr docutils literal notranslate"><span class="pre">prefix</span></code> match the names of
-parameters and buffers in this module</p></li>
-<li><p><strong>missing_keys</strong> (<em>list of str</em>) – if <code class="docutils literal notranslate"><span class="pre">strict=True</span></code>, add missing keys to
-this list</p></li>
-<li><p><strong>unexpected_keys</strong> (<em>list of str</em>) – if <code class="docutils literal notranslate"><span class="pre">strict=True</span></code>, add unexpected
-keys to this list</p></li>
-<li><p><strong>error_msgs</strong> (<em>list of str</em>) – error messages should be added to this
-list, and will be reported together in
-<code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code></p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty._named_members">
-<code class="sig-name descname">_named_members</code><span class="sig-paren">(</span><em class="sig-param">get_members_fn</em>, <em class="sig-param">prefix=''</em>, <em class="sig-param">recurse=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty._named_members" title="Permalink to this definition">¶</a></dt>
-<dd><p>Helper method for yielding various names + members of modules.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty._register_load_state_dict_pre_hook">
-<code class="sig-name descname">_register_load_state_dict_pre_hook</code><span class="sig-paren">(</span><em class="sig-param">hook</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty._register_load_state_dict_pre_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>These hooks will be called with arguments: <cite>state_dict</cite>, <cite>prefix</cite>,
-<cite>local_metadata</cite>, <cite>strict</cite>, <cite>missing_keys</cite>, <cite>unexpected_keys</cite>,
-<cite>error_msgs</cite>, before loading <cite>state_dict</cite> into <cite>self</cite>. These arguments
-are exactly the same as those of <cite>_load_from_state_dict</cite>.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty._register_state_dict_hook">
-<code class="sig-name descname">_register_state_dict_hook</code><span class="sig-paren">(</span><em class="sig-param">hook</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty._register_state_dict_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>These hooks will be called with arguments: <cite>self</cite>, <cite>state_dict</cite>,
-<cite>prefix</cite>, <cite>local_metadata</cite>, after the <cite>state_dict</cite> of <cite>self</cite> is set.
-Note that only parameters and buffers of <cite>self</cite> or its children are
-guaranteed to exist in <cite>state_dict</cite>. The hooks may modify <cite>state_dict</cite>
-inplace or return a new one.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty._save_to_state_dict">
-<code class="sig-name descname">_save_to_state_dict</code><span class="sig-paren">(</span><em class="sig-param">destination</em>, <em class="sig-param">prefix</em>, <em class="sig-param">keep_vars</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty._save_to_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Saves module state to <cite>destination</cite> dictionary, containing a state
-of the module, but not its descendants. This is called on every
-submodule in <code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code>.</p>
-<p>In rare cases, subclasses can achieve class-specific behavior by
-overriding this method with custom logic.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>destination</strong> (<em>dict</em>) – a dict where state will be stored</p></li>
-<li><p><strong>prefix</strong> (<em>str</em>) – the prefix for parameters and buffers used in this
-module</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.add_module">
-<code class="sig-name descname">add_module</code><span class="sig-paren">(</span><em class="sig-param">name: str, module: Optional[Module]</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.add_module" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a child module to the current module.</p>
-<p>The module can be accessed as an attribute using the given name.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the child module. The child module can be
-accessed from this module using the given name</p></li>
-<li><p><strong>module</strong> (<em>Module</em>) – child module to be added to the module.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.apply">
-<code class="sig-name descname">apply</code><span class="sig-paren">(</span><em class="sig-param">fn: Callable[Module, None]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.apply" title="Permalink to this definition">¶</a></dt>
-<dd><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>)
-as well as self. Typical use includes initializing the parameters of a model
-(see also <span class="xref std std-ref">nn-init-doc</span>).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>fn</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">Module</span></code> -&gt; None) – function to be applied to each submodule</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nd">@torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">()</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">init_weights</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">==</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">:</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="n">m</span><span class="o">.</span><span class="n">weight</span><span class="o">.</span><span class="n">fill_</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">weight</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">init_weights</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 1.,  1.],</span>
-<span class="go">        [ 1.,  1.]])</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 1.,  1.],</span>
-<span class="go">        [ 1.,  1.]])</span>
-<span class="go">Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-<span class="go">Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.bfloat16">
-<code class="sig-name descname">bfloat16</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.bfloat16" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.buffers">
-<code class="sig-name descname">buffers</code><span class="sig-paren">(</span><em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[torch.Tensor]<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.buffers" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module buffers.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields buffers of this module
-and all submodules. Otherwise, yields only buffers that
-are direct members of this module.</p>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>torch.Tensor</em> – module buffer</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">buf</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">buffers</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">buf</span><span class="p">),</span> <span class="n">buf</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L,)</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L, 1L, 5L, 5L)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.children">
-<code class="sig-name descname">children</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.modules.module.Module]<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.children" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over immediate children modules.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>Module</em> – a child module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.cpu">
-<code class="sig-name descname">cpu</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.cpu" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the CPU.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.cuda">
-<code class="sig-name descname">cuda</code><span class="sig-paren">(</span><em class="sig-param">device: Union[int</em>, <em class="sig-param">torch.device</em>, <em class="sig-param">None] = None</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.cuda" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the GPU.</p>
-<p>This also makes associated parameters and buffers different objects. So
-it should be called before constructing optimizer if the module will
-live on GPU while being optimized.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<em>int</em><em>, </em><em>optional</em>) – if specified, all parameters will be
-copied to that device</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.double">
-<code class="sig-name descname">double</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.double" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.eval">
-<code class="sig-name descname">eval</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.eval" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets the module in evaluation mode.</p>
-<p>This has any effect only on certain modules. See documentations of
-particular modules for details of their behaviors in training/evaluation
-mode, if they are affected, e.g. <code class="xref py py-class docutils literal notranslate"><span class="pre">Dropout</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">BatchNorm</span></code>,
-etc.</p>
-<p>This is equivalent with <code class="xref py py-meth docutils literal notranslate"><span class="pre">self.train(False)</span></code>.</p>
-<p>See <span class="xref std std-ref">locally-disable-grad-doc</span> for a comparison between
-<cite>.eval()</cite> and several similar mechanisms that may be confused with it.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.extra_repr">
-<code class="sig-name descname">extra_repr</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; str<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.extra_repr" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the extra representation of the module</p>
-<p>To print customized extra information, you should re-implement
-this method in your own modules. Both single-line and multi-line
-strings are acceptable.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.float">
-<code class="sig-name descname">float</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.float" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.forward">
-<code class="sig-name descname">forward</code><span class="sig-paren">(</span><em class="sig-param">input: torch.Tensor</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty.forward" title="Permalink to this definition">¶</a></dt>
-<dd><p>Forward call. Additional arguments and keyword-arguments are ignored.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.get_buffer">
-<code class="sig-name descname">get_buffer</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.get_buffer" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>See the docstring for <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for a more detailed
-explanation of this method’s functionality as well as how to
-correctly specify <code class="docutils literal notranslate"><span class="pre">target</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the buffer
-to look for. (See <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The buffer referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not a
-    buffer</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.get_parameter">
-<code class="sig-name descname">get_parameter</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.nn.parameter.Parameter<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.get_parameter" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>See the docstring for <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for a more detailed
-explanation of this method’s functionality as well as how to
-correctly specify <code class="docutils literal notranslate"><span class="pre">target</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the Parameter
-to look for. (See <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The Parameter referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.nn.Parameter</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not an
-    <code class="docutils literal notranslate"><span class="pre">nn.Parameter</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.get_submodule">
-<code class="sig-name descname">get_submodule</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.nn.modules.module.Module<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.get_submodule" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>For example, let’s say you have an <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code> <code class="docutils literal notranslate"><span class="pre">A</span></code> that
-looks like this:</p>
-<p>(The diagram shows an <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code> <code class="docutils literal notranslate"><span class="pre">A</span></code>. <code class="docutils literal notranslate"><span class="pre">A</span></code> has a nested
-submodule <code class="docutils literal notranslate"><span class="pre">net_b</span></code>, which itself has two submodules <code class="docutils literal notranslate"><span class="pre">net_c</span></code>
-and <code class="docutils literal notranslate"><span class="pre">linear</span></code>. <code class="docutils literal notranslate"><span class="pre">net_c</span></code> then has a submodule <code class="docutils literal notranslate"><span class="pre">conv</span></code>.)</p>
-<p>To check whether or not we have the <code class="docutils literal notranslate"><span class="pre">linear</span></code> submodule, we
-would call <code class="docutils literal notranslate"><span class="pre">get_submodule(&quot;net_b.linear&quot;)</span></code>. To check whether
-we have the <code class="docutils literal notranslate"><span class="pre">conv</span></code> submodule, we would call
-<code class="docutils literal notranslate"><span class="pre">get_submodule(&quot;net_b.net_c.conv&quot;)</span></code>.</p>
-<p>The runtime of <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> is bounded by the degree
-of module nesting in <code class="docutils literal notranslate"><span class="pre">target</span></code>. A query against
-<code class="docutils literal notranslate"><span class="pre">named_modules</span></code> achieves the same result, but it is O(N) in
-the number of transitive modules. So, for a simple check to see
-if some submodule exists, <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> should always be
-used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the submodule
-to look for. (See above example for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The submodule referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.nn.Module</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not an
-    <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.half">
-<code class="sig-name descname">half</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.half" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.load_state_dict">
-<code class="sig-name descname">load_state_dict</code><span class="sig-paren">(</span><em class="sig-param">state_dict: OrderedDict[str, Tensor], strict: bool = True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty.load_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into
-this module and its descendants. If <code class="xref py py-attr docutils literal notranslate"><span class="pre">strict</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>, then
-the keys of <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> must exactly match the keys returned
-by this module’s <code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code> function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>state_dict</strong> (<em>dict</em>) – a dict containing parameters and
-persistent buffers.</p></li>
-<li><p><strong>strict</strong> (<em>bool</em><em>, </em><em>optional</em>) – whether to strictly enforce that the keys
-in <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> match the keys returned by this module’s
-<code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code> function. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code></p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><strong>missing_keys</strong> is a list of str containing the missing keys</p></li>
-<li><p><strong>unexpected_keys</strong> is a list of str containing the unexpected keys</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><code class="docutils literal notranslate"><span class="pre">NamedTuple</span></code> with <code class="docutils literal notranslate"><span class="pre">missing_keys</span></code> and <code class="docutils literal notranslate"><span class="pre">unexpected_keys</span></code> fields</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.modules">
-<code class="sig-name descname">modules</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.modules.module.Module]<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.modules" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over all modules in the network.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>Module</em> – a module in the network</p>
-</dd>
-</dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>Duplicate modules are returned only once. In the following
-example, <code class="docutils literal notranslate"><span class="pre">l</span></code> will be returned only once.</p>
-</div>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">l</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">net</span><span class="o">.</span><span class="n">modules</span><span class="p">()):</span>
-<span class="go">        print(idx, &#39;-&gt;&#39;, m)</span>
-
-<span class="go">0 -&gt; Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-<span class="go">1 -&gt; Linear(in_features=2, out_features=2, bias=True)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.named_buffers">
-<code class="sig-name descname">named_buffers</code><span class="sig-paren">(</span><em class="sig-param">prefix: str = ''</em>, <em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.Tensor]]<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.named_buffers" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module buffers, yielding both the
-name of the buffer as well as the buffer itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>prefix</strong> (<em>str</em>) – prefix to prepend to all buffer names.</p></li>
-<li><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields buffers of this module
-and all submodules. Otherwise, yields only buffers that
-are direct members of this module.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, torch.Tensor)</em> – Tuple containing the name and buffer</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">buf</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">named_buffers</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>   <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;running_var&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>       <span class="nb">print</span><span class="p">(</span><span class="n">buf</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.named_children">
-<code class="sig-name descname">named_children</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.nn.modules.module.Module]]<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.named_children" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over immediate children modules, yielding both
-the name of the module as well as the module itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>(string, Module)</em> – Tuple containing a name and child module</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">module</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">named_children</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;conv4&#39;</span><span class="p">,</span> <span class="s1">&#39;conv5&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="nb">print</span><span class="p">(</span><span class="n">module</span><span class="p">)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.named_modules">
-<code class="sig-name descname">named_modules</code><span class="sig-paren">(</span><em class="sig-param">memo: Optional[Set[Module]] = None</em>, <em class="sig-param">prefix: str = ''</em>, <em class="sig-param">remove_duplicate: bool = True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty.named_modules" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over all modules in the network, yielding
-both the name of the module as well as the module itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>memo</strong> – a memo to store the set of modules already added to the result</p></li>
-<li><p><strong>prefix</strong> – a prefix that will be added to the name of the module</p></li>
-<li><p><strong>remove_duplicate</strong> – whether to remove the duplicated module instances in the result</p></li>
-<li><p><strong>not</strong> (<em>or</em>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, Module)</em> – Tuple of name and module</p>
-</dd>
-</dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>Duplicate modules are returned only once. In the following
-example, <code class="docutils literal notranslate"><span class="pre">l</span></code> will be returned only once.</p>
-</div>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">l</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">net</span><span class="o">.</span><span class="n">named_modules</span><span class="p">()):</span>
-<span class="go">        print(idx, &#39;-&gt;&#39;, m)</span>
-
-<span class="go">0 -&gt; (&#39;&#39;, Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">))</span>
-<span class="go">1 -&gt; (&#39;0&#39;, Linear(in_features=2, out_features=2, bias=True))</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.named_parameters">
-<code class="sig-name descname">named_parameters</code><span class="sig-paren">(</span><em class="sig-param">prefix: str = ''</em>, <em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.nn.parameter.Parameter]]<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.named_parameters" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module parameters, yielding both the
-name of the parameter as well as the parameter itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>prefix</strong> (<em>str</em>) – prefix to prepend to all parameter names.</p></li>
-<li><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields parameters of this module
-and all submodules. Otherwise, yields only parameters that
-are direct members of this module.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, Parameter)</em> – Tuple containing the name and parameter</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">param</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">named_parameters</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>   <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;bias&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>       <span class="nb">print</span><span class="p">(</span><span class="n">param</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.parameters">
-<code class="sig-name descname">parameters</code><span class="sig-paren">(</span><em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.parameter.Parameter]<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.parameters" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module parameters.</p>
-<p>This is typically passed to an optimizer.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields parameters of this module
-and all submodules. Otherwise, yields only parameters that
-are direct members of this module.</p>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>Parameter</em> – module parameter</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">param</span><span class="p">),</span> <span class="n">param</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L,)</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L, 1L, 5L, 5L)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.register_backward_hook">
-<code class="sig-name descname">register_backward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[[Module, Union[Tuple[torch.Tensor, ...], torch.Tensor], Union[Tuple[torch.Tensor, ...], torch.Tensor]], Union[None, torch.Tensor]]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.register_backward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a backward hook on the module.</p>
-<p>This function is deprecated in favor of <code class="xref py py-meth docutils literal notranslate"><span class="pre">nn.Module.register_full_backward_hook()</span></code> and
-the behavior of this function will change in future versions.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.register_buffer">
-<code class="sig-name descname">register_buffer</code><span class="sig-paren">(</span><em class="sig-param">name: str, tensor: Optional[torch.Tensor], persistent: bool = True</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.register_buffer" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a buffer to the module.</p>
-<p>This is typically used to register a buffer that should not to be
-considered a model parameter. For example, BatchNorm’s <code class="docutils literal notranslate"><span class="pre">running_mean</span></code>
-is not a parameter, but is part of the module’s state. Buffers, by
-default, are persistent and will be saved alongside parameters. This
-behavior can be changed by setting <code class="xref py py-attr docutils literal notranslate"><span class="pre">persistent</span></code> to <code class="docutils literal notranslate"><span class="pre">False</span></code>. The
-only difference between a persistent buffer and a non-persistent buffer
-is that the latter will not be a part of this module’s
-<a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a>.</p>
-<p>Buffers can be accessed as attributes using given names.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the buffer. The buffer can be accessed
-from this module using the given name</p></li>
-<li><p><strong>tensor</strong> (<em>Tensor</em>) – buffer to be registered.</p></li>
-<li><p><strong>persistent</strong> (<em>bool</em>) – whether the buffer is part of this module’s
-<a class="reference internal" href="#netcal.regularization.ConfidencePenalty.state_dict" title="netcal.regularization.ConfidencePenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a>.</p></li>
-</ul>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">&#39;running_mean&#39;</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">num_features</span><span class="p">))</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.register_forward_hook">
-<code class="sig-name descname">register_forward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[..., None]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.register_forward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a forward hook on the module.</p>
-<p>The hook will be called every time after <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.forward" title="netcal.regularization.ConfidencePenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> has computed an output.
-It should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="n">output</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">modified</span> <span class="n">output</span>
-</pre></div>
-</div>
-<p>The input contains only the positional arguments given to the module.
-Keyword arguments won’t be passed to the hooks and only to the <code class="docutils literal notranslate"><span class="pre">forward</span></code>.
-The hook can modify the output. It can modify the input inplace but
-it will not have effect on forward since this is called after
-<a class="reference internal" href="#netcal.regularization.ConfidencePenalty.forward" title="netcal.regularization.ConfidencePenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> is called.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.register_forward_pre_hook">
-<code class="sig-name descname">register_forward_pre_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[..., None]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.register_forward_pre_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a forward pre-hook on the module.</p>
-<p>The hook will be called every time before <a class="reference internal" href="#netcal.regularization.ConfidencePenalty.forward" title="netcal.regularization.ConfidencePenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> is invoked.
-It should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="nb">input</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">modified</span> <span class="nb">input</span>
-</pre></div>
-</div>
-<p>The input contains only the positional arguments given to the module.
-Keyword arguments won’t be passed to the hooks and only to the <code class="docutils literal notranslate"><span class="pre">forward</span></code>.
-The hook can modify the input. User can either return a tuple or a
-single modified value in the hook. We will wrap the value into a tuple
-if a single value is returned(unless that value is already a tuple).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.register_full_backward_hook">
-<code class="sig-name descname">register_full_backward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[[Module, Union[Tuple[torch.Tensor, ...], torch.Tensor], Union[Tuple[torch.Tensor, ...], torch.Tensor]], Union[None, torch.Tensor]]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.register_full_backward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a backward hook on the module.</p>
-<p>The hook will be called every time the gradients with respect to module
-inputs are computed. The hook should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">grad_input</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">Tensor</span><span class="p">)</span> <span class="ow">or</span> <span class="kc">None</span>
-</pre></div>
-</div>
-<p>The <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_output</span></code> are tuples that contain the gradients
-with respect to the inputs and outputs respectively. The hook should
-not modify its arguments, but it can optionally return a new gradient with
-respect to the input that will be used in place of <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> in
-subsequent computations. <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> will only correspond to the inputs given
-as positional arguments and all kwarg arguments are ignored. Entries
-in <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_output</span></code> will be <code class="docutils literal notranslate"><span class="pre">None</span></code> for all non-Tensor
-arguments.</p>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>Modifying inputs or outputs inplace is not allowed when using backward hooks and
-will raise an error.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.register_parameter">
-<code class="sig-name descname">register_parameter</code><span class="sig-paren">(</span><em class="sig-param">name: str, param: Optional[torch.nn.parameter.Parameter]</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.register_parameter" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a parameter to the module.</p>
-<p>The parameter can be accessed as an attribute using given name.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the parameter. The parameter can be accessed
-from this module using the given name</p></li>
-<li><p><strong>param</strong> (<em>Parameter</em>) – parameter to be added to the module.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.requires_grad_">
-<code class="sig-name descname">requires_grad_</code><span class="sig-paren">(</span><em class="sig-param">requires_grad: bool = True</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.requires_grad_" title="Permalink to this definition">¶</a></dt>
-<dd><p>Change if autograd should record operations on parameters in this
-module.</p>
-<p>This method sets the parameters’ <code class="xref py py-attr docutils literal notranslate"><span class="pre">requires_grad</span></code> attributes
-in-place.</p>
-<p>This method is helpful for freezing part of the module for finetuning
-or training parts of a model individually (e.g., GAN training).</p>
-<p>See <span class="xref std std-ref">locally-disable-grad-doc</span> for a comparison between
-<cite>.requires_grad_()</cite> and several similar mechanisms that may be confused with it.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>requires_grad</strong> (<em>bool</em>) – whether autograd should record operations on
-parameters in this module. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.share_memory">
-<code class="sig-name descname">share_memory</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.share_memory" title="Permalink to this definition">¶</a></dt>
-<dd><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.state_dict">
-<code class="sig-name descname">state_dict</code><span class="sig-paren">(</span><em class="sig-param">destination=None</em>, <em class="sig-param">prefix=''</em>, <em class="sig-param">keep_vars=False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty.state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns a dictionary containing a whole state of the module.</p>
-<p>Both parameters and persistent buffers (e.g. running averages) are
-included. Keys are corresponding parameter and buffer names.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a dictionary containing a whole state of the module</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>dict</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">module</span><span class="o">.</span><span class="n">state_dict</span><span class="p">()</span><span class="o">.</span><span class="n">keys</span><span class="p">()</span>
-<span class="go">[&#39;bias&#39;, &#39;weight&#39;]</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.ConfidencePenalty.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves and/or casts the parameters and buffers.</p>
-<p>This can be called as</p>
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device=None</em>, <em class="sig-param">dtype=None</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">dtype</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">tensor</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">memory_format=torch.channels_last</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<p>Its signature is similar to <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.to()</span></code>, but only accepts
-floating point or complex <code class="xref py py-attr docutils literal notranslate"><span class="pre">dtype`s.</span> <span class="pre">In</span> <span class="pre">addition,</span> <span class="pre">this</span> <span class="pre">method</span> <span class="pre">will</span>
-<span class="pre">only</span> <span class="pre">cast</span> <span class="pre">the</span> <span class="pre">floating</span> <span class="pre">point</span> <span class="pre">or</span> <span class="pre">complex</span> <span class="pre">parameters</span> <span class="pre">and</span> <span class="pre">buffers</span> <span class="pre">to</span> <span class="pre">:attr:`dtype</span></code>
-(if given). The integral parameters and buffers will be moved
-<code class="xref py py-attr docutils literal notranslate"><span class="pre">device</span></code>, if that is given, but with dtypes unchanged. When
-<code class="xref py py-attr docutils literal notranslate"><span class="pre">non_blocking</span></code> is set, it tries to convert/move asynchronously
-with respect to the host if possible, e.g., moving CPU Tensors with
-pinned memory to CUDA devices.</p>
-<p>See below for examples.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>device</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.device</span></code>) – the desired device of the parameters
-and buffers in this module</p></li>
-<li><p><strong>dtype</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.dtype</span></code>) – the desired floating point or complex dtype of
-the parameters and buffers in this module</p></li>
-<li><p><strong>tensor</strong> (<em>torch.Tensor</em>) – Tensor whose dtype and device are the desired
-dtype and device for all parameters and buffers in this module</p></li>
-<li><p><strong>memory_format</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.memory_format</span></code>) – the desired memory
-format for 4D parameters and buffers in this module (keyword
-only argument)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-<p>Examples:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1913, -0.3420],</span>
-<span class="go">        [-0.5113, -0.2325]])</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">double</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1913, -0.3420],</span>
-<span class="go">        [-0.5113, -0.2325]], dtype=torch.float64)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">gpu1</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s2">&quot;cuda:1&quot;</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">gpu1</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">half</span><span class="p">,</span> <span class="n">non_blocking</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1914, -0.3420],</span>
-<span class="go">        [-0.5112, -0.2324]], dtype=torch.float16, device=&#39;cuda:1&#39;)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">cpu</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s2">&quot;cpu&quot;</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">cpu</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1914, -0.3420],</span>
-<span class="go">        [-0.5112, -0.2324]], dtype=torch.float16)</span>
-
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">cdouble</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.3741+0.j,  0.2382+0.j],</span>
-<span class="go">        [ 0.5593+0.j, -0.4443+0.j]], dtype=torch.complex128)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">cdouble</span><span class="p">))</span>
-<span class="go">tensor([[0.6122+0.j, 0.1150+0.j],</span>
-<span class="go">        [0.6122+0.j, 0.1150+0.j],</span>
-<span class="go">        [0.6122+0.j, 0.1150+0.j]], dtype=torch.complex128)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.to_empty">
-<code class="sig-name descname">to_empty</code><span class="sig-paren">(</span><em class="sig-param">*, device: Union[str, torch.device]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.to_empty" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves the parameters and buffers to the specified device without copying storage.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.device</span></code>) – The desired device of the parameters
-and buffers in this module.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.train">
-<code class="sig-name descname">train</code><span class="sig-paren">(</span><em class="sig-param">mode: bool = True</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.train" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets the module in training mode.</p>
-<p>This has any effect only on certain modules. See documentations of
-particular modules for details of their behaviors in training/evaluation
-mode, if they are affected, e.g. <code class="xref py py-class docutils literal notranslate"><span class="pre">Dropout</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">BatchNorm</span></code>,
-etc.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>mode</strong> (<em>bool</em>) – whether to set training mode (<code class="docutils literal notranslate"><span class="pre">True</span></code>) or evaluation
-mode (<code class="docutils literal notranslate"><span class="pre">False</span></code>). Default: <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.type">
-<code class="sig-name descname">type</code><span class="sig-paren">(</span><em class="sig-param">dst_type: Union[torch.dtype, str]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.type" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>dst_type</strong> (<em>type</em><em> or </em><em>string</em>) – the desired type</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.xpu">
-<code class="sig-name descname">xpu</code><span class="sig-paren">(</span><em class="sig-param">device: Union[int</em>, <em class="sig-param">torch.device</em>, <em class="sig-param">None] = None</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.xpu" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the XPU.</p>
-<p>This also makes associated parameters and buffers different objects. So
-it should be called before constructing optimizer if the module will
-live on XPU while being optimized.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<em>int</em><em>, </em><em>optional</em>) – if specified, all parameters will be
-copied to that device</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.ConfidencePenalty.zero_grad">
-<code class="sig-name descname">zero_grad</code><span class="sig-paren">(</span><em class="sig-param">set_to_none: bool = False</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.ConfidencePenalty.zero_grad" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets gradients of all model parameters to zero. See similar function
-under <code class="xref py py-class docutils literal notranslate"><span class="pre">torch.optim.Optimizer</span></code> for more context.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>set_to_none</strong> (<em>bool</em>) – instead of setting to zero, set the grads to None.
-See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.optim.Optimizer.zero_grad()</span></code> for details.</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-</div>
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index 0538992..e01be2c 100644
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+<li><a class="reference internal" href="#">netcal.regularization.DCAPenalty</a><ul>
+<li><a class="reference internal" href="#netcal.regularization.DCAPenalty"><code class="docutils literal notranslate"><span class="pre">DCAPenalty</span></code></a><ul>
+<li><a class="reference internal" href="#netcal.regularization.DCAPenalty.__init__"><code class="docutils literal notranslate"><span class="pre">DCAPenalty.__init__()</span></code></a></li>
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-  <div class="section" id="netcal-regularization-dcapenalty">
-<h1>netcal.regularization.DCAPenalty<a class="headerlink" href="#netcal-regularization-dcapenalty" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.regularization.DCAPenalty">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.regularization.</code><code class="sig-name descname">DCAPenalty</code><span class="sig-paren">(</span><em class="sig-param">weight: float = 1.0</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.modules.loss._Loss</span></code></p>
-<p>Difference between Confidence and Accuracy (DCA) <a class="footnote-reference brackets" href="#id2" id="id1">1</a>. This regularization returns a single scalar indicating
-the difference between mean confidence and accuracy within a single batch.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+              <li><a href="netcal.regularization.MMCEPenalty.html" title="netcal.regularization.MMCEPenalty" accesskey="P">previous </a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.regularization.html#regularization-methods-for-confidence-calibration">Regularization Methods for Confidence Calibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.regularization.html#available-functions">Available functions</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.regularization.confidence_penalty.html">netcal.regularization.confidence_penalty</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.regularization.ConfidencePenalty.html">netcal.regularization.ConfidencePenalty</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.regularization.MMCEPenalty.html">netcal.regularization.MMCEPenalty</a></li>
+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.regularization.DCAPenalty</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.regularization.DCAPenalty"><code class="docutils literal notranslate"><span class="pre">DCAPenalty</span></code></a><ul>
+<li class="toctree-l5"><a class="reference internal" href="#netcal.regularization.DCAPenalty.__init__"><code class="docutils literal notranslate"><span class="pre">DCAPenalty.__init__()</span></code></a></li>
+</ul>
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+                  
+  <section id="netcal-regularization-dcapenalty">
+<h1>netcal.regularization.DCAPenalty<a class="headerlink" href="#netcal-regularization-dcapenalty" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regularization.DCAPenalty">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regularization.</span></span><span class="sig-name descname"><span class="pre">DCAPenalty</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty" title="Permalink to this definition">¶</a></dt>
+<dd><p>Difference between Confidence and Accuracy (DCA). This regularization has been proposed by <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> and
+returns a single scalar indicating the difference between mean confidence and accuracy within a single batch.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>weight</strong> (<em>float</em>) – Weight of DCA regularization.</p>
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Liang, Gongbo, et al.:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Liang, Gongbo, et al.:
 “Improved trainable calibration method for neural networks on medical imaging classification.”
 arXiv preprint arXiv:2009.04057 (2020).</p>
-</dd>
-</dl>
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.__init__">
-<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">weight: float = 1.0</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty.__init__" title="Permalink to this definition">¶</a></dt>
+</aside>
+</aside>
+<dl class="py method">
+<dt class="sig sig-object py" id="netcal.regularization.DCAPenalty.__init__">
+<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty.__init__" title="Permalink to this definition">¶</a></dt>
 <dd><p>Constructor. For parameter description, see class docstring.</p>
 </dd></dl>
 
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([weight])</p></td>
 <td><p>Constructor.</p></td>
@@ -115,1164 +253,157 @@ <h1>netcal.regularization.DCAPenalty<a class="headerlink" href="#netcal-regulari
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
 <td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(input, target)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(input, target, **ig_kwargs)</p></td>
 <td><p>Forward call of module.</p></td>
 </tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
 <td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
-<td><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into this module and its descendants.</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
 <td><p>Returns an iterator over all modules in the network.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
 <td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
 <td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
 <td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
 <td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
 <td><p>Returns an iterator over module parameters.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
 <td><p>Registers a backward hook on the module.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
 <td><p>Adds a buffer to the module.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
 <td><p>Registers a forward hook on the module.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
 <td><p>Registers a forward pre-hook on the module.</p></td>
 </tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, param)</p></td>
 <td><p>Adds a parameter to the module.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
 <td><p>Change if autograd should record operations on parameters in this module.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
 <td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>([destination, prefix, keep_vars])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
 <td><p>Returns a dictionary containing a whole state of the module.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
 <td><p>Moves and/or casts the parameters and buffers.</p></td>
 </tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
 <td><p>Sets the module in training mode.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
 <td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
 <td><p>Sets gradients of all model parameters to zero.</p></td>
 </tr>
 </tbody>
 </table>
 <p class="rubric">Attributes</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">dump_patches</span></code></p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">T_destination</span></code></p></td>
+<td><p>alias of TypeVar('T_destination', bound=<code class="xref py py-class docutils literal notranslate"><span class="pre">Dict</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code>])</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">dump_patches</span></code></p></td>
 <td><p></p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty._get_backward_hooks">
-<code class="sig-name descname">_get_backward_hooks</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty._get_backward_hooks" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the backward hooks for use in the call function.
-It returns two lists, one with the full backward hooks and one with the non-full
-backward hooks.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty._load_from_state_dict">
-<code class="sig-name descname">_load_from_state_dict</code><span class="sig-paren">(</span><em class="sig-param">state_dict</em>, <em class="sig-param">prefix</em>, <em class="sig-param">local_metadata</em>, <em class="sig-param">strict</em>, <em class="sig-param">missing_keys</em>, <em class="sig-param">unexpected_keys</em>, <em class="sig-param">error_msgs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty._load_from_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into only
-this module, but not its descendants. This is called on every submodule
-in <code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code>. Metadata saved for this
-module in input <a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> is provided as <code class="xref py py-attr docutils literal notranslate"><span class="pre">local_metadata</span></code>.
-For state dicts without metadata, <code class="xref py py-attr docutils literal notranslate"><span class="pre">local_metadata</span></code> is empty.
-Subclasses can achieve class-specific backward compatible loading using
-the version number at <cite>local_metadata.get(“version”, None)</cite>.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p><a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> is not the same object as the input
-<a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> to <code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code>. So
-it can be modified.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>state_dict</strong> (<em>dict</em>) – a dict containing parameters and
-persistent buffers.</p></li>
-<li><p><strong>prefix</strong> (<em>str</em>) – the prefix for parameters and buffers used in this
-module</p></li>
-<li><p><strong>local_metadata</strong> (<em>dict</em>) – a dict containing the metadata for this module.
-See</p></li>
-<li><p><strong>strict</strong> (<em>bool</em>) – whether to strictly enforce that the keys in
-<a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> with <code class="xref py py-attr docutils literal notranslate"><span class="pre">prefix</span></code> match the names of
-parameters and buffers in this module</p></li>
-<li><p><strong>missing_keys</strong> (<em>list of str</em>) – if <code class="docutils literal notranslate"><span class="pre">strict=True</span></code>, add missing keys to
-this list</p></li>
-<li><p><strong>unexpected_keys</strong> (<em>list of str</em>) – if <code class="docutils literal notranslate"><span class="pre">strict=True</span></code>, add unexpected
-keys to this list</p></li>
-<li><p><strong>error_msgs</strong> (<em>list of str</em>) – error messages should be added to this
-list, and will be reported together in
-<code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code></p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty._named_members">
-<code class="sig-name descname">_named_members</code><span class="sig-paren">(</span><em class="sig-param">get_members_fn</em>, <em class="sig-param">prefix=''</em>, <em class="sig-param">recurse=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty._named_members" title="Permalink to this definition">¶</a></dt>
-<dd><p>Helper method for yielding various names + members of modules.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty._register_load_state_dict_pre_hook">
-<code class="sig-name descname">_register_load_state_dict_pre_hook</code><span class="sig-paren">(</span><em class="sig-param">hook</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty._register_load_state_dict_pre_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>These hooks will be called with arguments: <cite>state_dict</cite>, <cite>prefix</cite>,
-<cite>local_metadata</cite>, <cite>strict</cite>, <cite>missing_keys</cite>, <cite>unexpected_keys</cite>,
-<cite>error_msgs</cite>, before loading <cite>state_dict</cite> into <cite>self</cite>. These arguments
-are exactly the same as those of <cite>_load_from_state_dict</cite>.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty._register_state_dict_hook">
-<code class="sig-name descname">_register_state_dict_hook</code><span class="sig-paren">(</span><em class="sig-param">hook</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty._register_state_dict_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>These hooks will be called with arguments: <cite>self</cite>, <cite>state_dict</cite>,
-<cite>prefix</cite>, <cite>local_metadata</cite>, after the <cite>state_dict</cite> of <cite>self</cite> is set.
-Note that only parameters and buffers of <cite>self</cite> or its children are
-guaranteed to exist in <cite>state_dict</cite>. The hooks may modify <cite>state_dict</cite>
-inplace or return a new one.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty._save_to_state_dict">
-<code class="sig-name descname">_save_to_state_dict</code><span class="sig-paren">(</span><em class="sig-param">destination</em>, <em class="sig-param">prefix</em>, <em class="sig-param">keep_vars</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty._save_to_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Saves module state to <cite>destination</cite> dictionary, containing a state
-of the module, but not its descendants. This is called on every
-submodule in <code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code>.</p>
-<p>In rare cases, subclasses can achieve class-specific behavior by
-overriding this method with custom logic.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>destination</strong> (<em>dict</em>) – a dict where state will be stored</p></li>
-<li><p><strong>prefix</strong> (<em>str</em>) – the prefix for parameters and buffers used in this
-module</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.add_module">
-<code class="sig-name descname">add_module</code><span class="sig-paren">(</span><em class="sig-param">name: str, module: Optional[Module]</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.DCAPenalty.add_module" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a child module to the current module.</p>
-<p>The module can be accessed as an attribute using the given name.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the child module. The child module can be
-accessed from this module using the given name</p></li>
-<li><p><strong>module</strong> (<em>Module</em>) – child module to be added to the module.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.apply">
-<code class="sig-name descname">apply</code><span class="sig-paren">(</span><em class="sig-param">fn: Callable[Module, None]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.apply" title="Permalink to this definition">¶</a></dt>
-<dd><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>)
-as well as self. Typical use includes initializing the parameters of a model
-(see also <span class="xref std std-ref">nn-init-doc</span>).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>fn</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">Module</span></code> -&gt; None) – function to be applied to each submodule</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nd">@torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">()</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">init_weights</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">==</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">:</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="n">m</span><span class="o">.</span><span class="n">weight</span><span class="o">.</span><span class="n">fill_</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">weight</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">init_weights</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 1.,  1.],</span>
-<span class="go">        [ 1.,  1.]])</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 1.,  1.],</span>
-<span class="go">        [ 1.,  1.]])</span>
-<span class="go">Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-<span class="go">Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.bfloat16">
-<code class="sig-name descname">bfloat16</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.bfloat16" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.buffers">
-<code class="sig-name descname">buffers</code><span class="sig-paren">(</span><em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[torch.Tensor]<a class="headerlink" href="#netcal.regularization.DCAPenalty.buffers" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module buffers.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields buffers of this module
-and all submodules. Otherwise, yields only buffers that
-are direct members of this module.</p>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>torch.Tensor</em> – module buffer</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">buf</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">buffers</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">buf</span><span class="p">),</span> <span class="n">buf</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L,)</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L, 1L, 5L, 5L)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.children">
-<code class="sig-name descname">children</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.modules.module.Module]<a class="headerlink" href="#netcal.regularization.DCAPenalty.children" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over immediate children modules.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>Module</em> – a child module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.cpu">
-<code class="sig-name descname">cpu</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.cpu" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the CPU.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.cuda">
-<code class="sig-name descname">cuda</code><span class="sig-paren">(</span><em class="sig-param">device: Union[int</em>, <em class="sig-param">torch.device</em>, <em class="sig-param">None] = None</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.cuda" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the GPU.</p>
-<p>This also makes associated parameters and buffers different objects. So
-it should be called before constructing optimizer if the module will
-live on GPU while being optimized.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<em>int</em><em>, </em><em>optional</em>) – if specified, all parameters will be
-copied to that device</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.double">
-<code class="sig-name descname">double</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.double" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.eval">
-<code class="sig-name descname">eval</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.eval" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets the module in evaluation mode.</p>
-<p>This has any effect only on certain modules. See documentations of
-particular modules for details of their behaviors in training/evaluation
-mode, if they are affected, e.g. <code class="xref py py-class docutils literal notranslate"><span class="pre">Dropout</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">BatchNorm</span></code>,
-etc.</p>
-<p>This is equivalent with <code class="xref py py-meth docutils literal notranslate"><span class="pre">self.train(False)</span></code>.</p>
-<p>See <span class="xref std std-ref">locally-disable-grad-doc</span> for a comparison between
-<cite>.eval()</cite> and several similar mechanisms that may be confused with it.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.extra_repr">
-<code class="sig-name descname">extra_repr</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; str<a class="headerlink" href="#netcal.regularization.DCAPenalty.extra_repr" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the extra representation of the module</p>
-<p>To print customized extra information, you should re-implement
-this method in your own modules. Both single-line and multi-line
-strings are acceptable.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.float">
-<code class="sig-name descname">float</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.float" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.forward">
-<code class="sig-name descname">forward</code><span class="sig-paren">(</span><em class="sig-param">input: torch.Tensor</em>, <em class="sig-param">target: torch.Tensor</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty.forward" title="Permalink to this definition">¶</a></dt>
-<dd><p>Forward call of module. Providing the target scores is mandatory.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.get_buffer">
-<code class="sig-name descname">get_buffer</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.regularization.DCAPenalty.get_buffer" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>See the docstring for <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for a more detailed
-explanation of this method’s functionality as well as how to
-correctly specify <code class="docutils literal notranslate"><span class="pre">target</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the buffer
-to look for. (See <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The buffer referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not a
-    buffer</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.get_parameter">
-<code class="sig-name descname">get_parameter</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.nn.parameter.Parameter<a class="headerlink" href="#netcal.regularization.DCAPenalty.get_parameter" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>See the docstring for <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for a more detailed
-explanation of this method’s functionality as well as how to
-correctly specify <code class="docutils literal notranslate"><span class="pre">target</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the Parameter
-to look for. (See <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The Parameter referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.nn.Parameter</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not an
-    <code class="docutils literal notranslate"><span class="pre">nn.Parameter</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.get_submodule">
-<code class="sig-name descname">get_submodule</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.nn.modules.module.Module<a class="headerlink" href="#netcal.regularization.DCAPenalty.get_submodule" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>For example, let’s say you have an <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code> <code class="docutils literal notranslate"><span class="pre">A</span></code> that
-looks like this:</p>
-<p>(The diagram shows an <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code> <code class="docutils literal notranslate"><span class="pre">A</span></code>. <code class="docutils literal notranslate"><span class="pre">A</span></code> has a nested
-submodule <code class="docutils literal notranslate"><span class="pre">net_b</span></code>, which itself has two submodules <code class="docutils literal notranslate"><span class="pre">net_c</span></code>
-and <code class="docutils literal notranslate"><span class="pre">linear</span></code>. <code class="docutils literal notranslate"><span class="pre">net_c</span></code> then has a submodule <code class="docutils literal notranslate"><span class="pre">conv</span></code>.)</p>
-<p>To check whether or not we have the <code class="docutils literal notranslate"><span class="pre">linear</span></code> submodule, we
-would call <code class="docutils literal notranslate"><span class="pre">get_submodule(&quot;net_b.linear&quot;)</span></code>. To check whether
-we have the <code class="docutils literal notranslate"><span class="pre">conv</span></code> submodule, we would call
-<code class="docutils literal notranslate"><span class="pre">get_submodule(&quot;net_b.net_c.conv&quot;)</span></code>.</p>
-<p>The runtime of <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> is bounded by the degree
-of module nesting in <code class="docutils literal notranslate"><span class="pre">target</span></code>. A query against
-<code class="docutils literal notranslate"><span class="pre">named_modules</span></code> achieves the same result, but it is O(N) in
-the number of transitive modules. So, for a simple check to see
-if some submodule exists, <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> should always be
-used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the submodule
-to look for. (See above example for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The submodule referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.nn.Module</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not an
-    <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.half">
-<code class="sig-name descname">half</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.half" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.load_state_dict">
-<code class="sig-name descname">load_state_dict</code><span class="sig-paren">(</span><em class="sig-param">state_dict: OrderedDict[str, Tensor], strict: bool = True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty.load_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into
-this module and its descendants. If <code class="xref py py-attr docutils literal notranslate"><span class="pre">strict</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>, then
-the keys of <a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> must exactly match the keys returned
-by this module’s <code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code> function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>state_dict</strong> (<em>dict</em>) – a dict containing parameters and
-persistent buffers.</p></li>
-<li><p><strong>strict</strong> (<em>bool</em><em>, </em><em>optional</em>) – whether to strictly enforce that the keys
-in <a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> match the keys returned by this module’s
-<code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code> function. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code></p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><strong>missing_keys</strong> is a list of str containing the missing keys</p></li>
-<li><p><strong>unexpected_keys</strong> is a list of str containing the unexpected keys</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><code class="docutils literal notranslate"><span class="pre">NamedTuple</span></code> with <code class="docutils literal notranslate"><span class="pre">missing_keys</span></code> and <code class="docutils literal notranslate"><span class="pre">unexpected_keys</span></code> fields</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.modules">
-<code class="sig-name descname">modules</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.modules.module.Module]<a class="headerlink" href="#netcal.regularization.DCAPenalty.modules" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over all modules in the network.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>Module</em> – a module in the network</p>
-</dd>
-</dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>Duplicate modules are returned only once. In the following
-example, <code class="docutils literal notranslate"><span class="pre">l</span></code> will be returned only once.</p>
-</div>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">l</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">net</span><span class="o">.</span><span class="n">modules</span><span class="p">()):</span>
-<span class="go">        print(idx, &#39;-&gt;&#39;, m)</span>
-
-<span class="go">0 -&gt; Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-<span class="go">1 -&gt; Linear(in_features=2, out_features=2, bias=True)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.named_buffers">
-<code class="sig-name descname">named_buffers</code><span class="sig-paren">(</span><em class="sig-param">prefix: str = ''</em>, <em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.Tensor]]<a class="headerlink" href="#netcal.regularization.DCAPenalty.named_buffers" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module buffers, yielding both the
-name of the buffer as well as the buffer itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>prefix</strong> (<em>str</em>) – prefix to prepend to all buffer names.</p></li>
-<li><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields buffers of this module
-and all submodules. Otherwise, yields only buffers that
-are direct members of this module.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, torch.Tensor)</em> – Tuple containing the name and buffer</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">buf</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">named_buffers</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>   <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;running_var&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>       <span class="nb">print</span><span class="p">(</span><span class="n">buf</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.named_children">
-<code class="sig-name descname">named_children</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.nn.modules.module.Module]]<a class="headerlink" href="#netcal.regularization.DCAPenalty.named_children" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over immediate children modules, yielding both
-the name of the module as well as the module itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>(string, Module)</em> – Tuple containing a name and child module</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">module</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">named_children</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;conv4&#39;</span><span class="p">,</span> <span class="s1">&#39;conv5&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="nb">print</span><span class="p">(</span><span class="n">module</span><span class="p">)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.named_modules">
-<code class="sig-name descname">named_modules</code><span class="sig-paren">(</span><em class="sig-param">memo: Optional[Set[Module]] = None</em>, <em class="sig-param">prefix: str = ''</em>, <em class="sig-param">remove_duplicate: bool = True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty.named_modules" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over all modules in the network, yielding
-both the name of the module as well as the module itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>memo</strong> – a memo to store the set of modules already added to the result</p></li>
-<li><p><strong>prefix</strong> – a prefix that will be added to the name of the module</p></li>
-<li><p><strong>remove_duplicate</strong> – whether to remove the duplicated module instances in the result</p></li>
-<li><p><strong>not</strong> (<em>or</em>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, Module)</em> – Tuple of name and module</p>
-</dd>
-</dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>Duplicate modules are returned only once. In the following
-example, <code class="docutils literal notranslate"><span class="pre">l</span></code> will be returned only once.</p>
-</div>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">l</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">net</span><span class="o">.</span><span class="n">named_modules</span><span class="p">()):</span>
-<span class="go">        print(idx, &#39;-&gt;&#39;, m)</span>
-
-<span class="go">0 -&gt; (&#39;&#39;, Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">))</span>
-<span class="go">1 -&gt; (&#39;0&#39;, Linear(in_features=2, out_features=2, bias=True))</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.named_parameters">
-<code class="sig-name descname">named_parameters</code><span class="sig-paren">(</span><em class="sig-param">prefix: str = ''</em>, <em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.nn.parameter.Parameter]]<a class="headerlink" href="#netcal.regularization.DCAPenalty.named_parameters" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module parameters, yielding both the
-name of the parameter as well as the parameter itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>prefix</strong> (<em>str</em>) – prefix to prepend to all parameter names.</p></li>
-<li><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields parameters of this module
-and all submodules. Otherwise, yields only parameters that
-are direct members of this module.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, Parameter)</em> – Tuple containing the name and parameter</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">param</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">named_parameters</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>   <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;bias&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>       <span class="nb">print</span><span class="p">(</span><span class="n">param</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.parameters">
-<code class="sig-name descname">parameters</code><span class="sig-paren">(</span><em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.parameter.Parameter]<a class="headerlink" href="#netcal.regularization.DCAPenalty.parameters" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module parameters.</p>
-<p>This is typically passed to an optimizer.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields parameters of this module
-and all submodules. Otherwise, yields only parameters that
-are direct members of this module.</p>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>Parameter</em> – module parameter</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">param</span><span class="p">),</span> <span class="n">param</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L,)</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L, 1L, 5L, 5L)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.register_backward_hook">
-<code class="sig-name descname">register_backward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[[Module, Union[Tuple[torch.Tensor, ...], torch.Tensor], Union[Tuple[torch.Tensor, ...], torch.Tensor]], Union[None, torch.Tensor]]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.DCAPenalty.register_backward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a backward hook on the module.</p>
-<p>This function is deprecated in favor of <code class="xref py py-meth docutils literal notranslate"><span class="pre">nn.Module.register_full_backward_hook()</span></code> and
-the behavior of this function will change in future versions.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.register_buffer">
-<code class="sig-name descname">register_buffer</code><span class="sig-paren">(</span><em class="sig-param">name: str, tensor: Optional[torch.Tensor], persistent: bool = True</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.DCAPenalty.register_buffer" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a buffer to the module.</p>
-<p>This is typically used to register a buffer that should not to be
-considered a model parameter. For example, BatchNorm’s <code class="docutils literal notranslate"><span class="pre">running_mean</span></code>
-is not a parameter, but is part of the module’s state. Buffers, by
-default, are persistent and will be saved alongside parameters. This
-behavior can be changed by setting <code class="xref py py-attr docutils literal notranslate"><span class="pre">persistent</span></code> to <code class="docutils literal notranslate"><span class="pre">False</span></code>. The
-only difference between a persistent buffer and a non-persistent buffer
-is that the latter will not be a part of this module’s
-<a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a>.</p>
-<p>Buffers can be accessed as attributes using given names.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the buffer. The buffer can be accessed
-from this module using the given name</p></li>
-<li><p><strong>tensor</strong> (<em>Tensor</em>) – buffer to be registered.</p></li>
-<li><p><strong>persistent</strong> (<em>bool</em>) – whether the buffer is part of this module’s
-<a class="reference internal" href="#netcal.regularization.DCAPenalty.state_dict" title="netcal.regularization.DCAPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a>.</p></li>
-</ul>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">&#39;running_mean&#39;</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">num_features</span><span class="p">))</span>
-</pre></div>
-</div>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.register_forward_hook">
-<code class="sig-name descname">register_forward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[..., None]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.DCAPenalty.register_forward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a forward hook on the module.</p>
-<p>The hook will be called every time after <a class="reference internal" href="#netcal.regularization.DCAPenalty.forward" title="netcal.regularization.DCAPenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> has computed an output.
-It should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="n">output</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">modified</span> <span class="n">output</span>
-</pre></div>
-</div>
-<p>The input contains only the positional arguments given to the module.
-Keyword arguments won’t be passed to the hooks and only to the <code class="docutils literal notranslate"><span class="pre">forward</span></code>.
-The hook can modify the output. It can modify the input inplace but
-it will not have effect on forward since this is called after
-<a class="reference internal" href="#netcal.regularization.DCAPenalty.forward" title="netcal.regularization.DCAPenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> is called.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.register_forward_pre_hook">
-<code class="sig-name descname">register_forward_pre_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[..., None]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.DCAPenalty.register_forward_pre_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a forward pre-hook on the module.</p>
-<p>The hook will be called every time before <a class="reference internal" href="#netcal.regularization.DCAPenalty.forward" title="netcal.regularization.DCAPenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> is invoked.
-It should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="nb">input</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">modified</span> <span class="nb">input</span>
-</pre></div>
-</div>
-<p>The input contains only the positional arguments given to the module.
-Keyword arguments won’t be passed to the hooks and only to the <code class="docutils literal notranslate"><span class="pre">forward</span></code>.
-The hook can modify the input. User can either return a tuple or a
-single modified value in the hook. We will wrap the value into a tuple
-if a single value is returned(unless that value is already a tuple).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.register_full_backward_hook">
-<code class="sig-name descname">register_full_backward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[[Module, Union[Tuple[torch.Tensor, ...], torch.Tensor], Union[Tuple[torch.Tensor, ...], torch.Tensor]], Union[None, torch.Tensor]]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.DCAPenalty.register_full_backward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a backward hook on the module.</p>
-<p>The hook will be called every time the gradients with respect to module
-inputs are computed. The hook should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">grad_input</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">Tensor</span><span class="p">)</span> <span class="ow">or</span> <span class="kc">None</span>
-</pre></div>
-</div>
-<p>The <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_output</span></code> are tuples that contain the gradients
-with respect to the inputs and outputs respectively. The hook should
-not modify its arguments, but it can optionally return a new gradient with
-respect to the input that will be used in place of <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> in
-subsequent computations. <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> will only correspond to the inputs given
-as positional arguments and all kwarg arguments are ignored. Entries
-in <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_output</span></code> will be <code class="docutils literal notranslate"><span class="pre">None</span></code> for all non-Tensor
-arguments.</p>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>Modifying inputs or outputs inplace is not allowed when using backward hooks and
-will raise an error.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.register_parameter">
-<code class="sig-name descname">register_parameter</code><span class="sig-paren">(</span><em class="sig-param">name: str, param: Optional[torch.nn.parameter.Parameter]</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.DCAPenalty.register_parameter" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a parameter to the module.</p>
-<p>The parameter can be accessed as an attribute using given name.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the parameter. The parameter can be accessed
-from this module using the given name</p></li>
-<li><p><strong>param</strong> (<em>Parameter</em>) – parameter to be added to the module.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.requires_grad_">
-<code class="sig-name descname">requires_grad_</code><span class="sig-paren">(</span><em class="sig-param">requires_grad: bool = True</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.requires_grad_" title="Permalink to this definition">¶</a></dt>
-<dd><p>Change if autograd should record operations on parameters in this
-module.</p>
-<p>This method sets the parameters’ <code class="xref py py-attr docutils literal notranslate"><span class="pre">requires_grad</span></code> attributes
-in-place.</p>
-<p>This method is helpful for freezing part of the module for finetuning
-or training parts of a model individually (e.g., GAN training).</p>
-<p>See <span class="xref std std-ref">locally-disable-grad-doc</span> for a comparison between
-<cite>.requires_grad_()</cite> and several similar mechanisms that may be confused with it.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>requires_grad</strong> (<em>bool</em>) – whether autograd should record operations on
-parameters in this module. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.share_memory">
-<code class="sig-name descname">share_memory</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.share_memory" title="Permalink to this definition">¶</a></dt>
-<dd><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.state_dict">
-<code class="sig-name descname">state_dict</code><span class="sig-paren">(</span><em class="sig-param">destination=None</em>, <em class="sig-param">prefix=''</em>, <em class="sig-param">keep_vars=False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty.state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns a dictionary containing a whole state of the module.</p>
-<p>Both parameters and persistent buffers (e.g. running averages) are
-included. Keys are corresponding parameter and buffer names.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a dictionary containing a whole state of the module</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>dict</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">module</span><span class="o">.</span><span class="n">state_dict</span><span class="p">()</span><span class="o">.</span><span class="n">keys</span><span class="p">()</span>
-<span class="go">[&#39;bias&#39;, &#39;weight&#39;]</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.DCAPenalty.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves and/or casts the parameters and buffers.</p>
-<p>This can be called as</p>
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device=None</em>, <em class="sig-param">dtype=None</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">dtype</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">tensor</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">memory_format=torch.channels_last</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<p>Its signature is similar to <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.to()</span></code>, but only accepts
-floating point or complex <code class="xref py py-attr docutils literal notranslate"><span class="pre">dtype`s.</span> <span class="pre">In</span> <span class="pre">addition,</span> <span class="pre">this</span> <span class="pre">method</span> <span class="pre">will</span>
-<span class="pre">only</span> <span class="pre">cast</span> <span class="pre">the</span> <span class="pre">floating</span> <span class="pre">point</span> <span class="pre">or</span> <span class="pre">complex</span> <span class="pre">parameters</span> <span class="pre">and</span> <span class="pre">buffers</span> <span class="pre">to</span> <span class="pre">:attr:`dtype</span></code>
-(if given). The integral parameters and buffers will be moved
-<code class="xref py py-attr docutils literal notranslate"><span class="pre">device</span></code>, if that is given, but with dtypes unchanged. When
-<code class="xref py py-attr docutils literal notranslate"><span class="pre">non_blocking</span></code> is set, it tries to convert/move asynchronously
-with respect to the host if possible, e.g., moving CPU Tensors with
-pinned memory to CUDA devices.</p>
-<p>See below for examples.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>device</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.device</span></code>) – the desired device of the parameters
-and buffers in this module</p></li>
-<li><p><strong>dtype</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.dtype</span></code>) – the desired floating point or complex dtype of
-the parameters and buffers in this module</p></li>
-<li><p><strong>tensor</strong> (<em>torch.Tensor</em>) – Tensor whose dtype and device are the desired
-dtype and device for all parameters and buffers in this module</p></li>
-<li><p><strong>memory_format</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.memory_format</span></code>) – the desired memory
-format for 4D parameters and buffers in this module (keyword
-only argument)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-<p>Examples:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1913, -0.3420],</span>
-<span class="go">        [-0.5113, -0.2325]])</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">double</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1913, -0.3420],</span>
-<span class="go">        [-0.5113, -0.2325]], dtype=torch.float64)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">gpu1</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s2">&quot;cuda:1&quot;</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">gpu1</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">half</span><span class="p">,</span> <span class="n">non_blocking</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1914, -0.3420],</span>
-<span class="go">        [-0.5112, -0.2324]], dtype=torch.float16, device=&#39;cuda:1&#39;)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">cpu</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s2">&quot;cpu&quot;</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">cpu</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1914, -0.3420],</span>
-<span class="go">        [-0.5112, -0.2324]], dtype=torch.float16)</span>
-
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">cdouble</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.3741+0.j,  0.2382+0.j],</span>
-<span class="go">        [ 0.5593+0.j, -0.4443+0.j]], dtype=torch.complex128)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">cdouble</span><span class="p">))</span>
-<span class="go">tensor([[0.6122+0.j, 0.1150+0.j],</span>
-<span class="go">        [0.6122+0.j, 0.1150+0.j],</span>
-<span class="go">        [0.6122+0.j, 0.1150+0.j]], dtype=torch.complex128)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.to_empty">
-<code class="sig-name descname">to_empty</code><span class="sig-paren">(</span><em class="sig-param">*, device: Union[str, torch.device]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.to_empty" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves the parameters and buffers to the specified device without copying storage.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.device</span></code>) – The desired device of the parameters
-and buffers in this module.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.train">
-<code class="sig-name descname">train</code><span class="sig-paren">(</span><em class="sig-param">mode: bool = True</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.train" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets the module in training mode.</p>
-<p>This has any effect only on certain modules. See documentations of
-particular modules for details of their behaviors in training/evaluation
-mode, if they are affected, e.g. <code class="xref py py-class docutils literal notranslate"><span class="pre">Dropout</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">BatchNorm</span></code>,
-etc.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>mode</strong> (<em>bool</em>) – whether to set training mode (<code class="docutils literal notranslate"><span class="pre">True</span></code>) or evaluation
-mode (<code class="docutils literal notranslate"><span class="pre">False</span></code>). Default: <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.type">
-<code class="sig-name descname">type</code><span class="sig-paren">(</span><em class="sig-param">dst_type: Union[torch.dtype, str]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.type" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>dst_type</strong> (<em>type</em><em> or </em><em>string</em>) – the desired type</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.xpu">
-<code class="sig-name descname">xpu</code><span class="sig-paren">(</span><em class="sig-param">device: Union[int</em>, <em class="sig-param">torch.device</em>, <em class="sig-param">None] = None</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.DCAPenalty.xpu" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the XPU.</p>
-<p>This also makes associated parameters and buffers different objects. So
-it should be called before constructing optimizer if the module will
-live on XPU while being optimized.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<em>int</em><em>, </em><em>optional</em>) – if specified, all parameters will be
-copied to that device</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.DCAPenalty.zero_grad">
-<code class="sig-name descname">zero_grad</code><span class="sig-paren">(</span><em class="sig-param">set_to_none: bool = False</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.DCAPenalty.zero_grad" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets gradients of all model parameters to zero. See similar function
-under <code class="xref py py-class docutils literal notranslate"><span class="pre">torch.optim.Optimizer</span></code> for more context.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>set_to_none</strong> (<em>bool</em>) – instead of setting to zero, set the grads to None.
-See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.optim.Optimizer.zero_grad()</span></code> for details.</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
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+<li><a class="reference internal" href="#netcal.regularization.MMCEPenalty"><code class="docutils literal notranslate"><span class="pre">MMCEPenalty</span></code></a><ul>
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-  <div class="section" id="netcal-regularization-mmcepenalty">
-<h1>netcal.regularization.MMCEPenalty<a class="headerlink" href="#netcal-regularization-mmcepenalty" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.regularization.MMCEPenalty">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.regularization.</code><code class="sig-name descname">MMCEPenalty</code><span class="sig-paren">(</span><em class="sig-param">weight: float = 1.0</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.modules.loss._Loss</span></code></p>
-<p>Maximum mean calibration error (MMCE) <a class="footnote-reference brackets" href="#id2" id="id1">1</a>. This term can be used for online confidence calibration directly
-during model training.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+              <li><a href="netcal.regularization.ConfidencePenalty.html" title="netcal.regularization.ConfidencePenalty" accesskey="P">previous </a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.regularization.html#regularization-methods-for-confidence-calibration">Regularization Methods for Confidence Calibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.regularization.html#available-functions">Available functions</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.regularization.confidence_penalty.html">netcal.regularization.confidence_penalty</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.regularization.ConfidencePenalty.html">netcal.regularization.ConfidencePenalty</a></li>
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+</ul>
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+  <section id="netcal-regularization-mmcepenalty">
+<h1>netcal.regularization.MMCEPenalty<a class="headerlink" href="#netcal-regularization-mmcepenalty" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.regularization.MMCEPenalty">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.regularization.</span></span><span class="sig-name descname"><span class="pre">MMCEPenalty</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty" title="Permalink to this definition">¶</a></dt>
+<dd><p>Maximum mean calibration error (MMCE). This technique has been proposed by <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> and can be used for online
+confidence calibration directly during model training.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>weight</strong> (<em>float</em>) – Weight of MMCE regularization.</p>
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain:
 “Trainable calibration measures for neural networks from kernel mean embeddings.”
 International Conference on Machine Learning. PMLR, 2018.
 <a class="reference external" href="http://proceedings.mlr.press/v80/kumar18a/kumar18a.pdf">Get source online:</a></p>
-</dd>
-</dl>
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.__init__">
-<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">weight: float = 1.0</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty.__init__" title="Permalink to this definition">¶</a></dt>
+</aside>
+</aside>
+<dl class="py method">
+<dt class="sig sig-object py" id="netcal.regularization.MMCEPenalty.__init__">
+<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty.__init__" title="Permalink to this definition">¶</a></dt>
 <dd><p>Constructor. For parameter description, see class docstring.</p>
 </dd></dl>
 
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([weight])</p></td>
 <td><p>Constructor.</p></td>
@@ -116,1176 +254,163 @@ <h1>netcal.regularization.MMCEPenalty<a class="headerlink" href="#netcal-regular
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">float</span></code>()</p></td>
 <td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(input, target)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">forward</span></code>(input, target, **ig_kwargs)</p></td>
 <td><p>Forward call of module.</p></td>
 </tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_buffer</span></code>(target)</p></td>
+<td><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_extra_state</span></code>()</p></td>
+<td><p>Returns any extra state to include in the module's state_dict.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_parameter</span></code>(target)</p></td>
+<td><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_submodule</span></code>(target)</p></td>
+<td><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists, otherwise throws an error.</p></td>
+</tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">half</span></code>()</p></td>
 <td><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">kernel</span></code>(c1, c2)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">ipu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the IPU.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">kernel</span></code>(c1, c2)</p></td>
 <td><p>Laplacian kernel</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
-<td><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into this module and its descendants.</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">load_state_dict</span></code>(state_dict[, strict])</p></td>
+<td><p>Copies parameters and buffers from <code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code> into this module and its descendants.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">modules</span></code>()</p></td>
 <td><p>Returns an iterator over all modules in the network.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_buffers</span></code>([prefix, recurse])</p></td>
 <td><p>Returns an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_children</span></code>()</p></td>
 <td><p>Returns an iterator over immediate children modules, yielding both the name of the module as well as the module itself.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_modules</span></code>([memo, prefix, remove_duplicate])</p></td>
 <td><p>Returns an iterator over all modules in the network, yielding both the name of the module as well as the module itself.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">named_parameters</span></code>([prefix, recurse])</p></td>
 <td><p>Returns an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameters</span></code>([recurse])</p></td>
 <td><p>Returns an iterator over module parameters.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_backward_hook</span></code>(hook)</p></td>
 <td><p>Registers a backward hook on the module.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_buffer</span></code>(name, tensor[, persistent])</p></td>
 <td><p>Adds a buffer to the module.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_hook</span></code>(hook)</p></td>
 <td><p>Registers a forward hook on the module.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_forward_pre_hook</span></code>(hook)</p></td>
 <td><p>Registers a forward pre-hook on the module.</p></td>
 </tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_full_backward_hook</span></code>(hook)</p></td>
+<td><p>Registers a backward hook on the module.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_load_state_dict_post_hook</span></code>(hook)</p></td>
+<td><p>Registers a post hook to be run after module's <code class="docutils literal notranslate"><span class="pre">load_state_dict</span></code> is called.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module</span></code>(name, module)</p></td>
+<td><p>Alias for <code class="xref py py-func docutils literal notranslate"><span class="pre">add_module()</span></code>.</p></td>
+</tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_parameter</span></code>(name, param)</p></td>
 <td><p>Adds a parameter to the module.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">requires_grad_</span></code>([requires_grad])</p></td>
 <td><p>Change if autograd should record operations on parameters in this module.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_extra_state</span></code>(state)</p></td>
+<td><p>This function is called from <code class="xref py py-func docutils literal notranslate"><span class="pre">load_state_dict()</span></code> to handle any extra state found within the <cite>state_dict</cite>.</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">share_memory</span></code>()</p></td>
 <td><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>([destination, prefix, keep_vars])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">state_dict</span></code>(*args[, destination, prefix, ...])</p></td>
 <td><p>Returns a dictionary containing a whole state of the module.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(*args, **kwargs)</p></td>
 <td><p>Moves and/or casts the parameters and buffers.</p></td>
 </tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_empty</span></code>(*, device)</p></td>
+<td><p>Moves the parameters and buffers to the specified device without copying storage.</p></td>
+</tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">train</span></code>([mode])</p></td>
 <td><p>Sets the module in training mode.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">type</span></code>(dst_type)</p></td>
 <td><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">xpu</span></code>([device])</p></td>
+<td><p>Moves all model parameters and buffers to the XPU.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">zero_grad</span></code>([set_to_none])</p></td>
 <td><p>Sets gradients of all model parameters to zero.</p></td>
 </tr>
 </tbody>
 </table>
 <p class="rubric">Attributes</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">dump_patches</span></code></p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">T_destination</span></code></p></td>
+<td><p>alias of TypeVar('T_destination', bound=<code class="xref py py-class docutils literal notranslate"><span class="pre">Dict</span></code>[<code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code>])</p></td>
+</tr>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">dump_patches</span></code></p></td>
 <td><p></p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">epsilon</span></code></p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">epsilon</span></code></p></td>
 <td><p></p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty._get_backward_hooks">
-<code class="sig-name descname">_get_backward_hooks</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty._get_backward_hooks" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the backward hooks for use in the call function.
-It returns two lists, one with the full backward hooks and one with the non-full
-backward hooks.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty._load_from_state_dict">
-<code class="sig-name descname">_load_from_state_dict</code><span class="sig-paren">(</span><em class="sig-param">state_dict</em>, <em class="sig-param">prefix</em>, <em class="sig-param">local_metadata</em>, <em class="sig-param">strict</em>, <em class="sig-param">missing_keys</em>, <em class="sig-param">unexpected_keys</em>, <em class="sig-param">error_msgs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty._load_from_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into only
-this module, but not its descendants. This is called on every submodule
-in <code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code>. Metadata saved for this
-module in input <a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> is provided as <code class="xref py py-attr docutils literal notranslate"><span class="pre">local_metadata</span></code>.
-For state dicts without metadata, <code class="xref py py-attr docutils literal notranslate"><span class="pre">local_metadata</span></code> is empty.
-Subclasses can achieve class-specific backward compatible loading using
-the version number at <cite>local_metadata.get(“version”, None)</cite>.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p><a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> is not the same object as the input
-<a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> to <code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code>. So
-it can be modified.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>state_dict</strong> (<em>dict</em>) – a dict containing parameters and
-persistent buffers.</p></li>
-<li><p><strong>prefix</strong> (<em>str</em>) – the prefix for parameters and buffers used in this
-module</p></li>
-<li><p><strong>local_metadata</strong> (<em>dict</em>) – a dict containing the metadata for this module.
-See</p></li>
-<li><p><strong>strict</strong> (<em>bool</em>) – whether to strictly enforce that the keys in
-<a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> with <code class="xref py py-attr docutils literal notranslate"><span class="pre">prefix</span></code> match the names of
-parameters and buffers in this module</p></li>
-<li><p><strong>missing_keys</strong> (<em>list of str</em>) – if <code class="docutils literal notranslate"><span class="pre">strict=True</span></code>, add missing keys to
-this list</p></li>
-<li><p><strong>unexpected_keys</strong> (<em>list of str</em>) – if <code class="docutils literal notranslate"><span class="pre">strict=True</span></code>, add unexpected
-keys to this list</p></li>
-<li><p><strong>error_msgs</strong> (<em>list of str</em>) – error messages should be added to this
-list, and will be reported together in
-<code class="xref py py-meth docutils literal notranslate"><span class="pre">load_state_dict()</span></code></p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty._named_members">
-<code class="sig-name descname">_named_members</code><span class="sig-paren">(</span><em class="sig-param">get_members_fn</em>, <em class="sig-param">prefix=''</em>, <em class="sig-param">recurse=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty._named_members" title="Permalink to this definition">¶</a></dt>
-<dd><p>Helper method for yielding various names + members of modules.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty._register_load_state_dict_pre_hook">
-<code class="sig-name descname">_register_load_state_dict_pre_hook</code><span class="sig-paren">(</span><em class="sig-param">hook</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty._register_load_state_dict_pre_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>These hooks will be called with arguments: <cite>state_dict</cite>, <cite>prefix</cite>,
-<cite>local_metadata</cite>, <cite>strict</cite>, <cite>missing_keys</cite>, <cite>unexpected_keys</cite>,
-<cite>error_msgs</cite>, before loading <cite>state_dict</cite> into <cite>self</cite>. These arguments
-are exactly the same as those of <cite>_load_from_state_dict</cite>.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty._register_state_dict_hook">
-<code class="sig-name descname">_register_state_dict_hook</code><span class="sig-paren">(</span><em class="sig-param">hook</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty._register_state_dict_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>These hooks will be called with arguments: <cite>self</cite>, <cite>state_dict</cite>,
-<cite>prefix</cite>, <cite>local_metadata</cite>, after the <cite>state_dict</cite> of <cite>self</cite> is set.
-Note that only parameters and buffers of <cite>self</cite> or its children are
-guaranteed to exist in <cite>state_dict</cite>. The hooks may modify <cite>state_dict</cite>
-inplace or return a new one.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty._save_to_state_dict">
-<code class="sig-name descname">_save_to_state_dict</code><span class="sig-paren">(</span><em class="sig-param">destination</em>, <em class="sig-param">prefix</em>, <em class="sig-param">keep_vars</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty._save_to_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Saves module state to <cite>destination</cite> dictionary, containing a state
-of the module, but not its descendants. This is called on every
-submodule in <code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code>.</p>
-<p>In rare cases, subclasses can achieve class-specific behavior by
-overriding this method with custom logic.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>destination</strong> (<em>dict</em>) – a dict where state will be stored</p></li>
-<li><p><strong>prefix</strong> (<em>str</em>) – the prefix for parameters and buffers used in this
-module</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.add_module">
-<code class="sig-name descname">add_module</code><span class="sig-paren">(</span><em class="sig-param">name: str, module: Optional[Module]</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.MMCEPenalty.add_module" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a child module to the current module.</p>
-<p>The module can be accessed as an attribute using the given name.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the child module. The child module can be
-accessed from this module using the given name</p></li>
-<li><p><strong>module</strong> (<em>Module</em>) – child module to be added to the module.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.apply">
-<code class="sig-name descname">apply</code><span class="sig-paren">(</span><em class="sig-param">fn: Callable[Module, None]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.apply" title="Permalink to this definition">¶</a></dt>
-<dd><p>Applies <code class="docutils literal notranslate"><span class="pre">fn</span></code> recursively to every submodule (as returned by <code class="docutils literal notranslate"><span class="pre">.children()</span></code>)
-as well as self. Typical use includes initializing the parameters of a model
-(see also <span class="xref std std-ref">nn-init-doc</span>).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>fn</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">Module</span></code> -&gt; None) – function to be applied to each submodule</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nd">@torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">()</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">init_weights</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">==</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">:</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="n">m</span><span class="o">.</span><span class="n">weight</span><span class="o">.</span><span class="n">fill_</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="nb">print</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">weight</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">init_weights</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 1.,  1.],</span>
-<span class="go">        [ 1.,  1.]])</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 1.,  1.],</span>
-<span class="go">        [ 1.,  1.]])</span>
-<span class="go">Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-<span class="go">Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.bfloat16">
-<code class="sig-name descname">bfloat16</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.bfloat16" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">bfloat16</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.buffers">
-<code class="sig-name descname">buffers</code><span class="sig-paren">(</span><em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[torch.Tensor]<a class="headerlink" href="#netcal.regularization.MMCEPenalty.buffers" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module buffers.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields buffers of this module
-and all submodules. Otherwise, yields only buffers that
-are direct members of this module.</p>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>torch.Tensor</em> – module buffer</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">buf</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">buffers</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">buf</span><span class="p">),</span> <span class="n">buf</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L,)</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L, 1L, 5L, 5L)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.children">
-<code class="sig-name descname">children</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.modules.module.Module]<a class="headerlink" href="#netcal.regularization.MMCEPenalty.children" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over immediate children modules.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>Module</em> – a child module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.cpu">
-<code class="sig-name descname">cpu</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.cpu" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the CPU.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.cuda">
-<code class="sig-name descname">cuda</code><span class="sig-paren">(</span><em class="sig-param">device: Union[int</em>, <em class="sig-param">torch.device</em>, <em class="sig-param">None] = None</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.cuda" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the GPU.</p>
-<p>This also makes associated parameters and buffers different objects. So
-it should be called before constructing optimizer if the module will
-live on GPU while being optimized.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<em>int</em><em>, </em><em>optional</em>) – if specified, all parameters will be
-copied to that device</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.double">
-<code class="sig-name descname">double</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.double" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">double</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.eval">
-<code class="sig-name descname">eval</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.eval" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets the module in evaluation mode.</p>
-<p>This has any effect only on certain modules. See documentations of
-particular modules for details of their behaviors in training/evaluation
-mode, if they are affected, e.g. <code class="xref py py-class docutils literal notranslate"><span class="pre">Dropout</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">BatchNorm</span></code>,
-etc.</p>
-<p>This is equivalent with <code class="xref py py-meth docutils literal notranslate"><span class="pre">self.train(False)</span></code>.</p>
-<p>See <span class="xref std std-ref">locally-disable-grad-doc</span> for a comparison between
-<cite>.eval()</cite> and several similar mechanisms that may be confused with it.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.extra_repr">
-<code class="sig-name descname">extra_repr</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; str<a class="headerlink" href="#netcal.regularization.MMCEPenalty.extra_repr" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the extra representation of the module</p>
-<p>To print customized extra information, you should re-implement
-this method in your own modules. Both single-line and multi-line
-strings are acceptable.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.float">
-<code class="sig-name descname">float</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.float" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">float</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.forward">
-<code class="sig-name descname">forward</code><span class="sig-paren">(</span><em class="sig-param">input: torch.Tensor</em>, <em class="sig-param">target: torch.Tensor</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty.forward" title="Permalink to this definition">¶</a></dt>
-<dd><p>Forward call of module. Returns a single scalar indicating the MMCE for the current batch.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.get_buffer">
-<code class="sig-name descname">get_buffer</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.regularization.MMCEPenalty.get_buffer" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the buffer given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>See the docstring for <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for a more detailed
-explanation of this method’s functionality as well as how to
-correctly specify <code class="docutils literal notranslate"><span class="pre">target</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the buffer
-to look for. (See <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The buffer referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not a
-    buffer</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.get_parameter">
-<code class="sig-name descname">get_parameter</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.nn.parameter.Parameter<a class="headerlink" href="#netcal.regularization.MMCEPenalty.get_parameter" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the parameter given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>See the docstring for <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for a more detailed
-explanation of this method’s functionality as well as how to
-correctly specify <code class="docutils literal notranslate"><span class="pre">target</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the Parameter
-to look for. (See <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The Parameter referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.nn.Parameter</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not an
-    <code class="docutils literal notranslate"><span class="pre">nn.Parameter</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.get_submodule">
-<code class="sig-name descname">get_submodule</code><span class="sig-paren">(</span><em class="sig-param">target: str</em><span class="sig-paren">)</span> &#x2192; torch.nn.modules.module.Module<a class="headerlink" href="#netcal.regularization.MMCEPenalty.get_submodule" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns the submodule given by <code class="docutils literal notranslate"><span class="pre">target</span></code> if it exists,
-otherwise throws an error.</p>
-<p>For example, let’s say you have an <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code> <code class="docutils literal notranslate"><span class="pre">A</span></code> that
-looks like this:</p>
-<p>(The diagram shows an <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code> <code class="docutils literal notranslate"><span class="pre">A</span></code>. <code class="docutils literal notranslate"><span class="pre">A</span></code> has a nested
-submodule <code class="docutils literal notranslate"><span class="pre">net_b</span></code>, which itself has two submodules <code class="docutils literal notranslate"><span class="pre">net_c</span></code>
-and <code class="docutils literal notranslate"><span class="pre">linear</span></code>. <code class="docutils literal notranslate"><span class="pre">net_c</span></code> then has a submodule <code class="docutils literal notranslate"><span class="pre">conv</span></code>.)</p>
-<p>To check whether or not we have the <code class="docutils literal notranslate"><span class="pre">linear</span></code> submodule, we
-would call <code class="docutils literal notranslate"><span class="pre">get_submodule(&quot;net_b.linear&quot;)</span></code>. To check whether
-we have the <code class="docutils literal notranslate"><span class="pre">conv</span></code> submodule, we would call
-<code class="docutils literal notranslate"><span class="pre">get_submodule(&quot;net_b.net_c.conv&quot;)</span></code>.</p>
-<p>The runtime of <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> is bounded by the degree
-of module nesting in <code class="docutils literal notranslate"><span class="pre">target</span></code>. A query against
-<code class="docutils literal notranslate"><span class="pre">named_modules</span></code> achieves the same result, but it is O(N) in
-the number of transitive modules. So, for a simple check to see
-if some submodule exists, <code class="docutils literal notranslate"><span class="pre">get_submodule</span></code> should always be
-used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>target</strong> – The fully-qualified string name of the submodule
-to look for. (See above example for how to specify a
-fully-qualified string.)</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>The submodule referenced by <code class="docutils literal notranslate"><span class="pre">target</span></code></p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.nn.Module</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – If the target string references an invalid
-    path or resolves to something that is not an
-    <code class="docutils literal notranslate"><span class="pre">nn.Module</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.half">
-<code class="sig-name descname">half</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.half" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all floating point parameters and buffers to <code class="docutils literal notranslate"><span class="pre">half</span></code> datatype.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>self</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.kernel">
-<code class="sig-name descname">kernel</code><span class="sig-paren">(</span><em class="sig-param">c1: torch.Tensor</em>, <em class="sig-param">c2: torch.Tensor</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.regularization.MMCEPenalty.kernel" title="Permalink to this definition">¶</a></dt>
-<dd><p>Laplacian kernel</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.load_state_dict">
-<code class="sig-name descname">load_state_dict</code><span class="sig-paren">(</span><em class="sig-param">state_dict: OrderedDict[str, Tensor], strict: bool = True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty.load_state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Copies parameters and buffers from <a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> into
-this module and its descendants. If <code class="xref py py-attr docutils literal notranslate"><span class="pre">strict</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code>, then
-the keys of <a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> must exactly match the keys returned
-by this module’s <code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code> function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>state_dict</strong> (<em>dict</em>) – a dict containing parameters and
-persistent buffers.</p></li>
-<li><p><strong>strict</strong> (<em>bool</em><em>, </em><em>optional</em>) – whether to strictly enforce that the keys
-in <a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a> match the keys returned by this module’s
-<code class="xref py py-meth docutils literal notranslate"><span class="pre">state_dict()</span></code> function. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code></p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><strong>missing_keys</strong> is a list of str containing the missing keys</p></li>
-<li><p><strong>unexpected_keys</strong> is a list of str containing the unexpected keys</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><code class="docutils literal notranslate"><span class="pre">NamedTuple</span></code> with <code class="docutils literal notranslate"><span class="pre">missing_keys</span></code> and <code class="docutils literal notranslate"><span class="pre">unexpected_keys</span></code> fields</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.modules">
-<code class="sig-name descname">modules</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.modules.module.Module]<a class="headerlink" href="#netcal.regularization.MMCEPenalty.modules" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over all modules in the network.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>Module</em> – a module in the network</p>
-</dd>
-</dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>Duplicate modules are returned only once. In the following
-example, <code class="docutils literal notranslate"><span class="pre">l</span></code> will be returned only once.</p>
-</div>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">l</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">net</span><span class="o">.</span><span class="n">modules</span><span class="p">()):</span>
-<span class="go">        print(idx, &#39;-&gt;&#39;, m)</span>
-
-<span class="go">0 -&gt; Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">)</span>
-<span class="go">1 -&gt; Linear(in_features=2, out_features=2, bias=True)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.named_buffers">
-<code class="sig-name descname">named_buffers</code><span class="sig-paren">(</span><em class="sig-param">prefix: str = ''</em>, <em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.Tensor]]<a class="headerlink" href="#netcal.regularization.MMCEPenalty.named_buffers" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module buffers, yielding both the
-name of the buffer as well as the buffer itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>prefix</strong> (<em>str</em>) – prefix to prepend to all buffer names.</p></li>
-<li><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields buffers of this module
-and all submodules. Otherwise, yields only buffers that
-are direct members of this module.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, torch.Tensor)</em> – Tuple containing the name and buffer</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">buf</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">named_buffers</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>   <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;running_var&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>       <span class="nb">print</span><span class="p">(</span><span class="n">buf</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.named_children">
-<code class="sig-name descname">named_children</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.nn.modules.module.Module]]<a class="headerlink" href="#netcal.regularization.MMCEPenalty.named_children" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over immediate children modules, yielding both
-the name of the module as well as the module itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Yields</dt>
-<dd class="field-odd"><p><em>(string, Module)</em> – Tuple containing a name and child module</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">module</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">named_children</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;conv4&#39;</span><span class="p">,</span> <span class="s1">&#39;conv5&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>        <span class="nb">print</span><span class="p">(</span><span class="n">module</span><span class="p">)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.named_modules">
-<code class="sig-name descname">named_modules</code><span class="sig-paren">(</span><em class="sig-param">memo: Optional[Set[Module]] = None</em>, <em class="sig-param">prefix: str = ''</em>, <em class="sig-param">remove_duplicate: bool = True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty.named_modules" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over all modules in the network, yielding
-both the name of the module as well as the module itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>memo</strong> – a memo to store the set of modules already added to the result</p></li>
-<li><p><strong>prefix</strong> – a prefix that will be added to the name of the module</p></li>
-<li><p><strong>remove_duplicate</strong> – whether to remove the duplicated module instances in the result</p></li>
-<li><p><strong>not</strong> (<em>or</em>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, Module)</em> – Tuple of name and module</p>
-</dd>
-</dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>Duplicate modules are returned only once. In the following
-example, <code class="docutils literal notranslate"><span class="pre">l</span></code> will be returned only once.</p>
-</div>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">l</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">net</span><span class="o">.</span><span class="n">named_modules</span><span class="p">()):</span>
-<span class="go">        print(idx, &#39;-&gt;&#39;, m)</span>
-
-<span class="go">0 -&gt; (&#39;&#39;, Sequential(</span>
-<span class="go">  (0): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">  (1): Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="go">))</span>
-<span class="go">1 -&gt; (&#39;0&#39;, Linear(in_features=2, out_features=2, bias=True))</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.named_parameters">
-<code class="sig-name descname">named_parameters</code><span class="sig-paren">(</span><em class="sig-param">prefix: str = ''</em>, <em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[Tuple[str, torch.nn.parameter.Parameter]]<a class="headerlink" href="#netcal.regularization.MMCEPenalty.named_parameters" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module parameters, yielding both the
-name of the parameter as well as the parameter itself.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>prefix</strong> (<em>str</em>) – prefix to prepend to all parameter names.</p></li>
-<li><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields parameters of this module
-and all submodules. Otherwise, yields only parameters that
-are direct members of this module.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>(string, Parameter)</em> – Tuple containing the name and parameter</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">param</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">named_parameters</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>   <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;bias&#39;</span><span class="p">]:</span>
-<span class="gp">&gt;&gt;&gt; </span>       <span class="nb">print</span><span class="p">(</span><span class="n">param</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.parameters">
-<code class="sig-name descname">parameters</code><span class="sig-paren">(</span><em class="sig-param">recurse: bool = True</em><span class="sig-paren">)</span> &#x2192; Iterator[torch.nn.parameter.Parameter]<a class="headerlink" href="#netcal.regularization.MMCEPenalty.parameters" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns an iterator over module parameters.</p>
-<p>This is typically passed to an optimizer.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>recurse</strong> (<em>bool</em>) – if True, then yields parameters of this module
-and all submodules. Otherwise, yields only parameters that
-are direct members of this module.</p>
-</dd>
-<dt class="field-even">Yields</dt>
-<dd class="field-even"><p><em>Parameter</em> – module parameter</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">():</span>
-<span class="gp">&gt;&gt;&gt; </span>    <span class="nb">print</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">param</span><span class="p">),</span> <span class="n">param</span><span class="o">.</span><span class="n">size</span><span class="p">())</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L,)</span>
-<span class="go">&lt;class &#39;torch.Tensor&#39;&gt; (20L, 1L, 5L, 5L)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.register_backward_hook">
-<code class="sig-name descname">register_backward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[[Module, Union[Tuple[torch.Tensor, ...], torch.Tensor], Union[Tuple[torch.Tensor, ...], torch.Tensor]], Union[None, torch.Tensor]]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.MMCEPenalty.register_backward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a backward hook on the module.</p>
-<p>This function is deprecated in favor of <code class="xref py py-meth docutils literal notranslate"><span class="pre">nn.Module.register_full_backward_hook()</span></code> and
-the behavior of this function will change in future versions.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.register_buffer">
-<code class="sig-name descname">register_buffer</code><span class="sig-paren">(</span><em class="sig-param">name: str, tensor: Optional[torch.Tensor], persistent: bool = True</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.MMCEPenalty.register_buffer" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a buffer to the module.</p>
-<p>This is typically used to register a buffer that should not to be
-considered a model parameter. For example, BatchNorm’s <code class="docutils literal notranslate"><span class="pre">running_mean</span></code>
-is not a parameter, but is part of the module’s state. Buffers, by
-default, are persistent and will be saved alongside parameters. This
-behavior can be changed by setting <code class="xref py py-attr docutils literal notranslate"><span class="pre">persistent</span></code> to <code class="docutils literal notranslate"><span class="pre">False</span></code>. The
-only difference between a persistent buffer and a non-persistent buffer
-is that the latter will not be a part of this module’s
-<a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a>.</p>
-<p>Buffers can be accessed as attributes using given names.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the buffer. The buffer can be accessed
-from this module using the given name</p></li>
-<li><p><strong>tensor</strong> (<em>Tensor</em>) – buffer to be registered.</p></li>
-<li><p><strong>persistent</strong> (<em>bool</em>) – whether the buffer is part of this module’s
-<a class="reference internal" href="#netcal.regularization.MMCEPenalty.state_dict" title="netcal.regularization.MMCEPenalty.state_dict"><code class="xref py py-attr docutils literal notranslate"><span class="pre">state_dict</span></code></a>.</p></li>
-</ul>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">&#39;running_mean&#39;</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">num_features</span><span class="p">))</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.register_forward_hook">
-<code class="sig-name descname">register_forward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[..., None]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.MMCEPenalty.register_forward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a forward hook on the module.</p>
-<p>The hook will be called every time after <a class="reference internal" href="#netcal.regularization.MMCEPenalty.forward" title="netcal.regularization.MMCEPenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> has computed an output.
-It should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="n">output</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">modified</span> <span class="n">output</span>
-</pre></div>
-</div>
-<p>The input contains only the positional arguments given to the module.
-Keyword arguments won’t be passed to the hooks and only to the <code class="docutils literal notranslate"><span class="pre">forward</span></code>.
-The hook can modify the output. It can modify the input inplace but
-it will not have effect on forward since this is called after
-<a class="reference internal" href="#netcal.regularization.MMCEPenalty.forward" title="netcal.regularization.MMCEPenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> is called.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.register_forward_pre_hook">
-<code class="sig-name descname">register_forward_pre_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[..., None]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.MMCEPenalty.register_forward_pre_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a forward pre-hook on the module.</p>
-<p>The hook will be called every time before <a class="reference internal" href="#netcal.regularization.MMCEPenalty.forward" title="netcal.regularization.MMCEPenalty.forward"><code class="xref py py-func docutils literal notranslate"><span class="pre">forward()</span></code></a> is invoked.
-It should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="nb">input</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">modified</span> <span class="nb">input</span>
-</pre></div>
-</div>
-<p>The input contains only the positional arguments given to the module.
-Keyword arguments won’t be passed to the hooks and only to the <code class="docutils literal notranslate"><span class="pre">forward</span></code>.
-The hook can modify the input. User can either return a tuple or a
-single modified value in the hook. We will wrap the value into a tuple
-if a single value is returned(unless that value is already a tuple).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.register_full_backward_hook">
-<code class="sig-name descname">register_full_backward_hook</code><span class="sig-paren">(</span><em class="sig-param">hook: Callable[[Module, Union[Tuple[torch.Tensor, ...], torch.Tensor], Union[Tuple[torch.Tensor, ...], torch.Tensor]], Union[None, torch.Tensor]]</em><span class="sig-paren">)</span> &#x2192; torch.utils.hooks.RemovableHandle<a class="headerlink" href="#netcal.regularization.MMCEPenalty.register_full_backward_hook" title="Permalink to this definition">¶</a></dt>
-<dd><p>Registers a backward hook on the module.</p>
-<p>The hook will be called every time the gradients with respect to module
-inputs are computed. The hook should have the following signature:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">module</span><span class="p">,</span> <span class="n">grad_input</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">Tensor</span><span class="p">)</span> <span class="ow">or</span> <span class="kc">None</span>
-</pre></div>
-</div>
-<p>The <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_output</span></code> are tuples that contain the gradients
-with respect to the inputs and outputs respectively. The hook should
-not modify its arguments, but it can optionally return a new gradient with
-respect to the input that will be used in place of <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> in
-subsequent computations. <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> will only correspond to the inputs given
-as positional arguments and all kwarg arguments are ignored. Entries
-in <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_input</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">grad_output</span></code> will be <code class="docutils literal notranslate"><span class="pre">None</span></code> for all non-Tensor
-arguments.</p>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>Modifying inputs or outputs inplace is not allowed when using backward hooks and
-will raise an error.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a handle that can be used to remove the added hook by calling
-<code class="docutils literal notranslate"><span class="pre">handle.remove()</span></code></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.utils.hooks.RemovableHandle</span></code></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.register_parameter">
-<code class="sig-name descname">register_parameter</code><span class="sig-paren">(</span><em class="sig-param">name: str, param: Optional[torch.nn.parameter.Parameter]</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.MMCEPenalty.register_parameter" title="Permalink to this definition">¶</a></dt>
-<dd><p>Adds a parameter to the module.</p>
-<p>The parameter can be accessed as an attribute using given name.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>name</strong> (<em>string</em>) – name of the parameter. The parameter can be accessed
-from this module using the given name</p></li>
-<li><p><strong>param</strong> (<em>Parameter</em>) – parameter to be added to the module.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.requires_grad_">
-<code class="sig-name descname">requires_grad_</code><span class="sig-paren">(</span><em class="sig-param">requires_grad: bool = True</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.requires_grad_" title="Permalink to this definition">¶</a></dt>
-<dd><p>Change if autograd should record operations on parameters in this
-module.</p>
-<p>This method sets the parameters’ <code class="xref py py-attr docutils literal notranslate"><span class="pre">requires_grad</span></code> attributes
-in-place.</p>
-<p>This method is helpful for freezing part of the module for finetuning
-or training parts of a model individually (e.g., GAN training).</p>
-<p>See <span class="xref std std-ref">locally-disable-grad-doc</span> for a comparison between
-<cite>.requires_grad_()</cite> and several similar mechanisms that may be confused with it.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>requires_grad</strong> (<em>bool</em>) – whether autograd should record operations on
-parameters in this module. Default: <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.share_memory">
-<code class="sig-name descname">share_memory</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.share_memory" title="Permalink to this definition">¶</a></dt>
-<dd><p>See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.share_memory_()</span></code></p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.state_dict">
-<code class="sig-name descname">state_dict</code><span class="sig-paren">(</span><em class="sig-param">destination=None</em>, <em class="sig-param">prefix=''</em>, <em class="sig-param">keep_vars=False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty.state_dict" title="Permalink to this definition">¶</a></dt>
-<dd><p>Returns a dictionary containing a whole state of the module.</p>
-<p>Both parameters and persistent buffers (e.g. running averages) are
-included. Keys are corresponding parameter and buffer names.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>a dictionary containing a whole state of the module</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>dict</p>
-</dd>
-</dl>
-<p>Example:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">module</span><span class="o">.</span><span class="n">state_dict</span><span class="p">()</span><span class="o">.</span><span class="n">keys</span><span class="p">()</span>
-<span class="go">[&#39;bias&#39;, &#39;weight&#39;]</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.regularization.MMCEPenalty.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves and/or casts the parameters and buffers.</p>
-<p>This can be called as</p>
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device=None</em>, <em class="sig-param">dtype=None</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">dtype</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">tensor</em>, <em class="sig-param">non_blocking=False</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<dl class="function">
-<dt>
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">memory_format=torch.channels_last</em><span class="sig-paren">)</span></dt>
-<dd></dd></dl>
-
-<p>Its signature is similar to <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.Tensor.to()</span></code>, but only accepts
-floating point or complex <code class="xref py py-attr docutils literal notranslate"><span class="pre">dtype`s.</span> <span class="pre">In</span> <span class="pre">addition,</span> <span class="pre">this</span> <span class="pre">method</span> <span class="pre">will</span>
-<span class="pre">only</span> <span class="pre">cast</span> <span class="pre">the</span> <span class="pre">floating</span> <span class="pre">point</span> <span class="pre">or</span> <span class="pre">complex</span> <span class="pre">parameters</span> <span class="pre">and</span> <span class="pre">buffers</span> <span class="pre">to</span> <span class="pre">:attr:`dtype</span></code>
-(if given). The integral parameters and buffers will be moved
-<code class="xref py py-attr docutils literal notranslate"><span class="pre">device</span></code>, if that is given, but with dtypes unchanged. When
-<code class="xref py py-attr docutils literal notranslate"><span class="pre">non_blocking</span></code> is set, it tries to convert/move asynchronously
-with respect to the host if possible, e.g., moving CPU Tensors with
-pinned memory to CUDA devices.</p>
-<p>See below for examples.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>device</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.device</span></code>) – the desired device of the parameters
-and buffers in this module</p></li>
-<li><p><strong>dtype</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.dtype</span></code>) – the desired floating point or complex dtype of
-the parameters and buffers in this module</p></li>
-<li><p><strong>tensor</strong> (<em>torch.Tensor</em>) – Tensor whose dtype and device are the desired
-dtype and device for all parameters and buffers in this module</p></li>
-<li><p><strong>memory_format</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.memory_format</span></code>) – the desired memory
-format for 4D parameters and buffers in this module (keyword
-only argument)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-<p>Examples:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1913, -0.3420],</span>
-<span class="go">        [-0.5113, -0.2325]])</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">double</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1913, -0.3420],</span>
-<span class="go">        [-0.5113, -0.2325]], dtype=torch.float64)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">gpu1</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s2">&quot;cuda:1&quot;</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">gpu1</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">half</span><span class="p">,</span> <span class="n">non_blocking</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1914, -0.3420],</span>
-<span class="go">        [-0.5112, -0.2324]], dtype=torch.float16, device=&#39;cuda:1&#39;)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">cpu</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s2">&quot;cpu&quot;</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">cpu</span><span class="p">)</span>
-<span class="go">Linear(in_features=2, out_features=2, bias=True)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.1914, -0.3420],</span>
-<span class="go">        [-0.5112, -0.2324]], dtype=torch.float16)</span>
-
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">cdouble</span><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="o">.</span><span class="n">weight</span>
-<span class="go">Parameter containing:</span>
-<span class="go">tensor([[ 0.3741+0.j,  0.2382+0.j],</span>
-<span class="go">        [ 0.5593+0.j, -0.4443+0.j]], dtype=torch.complex128)</span>
-<span class="gp">&gt;&gt;&gt; </span><span class="n">linear</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">cdouble</span><span class="p">))</span>
-<span class="go">tensor([[0.6122+0.j, 0.1150+0.j],</span>
-<span class="go">        [0.6122+0.j, 0.1150+0.j],</span>
-<span class="go">        [0.6122+0.j, 0.1150+0.j]], dtype=torch.complex128)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.to_empty">
-<code class="sig-name descname">to_empty</code><span class="sig-paren">(</span><em class="sig-param">*, device: Union[str, torch.device]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.to_empty" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves the parameters and buffers to the specified device without copying storage.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">torch.device</span></code>) – The desired device of the parameters
-and buffers in this module.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.train">
-<code class="sig-name descname">train</code><span class="sig-paren">(</span><em class="sig-param">mode: bool = True</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.train" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets the module in training mode.</p>
-<p>This has any effect only on certain modules. See documentations of
-particular modules for details of their behaviors in training/evaluation
-mode, if they are affected, e.g. <code class="xref py py-class docutils literal notranslate"><span class="pre">Dropout</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">BatchNorm</span></code>,
-etc.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>mode</strong> (<em>bool</em>) – whether to set training mode (<code class="docutils literal notranslate"><span class="pre">True</span></code>) or evaluation
-mode (<code class="docutils literal notranslate"><span class="pre">False</span></code>). Default: <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.type">
-<code class="sig-name descname">type</code><span class="sig-paren">(</span><em class="sig-param">dst_type: Union[torch.dtype, str]</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.type" title="Permalink to this definition">¶</a></dt>
-<dd><p>Casts all parameters and buffers to <code class="xref py py-attr docutils literal notranslate"><span class="pre">dst_type</span></code>.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>dst_type</strong> (<em>type</em><em> or </em><em>string</em>) – the desired type</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.xpu">
-<code class="sig-name descname">xpu</code><span class="sig-paren">(</span><em class="sig-param">device: Union[int</em>, <em class="sig-param">torch.device</em>, <em class="sig-param">None] = None</em><span class="sig-paren">)</span> &#x2192; T<a class="headerlink" href="#netcal.regularization.MMCEPenalty.xpu" title="Permalink to this definition">¶</a></dt>
-<dd><p>Moves all model parameters and buffers to the XPU.</p>
-<p>This also makes associated parameters and buffers different objects. So
-it should be called before constructing optimizer if the module will
-live on XPU while being optimized.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This method modifies the module in-place.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>device</strong> (<em>int</em><em>, </em><em>optional</em>) – if specified, all parameters will be
-copied to that device</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>Module</p>
-</dd>
-</dl>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.regularization.MMCEPenalty.zero_grad">
-<code class="sig-name descname">zero_grad</code><span class="sig-paren">(</span><em class="sig-param">set_to_none: bool = False</em><span class="sig-paren">)</span> &#x2192; None<a class="headerlink" href="#netcal.regularization.MMCEPenalty.zero_grad" title="Permalink to this definition">¶</a></dt>
-<dd><p>Sets gradients of all model parameters to zero. See similar function
-under <code class="xref py py-class docutils literal notranslate"><span class="pre">torch.optim.Optimizer</span></code> for more context.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>set_to_none</strong> (<em>bool</em>) – instead of setting to zero, set the grads to None.
-See <code class="xref py py-meth docutils literal notranslate"><span class="pre">torch.optim.Optimizer.zero_grad()</span></code> for details.</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-</div>
+</section>
 
 
+                </div>
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-  <div class="section" id="netcal-regularization-confidence-penalty">
-<h1>netcal.regularization.confidence_penalty<a class="headerlink" href="#netcal-regularization-confidence-penalty" title="Permalink to this headline">¶</a></h1>
-<dl class="function">
-<dt id="netcal.regularization.confidence_penalty">
-<code class="sig-prename descclassname">netcal.regularization.</code><code class="sig-name descname">confidence_penalty</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">weight: float</em>, <em class="sig-param">threshold: float = None</em>, <em class="sig-param">base: float = 2.718281828459045</em><span class="sig-paren">)</span> &#x2192; float<a class="headerlink" href="#netcal.regularization.confidence_penalty" title="Permalink to this definition">¶</a></dt>
-<dd><p>Confidence Penalty Regularization. This penalty term can be applied to any loss function as a regularizer <a class="footnote-reference brackets" href="#id2" id="id1">1</a>.</p>
+              <li><a href="../netcal.regularization.html" title="netcal.regularization" accesskey="P">previous </a></li>
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+  <section id="netcal-regularization-confidence-penalty">
+<h1>netcal.regularization.confidence_penalty<a class="headerlink" href="#netcal-regularization-confidence-penalty" title="Permalink to this heading">¶</a></h1>
+<dl class="py function">
+<dt class="sig sig-object py" id="netcal.regularization.confidence_penalty">
+<span class="sig-prename descclassname"><span class="pre">netcal.regularization.</span></span><span class="sig-name descname"><span class="pre">confidence_penalty</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">threshold</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">2.718281828459045</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="headerlink" href="#netcal.regularization.confidence_penalty" title="Permalink to this definition">¶</a></dt>
+<dd><p>Confidence Penalty Regularization. This penalty term can be applied to any loss function as a regularizer <a class="footnote-reference brackets" href="#id2" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction.
 1-D for binary classification, 2-D for multi class (softmax).</p></li>
@@ -61,81 +197,65 @@ <h1>netcal.regularization.confidence_penalty<a class="headerlink" href="#netcal-
 <li><p><strong>base</strong> (<em>float</em><em>, </em><em>optional</em><em>, </em><em>default: np.e</em>) – Base of logarithm (typically the number of classes to norm entropy).</p></li>
 </ul>
 </dd>
-<dt class="field-even">Returns</dt>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
 <dd class="field-even"><p>Confidence penalty of posterior distribution.</p>
 </dd>
-<dt class="field-odd">Return type</dt>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
 <dd class="field-odd"><p>float</p>
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>G. Pereyra, G. Tucker, J. Chorowski, Lukasz Kaiser, and G. Hinton:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id2" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>G. Pereyra, G. Tucker, J. Chorowski, Lukasz Kaiser, and G. Hinton:
 “Regularizing neural networks by penalizing confident output distributions.”
 CoRR, 2017.
 <a class="reference external" href="https://arxiv.org/pdf/1701.06548">Get source online</a></p>
-</dd>
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-  <div class="section" id="netcal-scaling-abstractlogisticregression">
-<h1>netcal.scaling.AbstractLogisticRegression<a class="headerlink" href="#netcal-scaling-abstractlogisticregression" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.scaling.AbstractLogisticRegression">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.scaling.</code><code class="sig-name descname">AbstractLogisticRegression</code><span class="sig-paren">(</span><em class="sig-param">method: str = 'mle'</em>, <em class="sig-param">momentum_epochs: int = 1000</em>, <em class="sig-param">mcmc_steps: int = 250</em>, <em class="sig-param">mcmc_chains: int = 1</em>, <em class="sig-param">mcmc_warmup_steps: int = 100</em>, <em class="sig-param">vi_epochs: int = 1000</em>, <em class="sig-param">detection: bool = False</em>, <em class="sig-param">independent_probabilities: bool = False</em>, <em class="sig-param">use_cuda: Union[str</em>, <em class="sig-param">bool] = False</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.AbstractCalibration.AbstractCalibration</span></code></p>
-<p>Abstract class for all calibration methods that base on logistic regression. We extended common
-scaling calibration methods by Bayesian epistemic uncertainty modelling <a class="footnote-reference brackets" href="#id3" id="id1">1</a>.
+
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+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.scaling.AbstractLogisticRegression</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.scaling.AbstractLogisticRegression"><code class="docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a></li>
+</ul>
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+  <section id="netcal-scaling-abstractlogisticregression">
+<h1>netcal.scaling.AbstractLogisticRegression<a class="headerlink" href="#netcal-scaling-abstractlogisticregression" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.scaling.AbstractLogisticRegression">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.scaling.</span></span><span class="sig-name descname"><span class="pre">AbstractLogisticRegression</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'mle'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">momentum_epochs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1000</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mcmc_steps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">250</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mcmc_chains</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mcmc_warmup_steps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vi_epochs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1000</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">independent_probabilities</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">use_cuda</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">bool</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression" title="Permalink to this definition">¶</a></dt>
+<dd><p>Abstract class for all calibration methods that base on logistic regression. We extended common
+scaling calibration methods by Bayesian epistemic uncertainty modelling <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
 On the one hand, this class supports Maximum Likelihood (MLE) estimates without uncertainty.
 This method is commonly solved by negative log likelihood optimization given by</p>
 <div class="math notranslate nohighlight">
@@ -72,9 +210,9 @@ <h1>netcal.scaling.AbstractLogisticRegression<a class="headerlink" href="#netcal
 distribution <span class="math notranslate nohighlight">\(q_\Phi(\theta)\)</span> (e.g. a normal distribution) for each weight parametrized by <span class="math notranslate nohighlight">\(\Phi\)</span>.
 The optimization objective is then the minimization of the Kullback-Leibler divergence between the
 variational distribution <span class="math notranslate nohighlight">\(q_\Phi(\theta))\)</span> and the true posterior <span class="math notranslate nohighlight">\(p(\theta | X, y)\)</span>.
-This can be solved using the ELBO method <a class="footnote-reference brackets" href="#id4" id="id2">2</a>. Variational Inference is faster than MCMC but also biased.</p>
+This can be solved using the ELBO method <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. Variational Inference is faster than MCMC but also biased.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>method</strong> (<em>str</em><em>, </em><em>default: &quot;mle&quot;</em>) – Method that is used to obtain a calibration mapping:
 - ‘mle’: Maximum likelihood estimate without uncertainty using a convex optimizer.
@@ -100,25 +238,23 @@ <h1>netcal.scaling.AbstractLogisticRegression<a class="headerlink" href="#netcal
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id3"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
 “Bayesian Confidence Calibration for Epistemic Uncertainty Modelling.”
 2021 IEEE Intelligent Vehicles Symposium (IV), 2021</p>
-</dd>
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Michael I Jordan, Zoubin Ghahramani, Tommi S Jaakkola, and Lawrence K Saul:
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Michael I Jordan, Zoubin Ghahramani, Tommi S Jaakkola, and Lawrence K Saul:
 “An introduction to variational methods for graphical models.” Machine learning, 37(2): 183–233, 1999.</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([method, momentum_epochs, …])</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([method, momentum_epochs, ...])</p></td>
 <td><p>Create an instance of <cite>AbstractLogisticRegression</cite>.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">clear</span></code>()</p></td>
@@ -157,399 +293,68 @@ <h1>netcal.scaling.AbstractLogisticRegression<a class="headerlink" href="#netcal
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X)</p></td>
 <td><p>Preprocessing of input data before called at the beginning of the fit-function.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>(dtype)</p></td>
 <td><p>Prior definition of the weights and intercept used for log regression.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
 <td><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, …])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, ...])</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
 <td><p>Perform variational inference using the guide.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.convex">
-<code class="sig-name descname">convex</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.convex" title="Permalink to this definition">¶</a></dt>
-<dd><p>Convex optimization to find the global optimum of current parameter search.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">tensorboard: bool = True</em>, <em class="sig-param">log_dir: str = None</em><span class="sig-paren">)</span> &#x2192; AbstractLogisticRegression<a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build logitic calibration model either conventional with single MLE estimate or with
-Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) algorithm to also obtain uncertainty estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.guide">
-<code class="sig-name descname">guide</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.guide" title="Permalink to this definition">¶</a></dt>
-<dd><p>Variational substitution definition for each parameter. The signature is the same as for the
-“self.model” function but the variables are not used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.mask">
-<code class="sig-name descname">mask</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Tuple[numpy.ndarray, List]<a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.mask" title="Permalink to this definition">¶</a></dt>
-<dd><p>Seek for all relevant weights whose values are negative. Mask those values with optimization constraints
-in the interval [0, 0].
-Constraints on the intercepts might also be set.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>Indices of masked values and list of boundary constraints for optimization.</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>tuple of (np.ndarray, list)</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.mcmc">
-<code class="sig-name descname">mcmc</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.mcmc" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform Markov-Chain Monte-Carlo sampling on the (unknown) posterior.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.model">
-<em class="property">abstract </em><code class="sig-name descname">model</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Definition of the log regression model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Logit of the log regression model.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.momentum">
-<code class="sig-name descname">momentum</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.momentum" title="Permalink to this definition">¶</a></dt>
-<dd><p>Momentum optimization to find the global optimum of current parameter search.
-This method is slow but tends to find the global optimum for non-convex optimization.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.prepare">
-<em class="property">abstract </em><code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Preprocessing of input data before called at the beginning of the fit-function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Prepared data vector X as torch tensor.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.prior">
-<em class="property">abstract </em><code class="sig-name descname">prior</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.prior" title="Permalink to this definition">¶</a></dt>
-<dd><p>Prior definition of the weights and intercept used for log regression. This function has to set the
-sites at least for “weights” and “bias”.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device: torch.device</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">num_samples: int = 1000</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">mean_estimate: bool = False</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>num_samples</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1000</em>) – Number of samples generated on MCMC sampling or Variational Inference.</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-<li><p><strong>mean_estimate</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, directly return the mean on probabilistic methods like MCMC or VI instead of the full
-distribution. This parameter has no effect on MLE.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>np.ndarray, shape=(n_samples, [n_classes]) on MLE or on MCMC/VI if ‘mean_estimate’ is True</em></p></li>
-<li><p><em>or shape=(n_parameters, n_samples, [n_classes]) on VI, MCMC if ‘mean_estimate’ is False</em> – On MLE without uncertainty, return NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).
-On VI or MCMC, return NumPy array with leading dimension as the number of sampled parameters from the
-log regression parameter distribution obtained by VI or MCMC.</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.AbstractLogisticRegression.variational">
-<code class="sig-name descname">variational</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.AbstractLogisticRegression.variational" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform variational inference using the guide.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
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-  <div class="section" id="netcal-scaling-betacalibration">
-<h1>netcal.scaling.BetaCalibration<a class="headerlink" href="#netcal-scaling-betacalibration" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.scaling.BetaCalibration">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.scaling.</code><code class="sig-name descname">BetaCalibration</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.scaling.AbstractLogisticRegression.AbstractLogisticRegression</span></code></p>
-<p>On classification, apply the beta calibration method to obtain a calibration mapping. The original method was
-proposed by <a class="footnote-reference brackets" href="#id4" id="id1">1</a>.
+
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.scaling.html#scaling-methods-for-confidence-calibration">Scaling Methods for Confidence Calibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.scaling.html#available-classes">Available classes</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html">netcal.scaling.AbstractLogisticRegression</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.scaling.LogisticCalibration.html">netcal.scaling.LogisticCalibration</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.scaling.LogisticCalibrationDependent.html">netcal.scaling.LogisticCalibrationDependent</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.scaling.TemperatureScaling.html">netcal.scaling.TemperatureScaling</a></li>
+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.scaling.BetaCalibration</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.scaling.BetaCalibration"><code class="docutils literal notranslate"><span class="pre">BetaCalibration</span></code></a></li>
+</ul>
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+  <section id="netcal-scaling-betacalibration">
+<h1>netcal.scaling.BetaCalibration<a class="headerlink" href="#netcal-scaling-betacalibration" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.scaling.BetaCalibration">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.scaling.</span></span><span class="sig-name descname"><span class="pre">BetaCalibration</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration" title="Permalink to this definition">¶</a></dt>
+<dd><p>On classification, apply the beta calibration method to obtain a calibration mapping. The original method was
+proposed by <a class="footnote-reference brackets" href="#id5" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
 For the multiclass case, we extended this method to work with multinomial logistic regression instead of a
 one vs. all calibration mapping.
 On detection mode, this calibration method uses multiple independent Beta distributions to obtain a
-calibration mapping by means of the confidence as well as additional features <a class="footnote-reference brackets" href="#id5" id="id2">2</a>. This calibration scheme
+calibration mapping by means of the confidence as well as additional features <a class="footnote-reference brackets" href="#id6" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. This calibration scheme
 assumes independence between all variables.</p>
 <p>On detection, it is necessary to provide all data in input parameter <code class="docutils literal notranslate"><span class="pre">X</span></code> as an NumPy array
 of shape <code class="docutils literal notranslate"><span class="pre">(n_samples,</span> <span class="pre">n_features)</span></code>,
@@ -75,7 +213,7 @@ <h1>netcal.scaling.BetaCalibration<a class="headerlink" href="#netcal-scaling-be
 input <span class="math notranslate nohighlight">\(s = (\hat{p}, \hat{r})\)</span> of size K by</p>
 <div class="math notranslate nohighlight">
 \[g(s) = \frac{1}{1 + \exp(-z(s))} ,\]</div>
-<p>According to <a class="footnote-reference brackets" href="#id4" id="id3">1</a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
+<p>According to <a class="footnote-reference brackets" href="#id5" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
 <div class="math notranslate nohighlight">
 \[z(s) = \log \frac{f(\text{m}=1 | s)}{f(\text{m}=0 | s)} \approx
 \log \frac{f(s | \text{m}=1)}{f(s | \text{m}=1)} = \ell r(s)\]</div>
@@ -95,8 +233,9 @@ <h1>netcal.scaling.BetaCalibration<a class="headerlink" href="#netcal-scaling-be
 <span class="math notranslate nohighlight">\(b_k=\beta_k^--\beta_k^+\)</span> and
 <span class="math notranslate nohighlight">\(c=\sum_k \log B(\alpha_k^-, \beta_k^-) - \log B(\alpha_k^+, \beta_k^+)\)</span>.
 We utilize standard optimization methods to determine the calibration mapping <span class="math notranslate nohighlight">\(g(s)\)</span>.</p>
+<p>Capturing epistemic uncertainty of the calibration method is also able with this implementation <a class="footnote-reference brackets" href="#id7" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>method</strong> (<em>str</em><em>, </em><em>default: &quot;mle&quot;</em>) – Method that is used to obtain a calibration mapping:
 - ‘mle’: Maximum likelihood estimate without uncertainty using a convex optimizer.
@@ -122,30 +261,30 @@ <h1>netcal.scaling.BetaCalibration<a class="headerlink" href="#netcal-scaling-be
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id4"><span class="brackets">1</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id3">2</a>)</span></dt>
-<dd><p>Kull, Meelis, Telmo Silva Filho, and Peter Flach:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id5" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id3">2</a>)</span>
+<p>Kull, Meelis, Telmo Silva Filho, and Peter Flach:
 “Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers”
 Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
 <a class="reference external" href="http://proceedings.mlr.press/v54/kull17a/kull17a.pdf">Get source online</a></p>
-</dd>
-<dt class="label" id="id5"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
-The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.</p>
-</dd>
-<dt class="label" id="id6"><span class="brackets">3</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.</p>
+</aside>
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">3</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
 “Bayesian Confidence Calibration for Epistemic Uncertainty Modelling.”
 2021 IEEE Intelligent Vehicles Symposium (IV), 2021</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(*args, **kwargs)</p></td>
 <td><p>Create an instance of <cite>BetaCalibration</cite>.</p></td>
@@ -186,410 +325,68 @@ <h1>netcal.scaling.BetaCalibration<a class="headerlink" href="#netcal-scaling-be
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X)</p></td>
 <td><p>Preprocessing of input data before called at the beginning of the fit-function.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>(dtype)</p></td>
 <td><p>Prior definition of the weights used for log regression.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
 <td><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, …])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, ...])</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
 <td><p>Perform variational inference using the guide.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.convex">
-<code class="sig-name descname">convex</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.convex" title="Permalink to this definition">¶</a></dt>
-<dd><p>Convex optimization to find the global optimum of current parameter search.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">tensorboard: bool = True</em>, <em class="sig-param">log_dir: str = None</em><span class="sig-paren">)</span> &#x2192; AbstractLogisticRegression<a class="headerlink" href="#netcal.scaling.BetaCalibration.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build logitic calibration model either conventional with single MLE estimate or with
-Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) algorithm to also obtain uncertainty estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.guide">
-<code class="sig-name descname">guide</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.guide" title="Permalink to this definition">¶</a></dt>
-<dd><p>Variational substitution definition for each parameter. The signature is the same as for the
-“self.model” function but the variables are not used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.intercept">
-<em class="property">property </em><code class="sig-name descname">intercept</code><a class="headerlink" href="#netcal.scaling.BetaCalibration.intercept" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for intercept of logistic calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.mask">
-<code class="sig-name descname">mask</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Tuple[numpy.ndarray, List]<a class="headerlink" href="#netcal.scaling.BetaCalibration.mask" title="Permalink to this definition">¶</a></dt>
-<dd><p>Seek for all relevant weights whose values are negative. Mask those values with optimization constraints
-in the interval [0, 0].</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>Indices of masked values.</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>list</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.mcmc">
-<code class="sig-name descname">mcmc</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.mcmc" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform Markov-Chain Monte-Carlo sampling on the (unknown) posterior.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.model">
-<code class="sig-name descname">model</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.BetaCalibration.model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Definition of the log regression model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Logit of the log regression model.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.momentum">
-<code class="sig-name descname">momentum</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.momentum" title="Permalink to this definition">¶</a></dt>
-<dd><p>Momentum optimization to find the global optimum of current parameter search.
-This method is slow but tends to find the global optimum for non-convex optimization.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.BetaCalibration.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Preprocessing of input data before called at the beginning of the fit-function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Prepared data vector X as torch tensor.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.prior">
-<code class="sig-name descname">prior</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.prior" title="Permalink to this definition">¶</a></dt>
-<dd><p>Prior definition of the weights used for log regression. This function has to set the
-variables ‘self.weight_prior_dist’, ‘self.weight_mean_init’ and ‘self.weight_stddev_init’.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.scaling.BetaCalibration.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.BetaCalibration.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device: torch.device</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">num_samples: int = 1000</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">mean_estimate: bool = False</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.BetaCalibration.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>num_samples</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1000</em>) – Number of samples generated on MCMC sampling or Variational Inference.</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-<li><p><strong>mean_estimate</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, directly return the mean on probabilistic methods like MCMC or VI instead of the full
-distribution. This parameter has no effect on MLE.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>np.ndarray, shape=(n_samples, [n_classes]) on MLE or on MCMC/VI if ‘mean_estimate’ is True</em></p></li>
-<li><p><em>or shape=(n_parameters, n_samples, [n_classes]) on VI, MCMC if ‘mean_estimate’ is False</em> – On MLE without uncertainty, return NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).
-On VI or MCMC, return NumPy array with leading dimension as the number of sampled parameters from the
-log regression parameter distribution obtained by VI or MCMC.</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.variational">
-<code class="sig-name descname">variational</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibration.variational" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform variational inference using the guide.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibration.weights">
-<em class="property">property </em><code class="sig-name descname">weights</code><a class="headerlink" href="#netcal.scaling.BetaCalibration.weights" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for weights of beta calibration.</p>
-</dd></dl>
-
-</dd></dl>
-
-</div>
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-  <div class="section" id="netcal-scaling-betacalibrationdependent">
-<h1>netcal.scaling.BetaCalibrationDependent<a class="headerlink" href="#netcal-scaling-betacalibrationdependent" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.scaling.BetaCalibrationDependent">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.scaling.</code><code class="sig-name descname">BetaCalibrationDependent</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">method: str = 'momentum'</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.scaling.AbstractLogisticRegression.AbstractLogisticRegression</span></code></p>
-<p>This calibration method uses a multivariate variant of a Beta distribution to obtain a
+
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+  <section id="netcal-scaling-betacalibrationdependent">
+<h1>netcal.scaling.BetaCalibrationDependent<a class="headerlink" href="#netcal-scaling-betacalibrationdependent" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.scaling.BetaCalibrationDependent">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.scaling.</span></span><span class="sig-name descname"><span class="pre">BetaCalibrationDependent</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'momentum'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent" title="Permalink to this definition">¶</a></dt>
+<dd><p>This calibration method uses a multivariate variant of a Beta distribution to obtain a
 calibration mapping by means of the confidence as well as additional features. This method is originally
-proposed by <a class="footnote-reference brackets" href="#id4" id="id1">1</a>. This calibration scheme
+proposed by <a class="footnote-reference brackets" href="#id5" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>. This calibration scheme
 tries to model several dependencies in the variables given by the input <code class="docutils literal notranslate"><span class="pre">X</span></code>.</p>
 <p>It is necessary to provide all data in input parameter <code class="docutils literal notranslate"><span class="pre">X</span></code> as an NumPy array of shape <code class="docutils literal notranslate"><span class="pre">(n_samples,</span> <span class="pre">n_features)</span></code>,
 whereas the confidence must be the first feature given in the input array. The ground-truth samples <code class="docutils literal notranslate"><span class="pre">y</span></code>
@@ -71,12 +209,12 @@ <h1>netcal.scaling.BetaCalibrationDependent<a class="headerlink" href="#netcal-s
 input <span class="math notranslate nohighlight">\(s = (\hat{p}, \hat{r})\)</span> of size K by</p>
 <div class="math notranslate nohighlight">
 \[g(s) = \frac{1}{1 + \exp(-z(s))} ,\]</div>
-<p>According to <a class="footnote-reference brackets" href="#id4" id="id2">1</a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
+<p>According to <a class="footnote-reference brackets" href="#id5" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
 <div class="math notranslate nohighlight">
 \[z(s) = \log \frac{f(\text{m}=1 | s)}{f(\text{m}=0 | s)} \approx
 \log \frac{f(s | \text{m}=1)}{f(s | \text{m}=1)} = \ell r(s)\]</div>
 <p>For a multivariate probability density function <span class="math notranslate nohighlight">\(f(s|\text{m})\)</span>, we use a variant of the beta distribution
-described in <a class="footnote-reference brackets" href="#id5" id="id3">2</a> and given by</p>
+described in <a class="footnote-reference brackets" href="#id6" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a> and given by</p>
 <div class="math notranslate nohighlight">
 \[f(s|\text{m}) =  \frac{1}{B(\alpha_0, ..., \alpha_K)}
                   \frac{\prod^K_{k=1} \lambda_k^{\alpha_k}(s_k^\ast)^{\alpha_k - 1}
@@ -99,8 +237,9 @@ <h1>netcal.scaling.BetaCalibrationDependent<a class="headerlink" href="#netcal-s
 <span class="math notranslate nohighlight">\(c=\log B(\alpha_0^-, ..., \alpha_k^-) - \log B(\alpha_0^+, ..., \alpha^+_k)\)</span>.</p>
 <p>This is optimized by an Adam optimizer with a learning rate of 1e-3 and a batch size of 256 for
 1000 iterations (default).</p>
+<p>Capturing epistemic uncertainty of the calibration method is also able with this implementation <a class="footnote-reference brackets" href="#id7" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>method</strong> (<em>str</em><em>, </em><em>default: &quot;momentum&quot;</em>) – Method that is used to obtain a calibration mapping:
 - ‘mle’: Maximum likelihood estimate without uncertainty using a convex optimizer.
@@ -122,29 +261,29 @@ <h1>netcal.scaling.BetaCalibrationDependent<a class="headerlink" href="#netcal-s
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id4"><span class="brackets">1</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id2">2</a>)</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id5" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id2">2</a>)</span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
-The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.</p>
-</dd>
-<dt class="label" id="id5"><span class="brackets"><a class="fn-backref" href="#id3">2</a></span></dt>
-<dd><p>Libby, David L., and Melvin R. Novick:
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.</p>
+</aside>
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">2</a><span class="fn-bracket">]</span></span>
+<p>Libby, David L., and Melvin R. Novick:
 “Multivariate generalized beta distributions with applications to utility assessment”
 Journal of Educational Statistics 7.4, pp. 271-294, 1982</p>
-</dd>
-<dt class="label" id="id6"><span class="brackets">3</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id7" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">3</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
 “Bayesian Confidence Calibration for Epistemic Uncertainty Modelling.”
 2021 IEEE Intelligent Vehicles Symposium (IV), 2021</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(*args[, method])</p></td>
 <td><p>Create an instance of <cite>BetaCalibrationDependent</cite>.</p></td>
@@ -185,417 +324,68 @@ <h1>netcal.scaling.BetaCalibrationDependent<a class="headerlink" href="#netcal-s
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X)</p></td>
 <td><p>Preprocessing of input data before called at the beginning of the fit-function.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>(dtype)</p></td>
 <td><p>Prior definition of the weights used for log regression.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
 <td><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, …])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, ...])</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
 <td><p>Perform variational inference using the guide.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.alphas">
-<em class="property">property </em><code class="sig-name descname">alphas</code><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.alphas" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for alpha values of dependent beta calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.betas">
-<em class="property">property </em><code class="sig-name descname">betas</code><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.betas" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for beta values of dependent beta calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.convex">
-<code class="sig-name descname">convex</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.convex" title="Permalink to this definition">¶</a></dt>
-<dd><p>Convex optimization to find the global optimum of current parameter search.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">tensorboard: bool = True</em>, <em class="sig-param">log_dir: str = None</em><span class="sig-paren">)</span> &#x2192; AbstractLogisticRegression<a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build logitic calibration model either conventional with single MLE estimate or with
-Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) algorithm to also obtain uncertainty estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.guide">
-<code class="sig-name descname">guide</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.guide" title="Permalink to this definition">¶</a></dt>
-<dd><p>Variational substitution definition for each parameter. The signature is the same as for the
-“self.model” function but the variables are not used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.intercept">
-<em class="property">property </em><code class="sig-name descname">intercept</code><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.intercept" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for intercept of dependent beta calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.mask">
-<code class="sig-name descname">mask</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Tuple[numpy.ndarray, List]<a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.mask" title="Permalink to this definition">¶</a></dt>
-<dd><p>Seek for all relevant weights whose values are negative. Mask those values with optimization constraints
-in the interval [0, 0].
-Constraints on the intercepts might also be set.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>Indices of masked values and list of boundary constraints for optimization.</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>tuple of (np.ndarray, list)</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.mcmc">
-<code class="sig-name descname">mcmc</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.mcmc" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform Markov-Chain Monte-Carlo sampling on the (unknown) posterior.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.model">
-<code class="sig-name descname">model</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Definition of the log regression model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Logit of the log regression model.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.momentum">
-<code class="sig-name descname">momentum</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.momentum" title="Permalink to this definition">¶</a></dt>
-<dd><p>Momentum optimization to find the global optimum of current parameter search.
-This method is slow but tends to find the global optimum for non-convex optimization.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Preprocessing of input data before called at the beginning of the fit-function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Prepared data vector X as torch tensor.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.prior">
-<code class="sig-name descname">prior</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.prior" title="Permalink to this definition">¶</a></dt>
-<dd><p>Prior definition of the weights used for log regression. This function has to set the
-variables ‘self.weight_prior_dist’, ‘self.weight_mean_init’ and ‘self.weight_stddev_init’.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device: torch.device</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">num_samples: int = 1000</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">mean_estimate: bool = False</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>num_samples</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1000</em>) – Number of samples generated on MCMC sampling or Variational Inference.</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-<li><p><strong>mean_estimate</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, directly return the mean on probabilistic methods like MCMC or VI instead of the full
-distribution. This parameter has no effect on MLE.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>np.ndarray, shape=(n_samples, [n_classes]) on MLE or on MCMC/VI if ‘mean_estimate’ is True</em></p></li>
-<li><p><em>or shape=(n_parameters, n_samples, [n_classes]) on VI, MCMC if ‘mean_estimate’ is False</em> – On MLE without uncertainty, return NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).
-On VI or MCMC, return NumPy array with leading dimension as the number of sampled parameters from the
-log regression parameter distribution obtained by VI or MCMC.</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.BetaCalibrationDependent.variational">
-<code class="sig-name descname">variational</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.BetaCalibrationDependent.variational" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform variational inference using the guide.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
 </dd></dl>
 
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-  <div class="section" id="netcal-scaling-logisticcalibration">
-<h1>netcal.scaling.LogisticCalibration<a class="headerlink" href="#netcal-scaling-logisticcalibration" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.scaling.LogisticCalibration">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.scaling.</code><code class="sig-name descname">LogisticCalibration</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">temperature_only: bool = False</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.scaling.AbstractLogisticRegression.AbstractLogisticRegression</span></code></p>
-<p>On classification, apply the logistic calibration method aka Platt scaling to obtain a
-calibration mapping. This method is originally proposed by <a class="footnote-reference brackets" href="#id7" id="id1">1</a>.
-For the multiclass case, we use the Vector scaling proposed in <a class="footnote-reference brackets" href="#id8" id="id2">2</a>.
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.scaling.html#scaling-methods-for-confidence-calibration">Scaling Methods for Confidence Calibration</a></li>
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+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.scaling.LogisticCalibration</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.scaling.LogisticCalibration"><code class="docutils literal notranslate"><span class="pre">LogisticCalibration</span></code></a></li>
+</ul>
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+  <section id="netcal-scaling-logisticcalibration">
+<h1>netcal.scaling.LogisticCalibration<a class="headerlink" href="#netcal-scaling-logisticcalibration" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.scaling.LogisticCalibration">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.scaling.</span></span><span class="sig-name descname"><span class="pre">LogisticCalibration</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">temperature_only</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration" title="Permalink to this definition">¶</a></dt>
+<dd><p>On classification, apply the logistic calibration method aka Platt scaling to obtain a
+calibration mapping. This method is originally proposed by <a class="footnote-reference brackets" href="#id8" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+For the multiclass case, we use the Vector scaling proposed in <a class="footnote-reference brackets" href="#id9" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.
 On detection mode, this calibration method uses multiple independent normal distributions to obtain a
-calibration mapping by means of the confidence as well as additional features <a class="footnote-reference brackets" href="#id10" id="id3">3</a>. This calibration scheme
+calibration mapping by means of the confidence as well as additional features <a class="footnote-reference brackets" href="#id10" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>. This calibration scheme
 assumes independence between all variables.</p>
 <p>On detection, it is necessary to provide all data in input parameter <code class="docutils literal notranslate"><span class="pre">X</span></code> as an NumPy array
 of shape <code class="docutils literal notranslate"><span class="pre">(n_samples,</span> <span class="pre">n_features)</span></code>,
@@ -74,7 +212,7 @@ <h1>netcal.scaling.LogisticCalibration<a class="headerlink" href="#netcal-scalin
 input <span class="math notranslate nohighlight">\(s = (\hat{p}, \hat{r})\)</span> of size K by</p>
 <div class="math notranslate nohighlight">
 \[g(s) = \frac{1}{1 + \exp(-z(s))} ,\]</div>
-<p>According to <a class="footnote-reference brackets" href="#id7" id="id4">1</a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
+<p>According to <a class="footnote-reference brackets" href="#id8" id="id4" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
 <div class="math notranslate nohighlight">
 \[z(s) = \log \frac{f(\text{m}=1 | s)}{f(\text{m}=0 | s)} \approx
 \log \frac{f(s | \text{m}=1)}{f(s | \text{m}=1)} = \ell r(s)\]</div>
@@ -83,14 +221,15 @@ <h1>netcal.scaling.LogisticCalibration<a class="headerlink" href="#netcal-scalin
 simply extend the scaling factor (from classification logistic calibration) to a scaling
 vector <span class="math notranslate nohighlight">\(w \in \mathbb{R}^K\)</span>.
 However, instead of using the uncalibrated confidence estimate <span class="math notranslate nohighlight">\(\hat{p}\)</span>, we use the logit of the
-network as part of <span class="math notranslate nohighlight">\(s\)</span> to be conform with the original formulation in <a class="footnote-reference brackets" href="#id7" id="id5">1</a> and <a class="footnote-reference brackets" href="#id8" id="id6">2</a>. Thus,
+network as part of <span class="math notranslate nohighlight">\(s\)</span> to be conform with the original formulation in <a class="footnote-reference brackets" href="#id8" id="id5" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> and <a class="footnote-reference brackets" href="#id9" id="id6" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>. Thus,
 the log-likelihood ratio can be expressed as</p>
 <div class="math notranslate nohighlight">
 \[\ell r(s) = s^T w + c,\]</div>
 <p>with bias <span class="math notranslate nohighlight">\(c \in \mathbb{R}\)</span>.
 We utilize standard optimization methods to determine the calibration mapping <span class="math notranslate nohighlight">\(g(s)\)</span>.</p>
+<p>Capturing epistemic uncertainty of the calibration method is also able with this implementation <a class="footnote-reference brackets" href="#id11" id="id7" role="doc-noteref"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>temperature_only</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If True, use Temperature Scaling instead of Platt/Vector Scaling.</p></li>
 <li><p><strong>method</strong> (<em>str</em><em>, </em><em>default: &quot;mle&quot;</em>) – Method that is used to obtain a calibration mapping:
@@ -117,36 +256,38 @@ <h1>netcal.scaling.LogisticCalibration<a class="headerlink" href="#netcal-scalin
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id7"><span class="brackets">1</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id4">2</a>,<a href="#id5">3</a>)</span></dt>
-<dd><p>Platt, John:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id8" role="note">
+<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id1">1</a>,<a role="doc-backlink" href="#id4">2</a>,<a role="doc-backlink" href="#id5">3</a>)</span>
+<p>Platt, John:
 “Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods.”
 Advances in large margin classifiers 10.3: 61-74, 1999
 <a class="reference external" href="https://www.researchgate.net/profile/John_Platt/publication/2594015_Probabilistic_Outputs_for_Support_Vector_Machines_and_Comparisons_to_Regularized_Likelihood_Methods/links/004635154cff5262d6000000.pdf">Get source online</a></p>
-</dd>
-<dt class="label" id="id8"><span class="brackets">2</span><span class="fn-backref">(<a href="#id2">1</a>,<a href="#id6">2</a>)</span></dt>
-<dd><p>Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
+</aside>
+<aside class="footnote brackets" id="id9" role="note">
+<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
+<span class="backrefs">(<a role="doc-backlink" href="#id2">1</a>,<a role="doc-backlink" href="#id6">2</a>)</span>
+<p>Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
 “On Calibration of Modern Neural Networks.”
 Proceedings of the 34th International Conference on Machine Learning-Volume 70. JMLR. org, 2017.
 <a class="reference external" href="https://arxiv.org/abs/1706.04599">Get source online</a></p>
-</dd>
-<dt class="label" id="id10"><span class="brackets"><a class="fn-backref" href="#id3">3</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id10" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
-The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.</p>
-</dd>
-<dt class="label" id="id11"><span class="brackets">4</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.</p>
+</aside>
+<aside class="footnote brackets" id="id11" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id7">4</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
 “Bayesian Confidence Calibration for Epistemic Uncertainty Modelling.”
 2021 IEEE Intelligent Vehicles Symposium (IV), 2021</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(*args[, temperature_only])</p></td>
 <td><p>Create an instance of <cite>LogisticCalibration</cite>.</p></td>
@@ -187,411 +328,68 @@ <h1>netcal.scaling.LogisticCalibration<a class="headerlink" href="#netcal-scalin
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X)</p></td>
 <td><p>Preprocessing of input data before called at the beginning of the fit-function.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>(dtype)</p></td>
 <td><p>Prior definition of the weights used for log regression.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
 <td><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, …])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, ...])</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
 <td><p>Perform variational inference using the guide.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.convex">
-<code class="sig-name descname">convex</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.convex" title="Permalink to this definition">¶</a></dt>
-<dd><p>Convex optimization to find the global optimum of current parameter search.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">tensorboard: bool = True</em>, <em class="sig-param">log_dir: str = None</em><span class="sig-paren">)</span> &#x2192; AbstractLogisticRegression<a class="headerlink" href="#netcal.scaling.LogisticCalibration.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build logitic calibration model either conventional with single MLE estimate or with
-Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) algorithm to also obtain uncertainty estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.guide">
-<code class="sig-name descname">guide</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.guide" title="Permalink to this definition">¶</a></dt>
-<dd><p>Variational substitution definition for each parameter. The signature is the same as for the
-“self.model” function but the variables are not used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.intercept">
-<em class="property">property </em><code class="sig-name descname">intercept</code><a class="headerlink" href="#netcal.scaling.LogisticCalibration.intercept" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for intercept of logistic calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.mask">
-<code class="sig-name descname">mask</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Tuple[numpy.ndarray, List]<a class="headerlink" href="#netcal.scaling.LogisticCalibration.mask" title="Permalink to this definition">¶</a></dt>
-<dd><p>Seek for all relevant weights whose values are negative. Mask those values with optimization constraints
-in the interval [0, 0].
-Constraints on the intercepts might also be set.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>Indices of masked values and list of boundary constraints for optimization.</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>tuple of (np.ndarray, list)</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.mcmc">
-<code class="sig-name descname">mcmc</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.mcmc" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform Markov-Chain Monte-Carlo sampling on the (unknown) posterior.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.model">
-<code class="sig-name descname">model</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.LogisticCalibration.model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Definition of the log regression model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Logit of the log regression model.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.momentum">
-<code class="sig-name descname">momentum</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.momentum" title="Permalink to this definition">¶</a></dt>
-<dd><p>Momentum optimization to find the global optimum of current parameter search.
-This method is slow but tends to find the global optimum for non-convex optimization.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.LogisticCalibration.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Preprocessing of input data before called at the beginning of the fit-function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Prepared data vector X as torch tensor.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.prior">
-<code class="sig-name descname">prior</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.prior" title="Permalink to this definition">¶</a></dt>
-<dd><p>Prior definition of the weights used for log regression. This function has to set the
-variables ‘self.weight_prior_dist’, ‘self.weight_mean_init’ and ‘self.weight_stddev_init’.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.scaling.LogisticCalibration.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.LogisticCalibration.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device: torch.device</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">num_samples: int = 1000</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">mean_estimate: bool = False</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.LogisticCalibration.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>num_samples</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1000</em>) – Number of samples generated on MCMC sampling or Variational Inference.</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-<li><p><strong>mean_estimate</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, directly return the mean on probabilistic methods like MCMC or VI instead of the full
-distribution. This parameter has no effect on MLE.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>np.ndarray, shape=(n_samples, [n_classes]) on MLE or on MCMC/VI if ‘mean_estimate’ is True</em></p></li>
-<li><p><em>or shape=(n_parameters, n_samples, [n_classes]) on VI, MCMC if ‘mean_estimate’ is False</em> – On MLE without uncertainty, return NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).
-On VI or MCMC, return NumPy array with leading dimension as the number of sampled parameters from the
-log regression parameter distribution obtained by VI or MCMC.</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.variational">
-<code class="sig-name descname">variational</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibration.variational" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform variational inference using the guide.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibration.weights">
-<em class="property">property </em><code class="sig-name descname">weights</code><a class="headerlink" href="#netcal.scaling.LogisticCalibration.weights" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for weights of logistic calibration.</p>
-</dd></dl>
-
-</dd></dl>
-
-</div>
+</section>
 
 
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diff --git a/docs/build/html/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html b/docs/build/html/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html
index b08f4f4..b388de1 100644
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-  <div class="section" id="netcal-scaling-logisticcalibrationdependent">
-<h1>netcal.scaling.LogisticCalibrationDependent<a class="headerlink" href="#netcal-scaling-logisticcalibrationdependent" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.scaling.LogisticCalibrationDependent">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.scaling.</code><code class="sig-name descname">LogisticCalibrationDependent</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.scaling.AbstractLogisticRegression.AbstractLogisticRegression</span></code></p>
-<p>This calibration method is for detection only and uses multivariate normal distributions to obtain a
+
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.scaling.html#scaling-methods-for-confidence-calibration">Scaling Methods for Confidence Calibration</a></li>
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+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.scaling.LogisticCalibrationDependent</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.scaling.LogisticCalibrationDependent"><code class="docutils literal notranslate"><span class="pre">LogisticCalibrationDependent</span></code></a></li>
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+  <section id="netcal-scaling-logisticcalibrationdependent">
+<h1>netcal.scaling.LogisticCalibrationDependent<a class="headerlink" href="#netcal-scaling-logisticcalibrationdependent" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.scaling.LogisticCalibrationDependent">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.scaling.</span></span><span class="sig-name descname"><span class="pre">LogisticCalibrationDependent</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent" title="Permalink to this definition">¶</a></dt>
+<dd><p>This calibration method is for detection only and uses multivariate normal distributions to obtain a
 calibration mapping by means of the confidence as well as additional features. This calibration scheme
-tries to model several dependencies in the variables given by the input <code class="docutils literal notranslate"><span class="pre">X</span></code> <a class="footnote-reference brackets" href="#id3" id="id1">1</a>.</p>
+tries to model several dependencies in the variables given by the input <code class="docutils literal notranslate"><span class="pre">X</span></code> <a class="footnote-reference brackets" href="#id4" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.</p>
 <p>It is necessary to provide all data in input parameter <code class="docutils literal notranslate"><span class="pre">X</span></code> as an NumPy array of shape <code class="docutils literal notranslate"><span class="pre">(n_samples,</span> <span class="pre">n_features)</span></code>,
 whereas the confidence must be the first feature given in the input array. The ground-truth samples <code class="docutils literal notranslate"><span class="pre">y</span></code>
 must be an array of shape <code class="docutils literal notranslate"><span class="pre">(n_samples,)</span></code> consisting of binary labels <span class="math notranslate nohighlight">\(y \in \{0, 1\}\)</span>. Those
@@ -70,7 +208,7 @@ <h1>netcal.scaling.LogisticCalibrationDependent<a class="headerlink" href="#netc
 input <span class="math notranslate nohighlight">\(s = (\hat{p}, \hat{r})\)</span> of size K by</p>
 <div class="math notranslate nohighlight">
 \[g(s) = \frac{1}{1 + \exp(-z(s))} ,\]</div>
-<p>According to <a class="footnote-reference brackets" href="#id4" id="id2">2</a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
+<p>According to <a class="footnote-reference brackets" href="#id5" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>, we can interpret the logit <span class="math notranslate nohighlight">\(z\)</span> as the logarithm of the posterior odds</p>
 <div class="math notranslate nohighlight">
 \[z(s) = \log \frac{f(\text{m}=1 | s)}{f(\text{m}=0 | s)} \approx
 \log \frac{f(s | \text{m}=1)}{f(s | \text{m}=1)} = \ell r(s)\]</div>
@@ -79,16 +217,17 @@ <h1>netcal.scaling.LogisticCalibrationDependent<a class="headerlink" href="#netc
 as the mean vectors and covariance matrices for <span class="math notranslate nohighlight">\(\text{m}=1\)</span> and
 <span class="math notranslate nohighlight">\(\text{m}=0\)</span>, respectively, we get a likelihood ratio of</p>
 <div class="math notranslate nohighlight">
-\[\ell r(s) = \log \frac{\Sigma^-}{\Sigma^+}
-+ \frac{1}{2} (s_-^T \Sigma_-^{-1}s^-) - (s_+^T \Sigma_+^{-1}s^+),\]</div>
+\[\ell r(s) = \log \frac{|\Sigma^-|}{|\Sigma^+|}
++ \frac{1}{2} \Big[ (s_-^T \Sigma_-^{-1}s^-) - (s_+^T \Sigma_+^{-1}s^+) \Big],\]</div>
 <p>with <span class="math notranslate nohighlight">\(s^+ = s - \mu^+\)</span> and <span class="math notranslate nohighlight">\(s^- = s - \mu^-\)</span>.</p>
 <p>To keep the restrictions to covariance matrices (symmetric and positive semidefinit), we optimize a decomposed
 matrix V as</p>
 <div class="math notranslate nohighlight">
 \[\Sigma = V^T V\]</div>
 <p>instead of estimating <span class="math notranslate nohighlight">\(\Sigma\)</span> directly. This guarantees both requirements.</p>
+<p>Capturing epistemic uncertainty of the calibration method is also able with this implementation <a class="footnote-reference brackets" href="#id6" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>method</strong> (<em>str</em><em>, </em><em>default: &quot;mle&quot;</em>) – Method that is used to obtain a calibration mapping:
 - ‘mle’: Maximum likelihood estimate without uncertainty using a convex optimizer.
@@ -110,30 +249,29 @@ <h1>netcal.scaling.LogisticCalibrationDependent<a class="headerlink" href="#netc
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id3"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
 “Multivariate Confidence Calibration for Object Detection.”
-The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops.</p>
-</dd>
-<dt class="label" id="id4"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
-<dd><p>Kull, Meelis, Telmo Silva Filho, and Peter Flach:
+The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.</p>
+</aside>
+<aside class="footnote brackets" id="id5" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Kull, Meelis, Telmo Silva Filho, and Peter Flach:
 “Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers”
 Artificial Intelligence and Statistics, PMLR 54:623-631, 2017
 <a class="reference external" href="http://proceedings.mlr.press/v54/kull17a/kull17a.pdf">Get source online</a></p>
-</dd>
-<dt class="label" id="id5"><span class="brackets">3</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id6" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">3</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
 “Bayesian Confidence Calibration for Epistemic Uncertainty Modelling.”
 2021 IEEE Intelligent Vehicles Symposium (IV), 2021</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(*args, **kwargs)</p></td>
 <td><p>Create an instance of <cite>LogisticCalibrationDependent</cite>.</p></td>
@@ -174,417 +312,68 @@ <h1>netcal.scaling.LogisticCalibrationDependent<a class="headerlink" href="#netc
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X)</p></td>
 <td><p>Preprocessing of input data before called at the beginning of the fit-function.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>(dtype)</p></td>
 <td><p>Prior definition of the weights used for log regression.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
 <td><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, …])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, ...])</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
 <td><p>Perform variational inference using the guide.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.convex">
-<code class="sig-name descname">convex</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.convex" title="Permalink to this definition">¶</a></dt>
-<dd><p>Convex optimization to find the global optimum of current parameter search.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.covariances">
-<em class="property">property </em><code class="sig-name descname">covariances</code><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.covariances" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for covariance matrices of dependent logistic calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">tensorboard: bool = True</em>, <em class="sig-param">log_dir: str = None</em><span class="sig-paren">)</span> &#x2192; AbstractLogisticRegression<a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build logitic calibration model either conventional with single MLE estimate or with
-Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) algorithm to also obtain uncertainty estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.guide">
-<code class="sig-name descname">guide</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.guide" title="Permalink to this definition">¶</a></dt>
-<dd><p>Variational substitution definition for each parameter. The signature is the same as for the
-“self.model” function but the variables are not used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.intercept">
-<em class="property">property </em><code class="sig-name descname">intercept</code><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.intercept" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for intercept of dependent logistic calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.mask">
-<code class="sig-name descname">mask</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Tuple[numpy.ndarray, List]<a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.mask" title="Permalink to this definition">¶</a></dt>
-<dd><p>Seek for all relevant weights whose values are negative. Mask those values with optimization constraints
-in the interval [0, 0].
-Constraints on the intercepts might also be set.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>Indices of masked values and list of boundary constraints for optimization.</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>tuple of (np.ndarray, list)</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.mcmc">
-<code class="sig-name descname">mcmc</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.mcmc" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform Markov-Chain Monte-Carlo sampling on the (unknown) posterior.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.means">
-<em class="property">property </em><code class="sig-name descname">means</code><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.means" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for mean vectors of dependent logistic calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.model">
-<code class="sig-name descname">model</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Definition of the log regression model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Logit of the log regression model.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.momentum">
-<code class="sig-name descname">momentum</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.momentum" title="Permalink to this definition">¶</a></dt>
-<dd><p>Momentum optimization to find the global optimum of current parameter search.
-This method is slow but tends to find the global optimum for non-convex optimization.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Preprocessing of input data before called at the beginning of the fit-function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Prepared data vector X as torch tensor.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.prior">
-<code class="sig-name descname">prior</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.prior" title="Permalink to this definition">¶</a></dt>
-<dd><p>Prior definition of the weights used for log regression. This function has to set the
-variables ‘self.weight_prior_dist’, ‘self.weight_mean_init’ and ‘self.weight_stddev_init’.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device: torch.device</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">num_samples: int = 1000</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">mean_estimate: bool = False</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>num_samples</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1000</em>) – Number of samples generated on MCMC sampling or Variational Inference.</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-<li><p><strong>mean_estimate</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, directly return the mean on probabilistic methods like MCMC or VI instead of the full
-distribution. This parameter has no effect on MLE.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>np.ndarray, shape=(n_samples, [n_classes]) on MLE or on MCMC/VI if ‘mean_estimate’ is True</em></p></li>
-<li><p><em>or shape=(n_parameters, n_samples, [n_classes]) on VI, MCMC if ‘mean_estimate’ is False</em> – On MLE without uncertainty, return NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).
-On VI or MCMC, return NumPy array with leading dimension as the number of sampled parameters from the
-log regression parameter distribution obtained by VI or MCMC.</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.LogisticCalibrationDependent.variational">
-<code class="sig-name descname">variational</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.LogisticCalibrationDependent.variational" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform variational inference using the guide.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
 </dd></dl>
 
-</div>
+</section>
 
 
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-  <div class="section" id="netcal-scaling-temperaturescaling">
-<h1>netcal.scaling.TemperatureScaling<a class="headerlink" href="#netcal-scaling-temperaturescaling" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.scaling.TemperatureScaling">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.scaling.</code><code class="sig-name descname">TemperatureScaling</code><span class="sig-paren">(</span><em class="sig-param">*args</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">netcal.scaling.LogisticCalibration.LogisticCalibration</span></code></p>
-<p>On classification or detection, apply the temperature scaling method described in <a class="footnote-reference brackets" href="#id2" id="id1">1</a> to obtain a
-calibration mapping. For confidence calibration in classification tasks, a
+
+          </ul>
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+<li class="toctree-l2"><a class="reference internal" href="../netcal.scaling.html#scaling-methods-for-confidence-calibration">Scaling Methods for Confidence Calibration</a></li>
+<li class="toctree-l2 current"><a class="reference internal" href="../netcal.scaling.html#available-classes">Available classes</a><ul class="current">
+<li class="toctree-l3"><a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html">netcal.scaling.AbstractLogisticRegression</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.scaling.LogisticCalibration.html">netcal.scaling.LogisticCalibration</a></li>
+<li class="toctree-l3"><a class="reference internal" href="netcal.scaling.LogisticCalibrationDependent.html">netcal.scaling.LogisticCalibrationDependent</a></li>
+<li class="toctree-l3 current"><a class="current reference internal" href="#">netcal.scaling.TemperatureScaling</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#netcal.scaling.TemperatureScaling"><code class="docutils literal notranslate"><span class="pre">TemperatureScaling</span></code></a></li>
+</ul>
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+  <section id="netcal-scaling-temperaturescaling">
+<h1>netcal.scaling.TemperatureScaling<a class="headerlink" href="#netcal-scaling-temperaturescaling" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.scaling.TemperatureScaling">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.scaling.</span></span><span class="sig-name descname"><span class="pre">TemperatureScaling</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling" title="Permalink to this definition">¶</a></dt>
+<dd><p>On classification or detection, apply the temperature scaling method to obtain a
+calibration mapping.
+This method has been proposed by <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.
+For confidence calibration in classification tasks, a
 confidence mapping <span class="math notranslate nohighlight">\(g\)</span> is applied on top of a miscalibrated scoring classifier <span class="math notranslate nohighlight">\(\hat{p} = h(x)\)</span> to
 deliver a calibrated confidence score <span class="math notranslate nohighlight">\(\hat{q} = g(h(x))\)</span>.</p>
 <p>For detection calibration, we can also use the additional box regression output which we denote as
@@ -66,9 +206,10 @@ <h1>netcal.scaling.TemperatureScaling<a class="headerlink" href="#netcal-scaling
 <p>with the temperature <span class="math notranslate nohighlight">\(T \in \mathbb{R}\)</span> as a single scalar value.
 The function <span class="math notranslate nohighlight">\(\sigma(*)\)</span> is either the sigmoid (on detection or binary classification) or the
 softmax operator (multiclass classification).</p>
-<p>We utilize standard optimization methods to determine the calibration mapping <span class="math notranslate nohighlight">\(g(s)\)</span>.</p>
+<p>We utilize standard optimization methods to determine the calibration mapping <span class="math notranslate nohighlight">\(g(s)\)</span>.
+Capturing epistemic uncertainty of the calibration method is also able with this implementation <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>method</strong> (<em>str</em><em>, </em><em>default: &quot;mle&quot;</em>) – Method that is used to obtain a calibration mapping:
 - ‘mle’: Maximum likelihood estimate without uncertainty using a convex optimizer.
@@ -94,30 +235,23 @@ <h1>netcal.scaling.TemperatureScaling<a class="headerlink" href="#netcal-scaling
 </dd>
 </dl>
 <p class="rubric">References</p>
-<dl class="footnote brackets">
-<dt class="label" id="id2"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
-<dd><p>Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
+<aside class="footnote-list brackets">
+<aside class="footnote brackets" id="id3" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
+<p>Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger:
 “On Calibration of Modern Neural Networks.”
 Proceedings of the 34th International Conference on Machine Learning-Volume 70. JMLR. org, 2017.
 <a class="reference external" href="https://arxiv.org/abs/1706.04599">Get source online</a></p>
-</dd>
-<dt class="label" id="id3"><span class="brackets">2</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff:
-“Multivariate Confidence Calibration for Object Detection.”
-The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020.</p>
-</dd>
-<dt class="label" id="id4"><span class="brackets">3</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
+</aside>
+<aside class="footnote brackets" id="id4" role="note">
+<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
+<p>Fabian Küppers, Jan Kronenberger, Jonas Schneider  and Anselm Haselhoff:
 “Bayesian Confidence Calibration for Epistemic Uncertainty Modelling.”
 2021 IEEE Intelligent Vehicles Symposium (IV), 2021</p>
-</dd>
-</dl>
+</aside>
+</aside>
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(*args, **kwargs)</p></td>
 <td><p>Create an instance of <cite>TemperatureScaling</cite>.</p></td>
@@ -158,417 +292,68 @@ <h1>netcal.scaling.TemperatureScaling<a class="headerlink" href="#netcal-scaling
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prepare</span></code>(X)</p></td>
 <td><p>Preprocessing of input data before called at the beginning of the fit-function.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>()</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">prior</span></code>(dtype)</p></td>
 <td><p>Prior definition of the weights used for log regression.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">to</span></code>(device)</p></td>
 <td><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, …])</p></td>
+<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X[, num_samples, random_state, ...])</p></td>
 <td><p>After model calibration, this function is used to get calibrated outputs of uncalibrated confidence estimates.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">variational</span></code>(data, y, tensorboard, log_dir)</p></td>
 <td><p>Perform variational inference using the guide.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.clear">
-<code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.convex">
-<code class="sig-name descname">convex</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.convex" title="Permalink to this definition">¶</a></dt>
-<dd><p>Convex optimization to find the global optimum of current parameter search.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.fit">
-<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">tensorboard: bool = True</em>, <em class="sig-param">log_dir: str = None</em><span class="sig-paren">)</span> &#x2192; AbstractLogisticRegression<a class="headerlink" href="#netcal.scaling.TemperatureScaling.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Build logitic calibration model either conventional with single MLE estimate or with
-Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) algorithm to also obtain uncertainty estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of class <a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.guide">
-<code class="sig-name descname">guide</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.guide" title="Permalink to this definition">¶</a></dt>
-<dd><p>Variational substitution definition for each parameter. The signature is the same as for the
-“self.model” function but the variables are not used.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.intercept">
-<em class="property">property </em><code class="sig-name descname">intercept</code><a class="headerlink" href="#netcal.scaling.TemperatureScaling.intercept" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for intercept of logistic calibration.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="../../_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.mask">
-<code class="sig-name descname">mask</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; Tuple[numpy.ndarray, List]<a class="headerlink" href="#netcal.scaling.TemperatureScaling.mask" title="Permalink to this definition">¶</a></dt>
-<dd><p>Seek for all relevant weights whose values are negative. Mask those values with optimization constraints
-in the interval [0, 0].
-Constraints on the intercepts might also be set.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p>Indices of masked values and list of boundary constraints for optimization.</p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>tuple of (np.ndarray, list)</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.mcmc">
-<code class="sig-name descname">mcmc</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.mcmc" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform Markov-Chain Monte-Carlo sampling on the (unknown) posterior.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.model">
-<code class="sig-name descname">model</code><span class="sig-paren">(</span><em class="sig-param">X: torch.Tensor = None</em>, <em class="sig-param">y: torch.Tensor = None</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.TemperatureScaling.model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Definition of the log regression model.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_log_regression_features</em><em>)</em>) – Input data that has been prepared by “self.prepare” function call.</p></li>
-<li><p><strong>y</strong> (<em>torch.Tensor</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – Torch tensor with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D) (for multiclass MLE only).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Logit of the log regression model.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor, shape=(n_samples, [n_classes])</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.momentum">
-<code class="sig-name descname">momentum</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.momentum" title="Permalink to this definition">¶</a></dt>
-<dd><p>Momentum optimization to find the global optimum of current parameter search.
-This method is slow but tends to find the global optimum for non-convex optimization.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.prepare">
-<code class="sig-name descname">prepare</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; torch.Tensor<a class="headerlink" href="#netcal.scaling.TemperatureScaling.prepare" title="Permalink to this definition">¶</a></dt>
-<dd><p>Preprocessing of input data before called at the beginning of the fit-function.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Prepared data vector X as torch tensor.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>torch.Tensor</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.prior">
-<code class="sig-name descname">prior</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.prior" title="Permalink to this definition">¶</a></dt>
-<dd><p>Prior definition of the weights used for log regression. This function has to set the
-variables ‘self.weight_prior_dist’, ‘self.weight_mean_init’ and ‘self.weight_stddev_init’.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.scaling.TemperatureScaling.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.TemperatureScaling.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.temperature">
-<em class="property">property </em><code class="sig-name descname">temperature</code><a class="headerlink" href="#netcal.scaling.TemperatureScaling.temperature" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for temperature of temperature scaling.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.to">
-<code class="sig-name descname">to</code><span class="sig-paren">(</span><em class="sig-param">device: torch.device</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.to" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set distribution parameters to the desired device in order to compute either on CPU or GPU.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.transform">
-<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">num_samples: int = 1000</em>, <em class="sig-param">random_state: int = None</em>, <em class="sig-param">mean_estimate: bool = False</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.scaling.TemperatureScaling.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>num_samples</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: 1000</em>) – Number of samples generated on MCMC sampling or Variational Inference.</p></li>
-<li><p><strong>random_state</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – Fix the random seed for the random number</p></li>
-<li><p><strong>mean_estimate</strong> (<em>bool</em><em>, </em><em>optional</em><em>, </em><em>default: False</em>) – If True, directly return the mean on probabilistic methods like MCMC or VI instead of the full
-distribution. This parameter has no effect on MLE.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><em>np.ndarray, shape=(n_samples, [n_classes]) on MLE or on MCMC/VI if ‘mean_estimate’ is True</em></p></li>
-<li><p><em>or shape=(n_parameters, n_samples, [n_classes]) on VI, MCMC if ‘mean_estimate’ is False</em> – On MLE without uncertainty, return NumPy array with calibrated confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).
-On VI or MCMC, return NumPy array with leading dimension as the number of sampled parameters from the
-log regression parameter distribution obtained by VI or MCMC.</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.variational">
-<code class="sig-name descname">variational</code><span class="sig-paren">(</span><em class="sig-param">data: torch.Tensor</em>, <em class="sig-param">y: torch.Tensor</em>, <em class="sig-param">tensorboard: bool</em>, <em class="sig-param">log_dir: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.scaling.TemperatureScaling.variational" title="Permalink to this definition">¶</a></dt>
-<dd><p>Perform variational inference using the guide.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data_input</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – NumPy 2-D array with data input.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>,</em><em>)</em>) – NumPy array with ground truth labels as 1-D vector (binary).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.scaling.TemperatureScaling.weights">
-<em class="property">property </em><code class="sig-name descname">weights</code><a class="headerlink" href="#netcal.scaling.TemperatureScaling.weights" title="Permalink to this definition">¶</a></dt>
-<dd><p>Getter for weights of logistic calibration.</p>
-</dd></dl>
-
-</dd></dl>
-
-</div>
+</section>
 
 
+                </div>
+              </div>
+            </div>
           </div>
         </div>
-      </div>
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-        <div class="sphinxsidebarwrapper">
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-<span id="netcal-binning"></span><h1>netcal.binning<a class="headerlink" href="#module-netcal.binning" title="Permalink to this headline">¶</a></h1>
-<p>Binning methods for confidence calibration.
-This package consists of several methods for confidence calibration which use binning to approximate
-confidence estimates to the measured accuracy.</p>
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+<li class="toctree-l2"><a class="reference internal" href="#binning-methods-for-confidence-calibration">Binning Methods for Confidence Calibration</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#available-classes">Available classes</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_binning/netcal.binning.HistogramBinning.html">netcal.binning.HistogramBinning</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_binning/netcal.binning.IsotonicRegression.html">netcal.binning.IsotonicRegression</a></li>
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+  <section id="module-netcal.binning">
+<span id="netcal-binning"></span><h1>netcal.binning<a class="headerlink" href="#module-netcal.binning" title="Permalink to this heading">¶</a></h1>
+<section id="binning-methods-for-confidence-calibration">
+<h2>Binning Methods for Confidence Calibration<a class="headerlink" href="#binning-methods-for-confidence-calibration" title="Permalink to this heading">¶</a></h2>
+<p>This package consists of several methods for confidence calibration which use binning to approximate
+confidence estimates to the measured accuracy. The most common calibration methods within this package
+are <em>netcal.binning.HistogramBinning</em> and <em>netcal.binning.IsotonicRegression</em>.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a>([bins, equal_intervals, …])</p></td>
-<td><p>Simple Histogram Binning calibration method <a href="#id5"><span class="problematic" id="id1">[1]_</span></a>.</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning" title="netcal.binning.HistogramBinning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">HistogramBinning</span></code></a>([bins, equal_intervals, ...])</p></td>
+<td><p>Simple Histogram Binning calibration method.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression" title="netcal.binning.IsotonicRegression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">IsotonicRegression</span></code></a>([detection, …])</p></td>
-<td><p>Isotonic Regression method <a href="#id6"><span class="problematic" id="id2">[1]_</span></a>.</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression" title="netcal.binning.IsotonicRegression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">IsotonicRegression</span></code></a>([detection, ...])</p></td>
+<td><p>Isotonic Regression method.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ" title="netcal.binning.BBQ"><code class="xref py py-obj docutils literal notranslate"><span class="pre">BBQ</span></code></a>([score_function, equal_intervals, …])</p></td>
-<td><p>Bayesian Binning into Quantiles (BBQ) <a href="#id7"><span class="problematic" id="id3">[1]_</span></a>.</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ" title="netcal.binning.BBQ"><code class="xref py py-obj docutils literal notranslate"><span class="pre">BBQ</span></code></a>([score_function, equal_intervals, ...])</p></td>
+<td><p>Bayesian Binning into Quantiles (BBQ).</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR" title="netcal.binning.ENIR"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ENIR</span></code></a>([score_function, quick_init, …])</p></td>
-<td><p>Ensemble of Near Isotonic Regression (ENIR) models <a href="#id8"><span class="problematic" id="id4">[1]_</span></a>.</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR" title="netcal.binning.ENIR"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ENIR</span></code></a>([score_function, quick_init, ...])</p></td>
+<td><p>Ensemble of Near Isotonic Regression (ENIR) models.</p></td>
 </tr>
 </tbody>
 </table>
-</div>
-</div>
+</section>
+</section>
 
 
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-  <div class="section" id="module-netcal.metrics">
-<span id="netcal-metrics"></span><h1>netcal.metrics<a class="headerlink" href="#module-netcal.metrics" title="Permalink to this headline">¶</a></h1>
-<p>Methods for measuring miscalibration. The common methods are given with the
-‘Average Calibration Error (ACE)’, ‘Expected Calibration Error (ECE)’ and ‘Maximum Calibration Error (MCE)’.
-Each methods bins the samples by their confidence and measures the accuracy in each bin. The ECE gives the
-mean gap between confidence and observed accuracy in each bin weighted by the number of samples.
-The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights each bin equally.</p>
-<div class="section" id="available-classes">
-<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this headline">¶</a></h2>
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+<h3><a href="../index.html">Table of Contents</a></h3>
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+<li class="toctree-l1 current"><a class="current reference internal" href="#">netcal.metrics</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#metrics-package-to-measure-miscalibration">Metrics Package to Measure Miscalibration</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#available-classes">Available classes</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.ACE.html">netcal.metrics.ACE</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.ECE.html">netcal.metrics.ECE</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.MCE.html">netcal.metrics.MCE</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.MMCE.html">netcal.metrics.MMCE</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.QuantileLoss.html">netcal.metrics.QuantileLoss</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.PinballLoss.html">netcal.metrics.PinballLoss</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.ENCE.html">netcal.metrics.ENCE</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.UCE.html">netcal.metrics.UCE</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.PICP.html">netcal.metrics.PICP</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric/netcal.metrics.QCE.html">netcal.metrics.QCE</a></li>
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+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric_submodules/netcal.metrics.confidence.html">netcal.metrics.confidence</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_metric_submodules/netcal.metrics.regression.html">netcal.metrics.regression</a></li>
+</ul>
+</li>
+</ul>
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+<li class="toctree-l1"><a class="reference internal" href="netcal.regression.html">netcal.regression</a></li>
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+<ul>
+<li class="toctree-l1"><a class="reference internal" href="../_autosummary_abstract_calibration/netcal.AbstractCalibration.html">netcal.AbstractCalibration</a></li>
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+                  
+  <section id="module-netcal.metrics">
+<span id="netcal-metrics"></span><h1>netcal.metrics<a class="headerlink" href="#module-netcal.metrics" title="Permalink to this heading">¶</a></h1>
+<section id="metrics-package-to-measure-miscalibration">
+<h2>Metrics Package to Measure Miscalibration<a class="headerlink" href="#metrics-package-to-measure-miscalibration" title="Permalink to this heading">¶</a></h2>
+<p>Methods for measuring miscalibration in the context of confidence calibration and regression uncertainty calibration.</p>
+<p>The common methods for confidence calibration evaluation are given with the
+<em>netcal.metrics.confidence.ECE</em> (ECE), <em>netcal.metrics.confidence.MCE</em> (MCE), and
+<em>netcal.metrics.confidence.ACE</em> (ACE). Each method bins the samples by their confidence and measures the
+accuracy in each bin. The ECE gives the mean gap between confidence and observed accuracy in each bin weighted by the
+number of samples. The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights
+each bin equally.</p>
+<p>The common methods for regression uncertainty evaluation are <em>netcal.metrics.regression.PinballLoss</em> (Pinball
+loss), the <em>netcal.metrics.regression.NLL</em> (NLL), and the <em>netcal.metrics.regression.QCE</em> (M-QCE and
+C-QCE). The Pinball loss as well as the Marginal/Conditional Quantile Calibration Error (M-QCE and C-QCE) evaluate
+the quality of the estimated quantiles compared to the observed ground-truth quantile coverage. The NLL is a proper
+scoring rule to measure the overall quality of the predicted probability distributions.</p>
+<p>For a detailed description of the available metrics within regression calibration, see the module doc of
+<em>netcal.regression</em>.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE" title="netcal.metrics.ACE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ACE</span></code></a>([bins, equal_intervals, detection, …])</p></td>
-<td><p>Average Calibration Error (ACE).</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE" title="netcal.metrics.ACE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ACE</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Average Calibration Error (ACE) for classification and Detection Average Calibration Error (D-ACE) for object detection or segmentation.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE" title="netcal.metrics.ECE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ECE</span></code></a>([bins, equal_intervals, detection, …])</p></td>
-<td><p>Expected Calibration Error (ECE).</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE" title="netcal.metrics.ECE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ECE</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Expected Calibration Error (ECE) for classification and Detection Expected Calibration Error (D-ECE) for object detection or segmentation.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE" title="netcal.metrics.MCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MCE</span></code></a>([bins, equal_intervals, detection, …])</p></td>
-<td><p>Maximum Calibration Error (MCE).</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE" title="netcal.metrics.MCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MCE</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Maximum Calibration Error (MCE) for classification and Detection Maximum Calibration Error (D-MCE) for object detection or segmentation.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.MMCE.html#netcal.metrics.MMCE" title="netcal.metrics.MMCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MMCE</span></code></a>([detection])</p></td>
-<td><p>Maximum Mean Calibration Error (MMCE) <a href="#id4"><span class="problematic" id="id1">[1]_</span></a>.</p></td>
+<td><p>Maximum Mean Calibration Error (MMCE).</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.QuantileLoss.html#netcal.metrics.QuantileLoss" title="netcal.metrics.QuantileLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QuantileLoss</span></code></a>()</p></td>
+<td><p>Pinball aka quantile loss within regression calibration to test for <em>quantile calibration</em> of a probabilistic regression model.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.PinballLoss.html#netcal.metrics.PinballLoss" title="netcal.metrics.PinballLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PinballLoss</span></code></a>()</p></td>
+<td><p>Synonym for Quantile loss.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP" title="netcal.metrics.PICP"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PICP</span></code></a>([bins, equal_intervals, detection, …])</p></td>
-<td><p>Compute Prediction Interval Coverage Probability (PICP) <a href="#id5"><span class="problematic" id="id2">[1]_</span></a>,[2]_ and Mean Prediction Interval Width (MPIW) <a href="#id6"><span class="problematic" id="id3">[2]_</span></a>.</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.ENCE.html#netcal.metrics.ENCE" title="netcal.metrics.ENCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ENCE</span></code></a>([bins, sample_threshold])</p></td>
+<td><p>Expected Normalized Calibration Error (ENCE) for a regression calibration evaluation to test for <em>variance calibration</em>.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.UCE.html#netcal.metrics.UCE" title="netcal.metrics.UCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UCE</span></code></a>([bins, sample_threshold])</p></td>
+<td><p>Uncertainty Calibration Error (UCE) for a regression calibration evaluation to test for <em>variance calibration</em>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP" title="netcal.metrics.PICP"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PICP</span></code></a>([bins, equal_intervals, detection, ...])</p></td>
+<td><p>Compute Prediction Interval Coverage Probability (PICP) and Mean Prediction Interval Width (MPIW).</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.QCE.html#netcal.metrics.QCE" title="netcal.metrics.QCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QCE</span></code></a>([bins, marginal, sample_threshold])</p></td>
+<td><p>Marginal Quantile Calibration Error (M-QCE) and Conditional Quantile Calibration Error (C-QCE) which both measure the gap between predicted quantiles and observed quantile coverage also for multivariate distributions.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric/netcal.metrics.NLL.html#netcal.metrics.NLL" title="netcal.metrics.NLL"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NLL</span></code></a>()</p></td>
+<td><p>Negative log likelihood (NLL) for probabilistic regression models.</p></td>
 </tr>
 </tbody>
 </table>
-</div>
-</div>
+</section>
+<section id="packages">
+<h2>Packages<a class="headerlink" href="#packages" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_metric_submodules/netcal.metrics.confidence.html#module-netcal.metrics.confidence" title="netcal.metrics.confidence"><code class="xref py py-obj docutils literal notranslate"><span class="pre">confidence</span></code></a></p></td>
+<td><p>Metrics for Confidence Calibration
+
+Methods for measuring miscalibration in the context of confidence calibration.
+
+The common methods for confidence calibration evaluation are given with the
+netcal.metrics.confidence.ECE (ECE), netcal.metrics.confidence.MCE (MCE), and
+netcal.metrics.confidence.ACE (ACE). Each method bins the samples by their confidence and measures the
+accuracy in each bin. The ECE gives the mean gap between confidence and observed accuracy in each bin weighted by the
+number of samples. The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights
+each bin equally.
+
+A further metric is the Maximum Mean Calibration Error (MMCE) which is a differentiable variant of the ECE that
+might also be used as a regularization technique during model training.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_metric_submodules/netcal.metrics.regression.html#module-netcal.metrics.regression" title="netcal.metrics.regression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">regression</span></code></a></p></td>
+<td><p>Metrics for Regression Uncertainty Calibration
+
+Methods for measuring miscalibration in the context of regression uncertainty calibration for probabilistic
+regression models.
+
+The common methods for regression uncertainty evaluation are netcal.metrics.regression.PinballLoss (Pinball
+loss), the netcal.metrics.regression.NLL (NLL), and the netcal.metrics.regression.QCE (M-QCE and
+C-QCE). The Pinball loss as well as the Marginal/Conditional Quantile Calibration Error (M-QCE and C-QCE) evaluate
+the quality of the estimated quantiles compared to the observed ground-truth quantile coverage. The NLL is a proper
+scoring rule to measure the overall quality of the predicted probability distributions.
 
+Further metrics are the netcal.metrics.regression.UCE (UCE) and the netcal.metrics.regression.ENCE
+(ENCE) which both apply a binning scheme over the predicted standard deviation/variance and test for variance
+calibration.
 
+For a detailed description of the available metrics within regression calibration, see the module doc of
+netcal.regression.</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+</section>
+
+
+                </div>
+              </div>
+            </div>
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-  <div class="section" id="module-netcal.presentation">
-<span id="netcal-presentation"></span><h1>netcal.presentation<a class="headerlink" href="#module-netcal.presentation" title="Permalink to this headline">¶</a></h1>
-<p>Methods for the visualization of miscalibration. This package consists of a Reliability Diagram method.
-This method bins similar to the ACE or ECE the samples in equally sized bins by their confidence and
+
+          </ul>
+
+        </div>
+      </div>
+    </div>
+    
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+<h3><a href="../index.html">Table of Contents</a></h3>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="netcal.binning.html">netcal.binning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="netcal.scaling.html">netcal.scaling</a></li>
+<li class="toctree-l1"><a class="reference internal" href="netcal.regularization.html">netcal.regularization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="netcal.metrics.html">netcal.metrics</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">netcal.presentation</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#visualization-package">Visualization Package</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#available-classes">Available classes</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html">netcal.presentation.ReliabilityDiagram</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_presentation/netcal.presentation.ReliabilityRegression.html">netcal.presentation.ReliabilityRegression</a></li>
+<li class="toctree-l3"><a class="reference internal" href="_autosummary_presentation/netcal.presentation.ReliabilityQCE.html">netcal.presentation.ReliabilityQCE</a></li>
+</ul>
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+</ul>
+<ul>
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+  <section id="module-netcal.presentation">
+<span id="netcal-presentation"></span><h1>netcal.presentation<a class="headerlink" href="#module-netcal.presentation" title="Permalink to this heading">¶</a></h1>
+<section id="visualization-package">
+<h2>Visualization Package<a class="headerlink" href="#visualization-package" title="Permalink to this heading">¶</a></h2>
+<p>Methods for the visualization of miscalibration in the scope of confidence calibration and regression uncertainty
+calibration.</p>
+<p>This package consists of a <em>netcal.presentation.ReliabilityDiagram</em> (Reliability Diagram) method used to
+visualize the calibration properties for confidence
+calibration in the scope of classification, object detection (semantic label confidence) or segmentation.
+Similar to the ACE or ECE, this method bins the samples in equally sized bins by their confidence and
 displays the gap between confidence and observed accuracy in each bin.</p>
-<div class="section" id="available-classes">
-<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this headline">¶</a></h2>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<p>For regression uncertainty calibration, this package also holds the <em>netcal.presentation.ReliabilityRegression</em>
+method that is able to visualize the quantile calibration properties of probabilistic regression models, e.g., within
+probabilistic regression or object detection (spatial position uncertainty).
+A complementary diagram is the <em>netcal.presentation.ReliabilityQCE</em> that visualizes the computation of the <em>netcal.metrics.regression.QCE</em> (C-QCE) metric.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html#netcal.presentation.ReliabilityDiagram" title="netcal.presentation.ReliabilityDiagram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ReliabilityDiagram</span></code></a>([bins, equal_intervals, …])</p></td>
-<td><p>Plot Confidence Histogram and Reliability Diagram to visualize miscalibration.</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html#netcal.presentation.ReliabilityDiagram" title="netcal.presentation.ReliabilityDiagram"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ReliabilityDiagram</span></code></a>([bins, equal_intervals, ...])</p></td>
+<td><p>Plot Confidence Histogram and Reliability Diagram to visualize miscalibration in the context of confidence calibration.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_presentation/netcal.presentation.ReliabilityRegression.html#netcal.presentation.ReliabilityRegression" title="netcal.presentation.ReliabilityRegression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ReliabilityRegression</span></code></a>([quantiles])</p></td>
+<td><p>Reliability diagram in the scope of regression calibration for probabilistic regression models.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_presentation/netcal.presentation.ReliabilityQCE.html#netcal.presentation.ReliabilityQCE" title="netcal.presentation.ReliabilityQCE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ReliabilityQCE</span></code></a>([bins])</p></td>
+<td><p>Visualizes the Conditional Quantile Calibration Error (C-QCE) in the scope of regression calibration as a bar chart for probabilistic regression models.</p></td>
 </tr>
 </tbody>
 </table>
-</div>
-</div>
+</section>
+</section>
 
 
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+<li class="toctree-l3"><a class="reference internal" href="#references">References</a></li>
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+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="#package-for-gaussian-process-optimization">Package for Gaussian process optimization</a><ul>
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+  <section id="module-netcal.regression">
+<span id="netcal-regression"></span><h1>netcal.regression<a class="headerlink" href="#module-netcal.regression" title="Permalink to this heading">¶</a></h1>
+<section id="probabilistic-regression-calibration-package">
+<h2>Probabilistic Regression Calibration Package<a class="headerlink" href="#probabilistic-regression-calibration-package" title="Permalink to this heading">¶</a></h2>
+<p>Methods for uncertainty calibration of probabilistic regression tasks.
+A probabilistic regression model does not only provide a continuous estimate but also an according uncertainty
+(commonly a Gaussian standard deviation/variance).
+The methods within this package are able to recalibrate this uncertainty by means of <em>quantile calibration</em> [1],
+<em>distribution calibration</em> [2], or <em>variance calibration</em> [3], [4].</p>
+<p><em>Quantile calibration</em> [1] requires that a predicted quantile for a quantile level <em>t</em> covers
+approx. <em>100t%</em> of the ground-truth samples.</p>
+<p>Methods for <em>quantile calibration</em>:</p>
+<ul class="simple">
+<li><p><em>IsotonicRegression</em> [1].</p></li>
+</ul>
+<p><em>Distribution calibration</em> [2] requires that a predicted probability distribution should be equal to the observed
+error distribution. This must hold for all statistical moments.</p>
+<p>Methods for <em>distribution calibration</em>:</p>
+<ul class="simple">
+<li><p><em>GPBeta</em> [2].</p></li>
+<li><p><em>GPNormal</em> [5].</p></li>
+<li><p><em>GPCauchy</em> [5].</p></li>
+</ul>
+<p><em>Variance calibration</em> [3], [4] requires that the predicted variance of a Gaussian distribution should match the
+observed error variance which is equivalent to the root mean squared error.</p>
+<p>Methods for <em>variance calibration</em>:</p>
+<ul class="simple">
+<li><p><em>VarianceScaling</em> [3], [4].</p></li>
+<li><p><em>GPNormal</em> [5].</p></li>
+</ul>
+<section id="references">
+<h3>References<a class="headerlink" href="#references" title="Permalink to this heading">¶</a></h3>
+<p>[1] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+“Accurate uncertainties for deep learning using calibrated regression.”
+International Conference on Machine Learning. PMLR, 2018.
+<a class="reference external" href="http://proceedings.mlr.press/v80/kuleshov18a/kuleshov18a.pdf">Get source online</a></p>
+<p>[2] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+“Distribution calibration for regression.”
+International Conference on Machine Learning. PMLR, 2019.
+<a class="reference external" href="http://proceedings.mlr.press/v97/song19a/song19a.pdf">Get source online</a></p>
+<p>[3] Levi, Dan, et al.:
+“Evaluating and calibrating uncertainty prediction in regression tasks.”
+arXiv preprint arXiv:1905.11659 (2019).
+<a class="reference external" href="https://arxiv.org/pdf/1905.11659.pdf">Get source online</a></p>
+<p>[4] Laves, Max-Heinrich, et al.:
+“Well-calibrated regression uncertainty in medical imaging with deep learning.”
+Medical Imaging with Deep Learning. PMLR, 2020.
+<a class="reference external" href="http://proceedings.mlr.press/v121/laves20a/laves20a.pdf">Get source online</a></p>
+<p>[5] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+“Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.”
+ArXiv preprint arXiv:2207.01242, 2022.
+<a class="reference external" href="https://arxiv.org/pdf/2207.01242.pdf">Get source online</a></p>
+</section>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression/netcal.regression.IsotonicRegression.html#netcal.regression.IsotonicRegression" title="netcal.regression.IsotonicRegression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">IsotonicRegression</span></code></a>()</p></td>
+<td><p>Isotonic regression calibration for probabilistic regression models with multiple independent output dimensions (optionally).</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regression/netcal.regression.VarianceScaling.html#netcal.regression.VarianceScaling" title="netcal.regression.VarianceScaling"><code class="xref py py-obj docutils literal notranslate"><span class="pre">VarianceScaling</span></code></a>()</p></td>
+<td><p>Variance recalibration using maximum likelihood estimation for multiple independent dimensions (optionally).</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression/netcal.regression.GPBeta.html#netcal.regression.GPBeta" title="netcal.regression.GPBeta"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GPBeta</span></code></a>([n_inducing_points, ...])</p></td>
+<td><p>GP-Beta recalibration method for regression uncertainty calibration using the well-known Beta calibration method from  classification calibration in combination with a Gaussian process (GP) parameter estimation.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regression/netcal.regression.GPNormal.html#netcal.regression.GPNormal" title="netcal.regression.GPNormal"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GPNormal</span></code></a>([n_inducing_points, ...])</p></td>
+<td><p>GP-Normal recalibration method for regression uncertainty calibration using a temperature scaling for the variance of a normal distribution but using the Gaussian process (GP) parameter estimation to adaptively obtain the scaling parameter for each input individually.</p></td>
+</tr>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression/netcal.regression.GPCauchy.html#netcal.regression.GPCauchy" title="netcal.regression.GPCauchy"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GPCauchy</span></code></a>([n_inducing_points, ...])</p></td>
+<td><p>GP-Cauchy recalibration method for regression uncertainty calibration that consumes an uncalibrated Gaussian distribution but converts it to a calibrated Cauchy distribution.</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+<section id="package-for-gaussian-process-optimization">
+<h2>Package for Gaussian process optimization<a class="headerlink" href="#package-for-gaussian-process-optimization" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
+<tbody>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regression_gp/netcal.regression.gp.html#module-netcal.regression.gp" title="netcal.regression.gp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">gp</span></code></a></p></td>
+<td><p>Regression GP Calibration Package
+
+This package provides the framework for all Gaussian Process (GP) recalibration schemes.
+These are GP-Beta [2], GP-Normal [3], and GP-Cauchy [3]. The goal of regression calibration using a GP scheme is to achieve
+distribution calibration, i.e., to match the predicted moments (mean, variance) to the true observed ones.
+In contrast to quantile calibration [1], where only the marginal calibration is of interest, the distribution calibration [2] is more
+restrictive. It requires that the predicted moments should match the observed ones given a certain probability
+distribution. Therefore, the authors in [2] propose to use Gaussian process to estimate the recalibration
+parameters of a Beta calibration function locally (i.e., matching the observed moments of neighboring samples).
+The GP-Normal and the GP-Cauchy follow the same principle but return parametric output distributions after calibration.
+
+References
+
+[1] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+&quot;Accurate uncertainties for deep learning using calibrated regression.&quot;
+International Conference on Machine Learning. PMLR, 2018.
+Get source online
+
+[2] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+&quot;Distribution calibration for regression.&quot;
+International Conference on Machine Learning. PMLR, 2019.
+Get source online
+
+[3] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+&quot;Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.&quot;
+ArXiv preprint arXiv:2207.01242, 2022.
+Get source online</p></td>
+</tr>
+</tbody>
+</table>
+</section>
+</section>
+
+
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+  <section id="module-netcal.regularization">
+<span id="netcal-regularization"></span><h1>netcal.regularization<a class="headerlink" href="#module-netcal.regularization" title="Permalink to this heading">¶</a></h1>
+<section id="regularization-methods-for-confidence-calibration">
+<h2>Regularization Methods for Confidence Calibration<a class="headerlink" href="#regularization-methods-for-confidence-calibration" title="Permalink to this heading">¶</a></h2>
 <p>Regularization methods which are applied during model training. These methods should achieve a
 confidence calibration during model training. For example, the Confidence Penalty
 penalizes confident predictions and prohibits over-confident estimates.
 Use the functions to obtain the regularization and callback instances with prebuild parameters.</p>
-<div class="section" id="available-functions">
-<h2>Available functions<a class="headerlink" href="#available-functions" title="Permalink to this headline">¶</a></h2>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+</section>
+<section id="available-functions">
+<h2>Available functions<a class="headerlink" href="#available-functions" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regularization_func/netcal.regularization.confidence_penalty.html#netcal.regularization.confidence_penalty" title="netcal.regularization.confidence_penalty"><code class="xref py py-obj docutils literal notranslate"><span class="pre">confidence_penalty</span></code></a>(X, weight[, threshold, base])</p></td>
 <td><p>Confidence Penalty Regularization.</p></td>
@@ -65,78 +197,53 @@ <h2>Available functions<a class="headerlink" href="#available-functions" title="
 <td><p>Confidence penalty regularization implementation for PyTorch.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty" title="netcal.regularization.MMCEPenalty"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MMCEPenalty</span></code></a>([weight])</p></td>
-<td><p>Maximum mean calibration error (MMCE) <a href="#id3"><span class="problematic" id="id1">[1]_</span></a>.</p></td>
+<td><p>Maximum mean calibration error (MMCE).</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty" title="netcal.regularization.DCAPenalty"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DCAPenalty</span></code></a>([weight])</p></td>
-<td><p>Difference between Confidence and Accuracy (DCA) <a href="#id4"><span class="problematic" id="id2">[1]_</span></a>.</p></td>
+<td><p>Difference between Confidence and Accuracy (DCA).</p></td>
 </tr>
 </tbody>
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-  <div class="section" id="module-netcal.scaling">
-<span id="netcal-scaling"></span><h1>netcal.scaling<a class="headerlink" href="#module-netcal.scaling" title="Permalink to this headline">¶</a></h1>
-<p>Scaling methods for confidence calibration.
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+<li class="toctree-l3"><a class="reference internal" href="_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html">netcal.scaling.BetaCalibrationDependent</a></li>
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+  <section id="module-netcal.scaling">
+<span id="netcal-scaling"></span><h1>netcal.scaling<a class="headerlink" href="#module-netcal.scaling" title="Permalink to this heading">¶</a></h1>
+<section id="scaling-methods-for-confidence-calibration">
+<h2>Scaling Methods for Confidence Calibration<a class="headerlink" href="#scaling-methods-for-confidence-calibration" title="Permalink to this heading">¶</a></h2>
+<p>This package consists of several methods for confidence calibration which use confidence scaling to approximate
+confidence estimates to observed accuracy. The most common scaling methods are
+<em>netcal.scaling.TemperatureScaling</em>, <em>netcal.scaling.LogisticCalibration</em>, and <em>netcal.scaling.BetaCalibration</em>.
+Note that all methods can also be applied to object detection and are capable of additional influenting factors
+such as object position and/or shape.
+The advanced methods <em>netcal.scaling.LogisticCalibrationDependent</em> and <em>netcal.scaling.BetaCalibrationDependent</em>
+are able to better represent possible correlations as the underlying probability distributions are joint
+multivariate distributions with possible correlations.</p>
+</section>
+<section id="available-classes">
+<h2>Available classes<a class="headerlink" href="#available-classes" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>([method, …])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression" title="netcal.scaling.AbstractLogisticRegression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AbstractLogisticRegression</span></code></a>([method, ...])</p></td>
 <td><p>Abstract class for all calibration methods that base on logistic regression.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration" title="netcal.scaling.LogisticCalibration"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LogisticCalibration</span></code></a>(*args[, temperature_only])</p></td>
@@ -67,7 +206,7 @@ <h2>Available classes<a class="headerlink" href="#available-classes" title="Perm
 <td><p>This calibration method is for detection only and uses multivariate normal distributions to obtain a calibration mapping by means of the confidence as well as additional features.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling" title="netcal.scaling.TemperatureScaling"><code class="xref py py-obj docutils literal notranslate"><span class="pre">TemperatureScaling</span></code></a>(*args, **kwargs)</p></td>
-<td><p>On classification or detection, apply the temperature scaling method described in <a href="#id2"><span class="problematic" id="id1">[1]_</span></a> to obtain a calibration mapping.</p></td>
+<td><p>On classification or detection, apply the temperature scaling method to obtain a calibration mapping.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration" title="netcal.scaling.BetaCalibration"><code class="xref py py-obj docutils literal notranslate"><span class="pre">BetaCalibration</span></code></a>(*args, **kwargs)</p></td>
 <td><p>On classification, apply the beta calibration method to obtain a calibration mapping.</p></td>
@@ -77,71 +216,46 @@ <h2>Available classes<a class="headerlink" href="#available-classes" title="Perm
 </tr>
 </tbody>
 </table>
-</div>
-</div>
+</section>
+</section>
 
 
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-  <div class="section" id="netcal-abstractcalibration">
-<h1>netcal.AbstractCalibration<a class="headerlink" href="#netcal-abstractcalibration" title="Permalink to this headline">¶</a></h1>
-<dl class="class">
-<dt id="netcal.AbstractCalibration">
-<em class="property">class </em><code class="sig-prename descclassname">netcal.</code><code class="sig-name descname">AbstractCalibration</code><span class="sig-paren">(</span><em class="sig-param">detection: bool = False</em>, <em class="sig-param">independent_probabilities: bool = False</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.AbstractCalibration" title="Permalink to this definition">¶</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.base.BaseEstimator</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.base.TransformerMixin</span></code></p>
-<p>Abstract base class for all calibration methods.
+              <li><a href="../_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.CauchyLikelihood.html" title="netcal.regression.gp.likelihood.CauchyLikelihood" accesskey="P">previous </a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../_autosummary/netcal.scaling.html">netcal.scaling</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../_autosummary/netcal.regularization.html">netcal.regularization</a></li>
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+<ul class="current">
+<li class="toctree-l1 current"><a class="current reference internal" href="#">netcal.AbstractCalibration</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#netcal.AbstractCalibration"><code class="docutils literal notranslate"><span class="pre">AbstractCalibration</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#netcal.AbstractCalibration.epsilon"><code class="docutils literal notranslate"><span class="pre">AbstractCalibration.epsilon</span></code></a></li>
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+  <section id="netcal-abstractcalibration">
+<h1>netcal.AbstractCalibration<a class="headerlink" href="#netcal-abstractcalibration" title="Permalink to this heading">¶</a></h1>
+<dl class="py class">
+<dt class="sig sig-object py" id="netcal.AbstractCalibration">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">netcal.</span></span><span class="sig-name descname"><span class="pre">AbstractCalibration</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">detection</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">independent_probabilities</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.AbstractCalibration" title="Permalink to this definition">¶</a></dt>
+<dd><p>Abstract base class for all calibration methods.
 Inherits functions from sklearn’s BaseEstimator.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>detection</strong> (<em>bool</em><em>, </em><em>default: False</em>) – If False, the input array ‘X’ is treated as multi-class confidence input (softmax)
 with shape (n_samples, [n_classes]).
@@ -61,24 +193,20 @@ <h1>netcal.AbstractCalibration<a class="headerlink" href="#netcal-abstractcalibr
 </ul>
 </dd>
 </dl>
-<dl class="attribute">
-<dt id="netcal.AbstractCalibration.epsilon">
-<code class="sig-name descname">epsilon</code><a class="headerlink" href="#netcal.AbstractCalibration.epsilon" title="Permalink to this definition">¶</a></dt>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="netcal.AbstractCalibration.epsilon">
+<span class="sig-name descname"><span class="pre">epsilon</span></span><a class="headerlink" href="#netcal.AbstractCalibration.epsilon" title="Permalink to this definition">¶</a></dt>
 <dd><p>Lowest possible digit that can be computed. Needed for several operations like divisions or log to guarantee
 values inequal to 0 or 1.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Type</dt>
+<dt class="field-odd">Type<span class="colon">:</span></dt>
 <dd class="field-odd"><p>float</p>
 </dd>
 </dl>
 </dd></dl>
 
 <p class="rubric">Methods</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>([detection, independent_probabilities])</p></td>
 <td><p>Create an instance of <cite>AbstractCalibration</cite>.</p></td>
@@ -99,249 +227,56 @@ <h1>netcal.AbstractCalibration<a class="headerlink" href="#netcal-abstractcalibr
 <td><p>Load model from saved torch dump.</p></td>
 </tr>
 <tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">save_model</span></code>(filename)</p></td>
-<td><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p></td>
+<td><p>Save model instance as with torch's save function as this is safer for torch tensors.</p></td>
 </tr>
 <tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code>(**params)</p></td>
 <td><p>Set the parameters of this estimator.</p></td>
 </tr>
-<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">squeeze_generic</span></code>(a, axes_to_keep)</p></td>
-<td><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is of size 1.</p></td>
-</tr>
-<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
+<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code>(X)</p></td>
 <td><p>Abstract function.</p></td>
 </tr>
 </tbody>
 </table>
-<dl class="method">
-<dt id="netcal.AbstractCalibration.clear">
-<em class="property">abstract </em><code class="sig-name descname">clear</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#netcal.AbstractCalibration.clear" title="Permalink to this definition">¶</a></dt>
-<dd><p>Clear model parameters.</p>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.AbstractCalibration.fit">
-<em class="property">abstract </em><code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em>, <em class="sig-param">y: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; Tuple[numpy.ndarray, numpy.ndarray]<a class="headerlink" href="#netcal.AbstractCalibration.fit" title="Permalink to this definition">¶</a></dt>
-<dd><p>Abstract function call to build the calibration model.
-This function performs several checks and returns the improved X and y.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p></li>
-<li><p><strong>y</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>)</em>) – NumPy array with ground truth labels.
-Either as label vector (1-D) or as one-hot encoded ground truth array (2-D).</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Checked and converted X and y.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>tuple</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>AttributeError</strong> – <ul class="simple">
-<li><p>If ‘X’ has more than 2 dimensions
-    - If ‘y’ has more than 2 dimensions
-    - If ‘y’ as one-hot encoded ground truth does not match to detected number of classes</p></li>
-</ul>
-</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.AbstractCalibration.fit_transform">
-<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.AbstractCalibration.fit_transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Fit to data, then transform it.</p>
-<p>Fits transformer to X and y with optional parameters fit_params
-and returns a transformed version of X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>X</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training set.</p></li>
-<li><p><strong>y</strong> (<em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Target values.</p></li>
-<li><p><strong>**fit_params</strong> (<em>dict</em>) – Additional fit parameters.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>X_new</strong> – Transformed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>numpy array of shape [n_samples, n_features_new]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.AbstractCalibration.get_params">
-<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.AbstractCalibration.get_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Get parameters for this estimator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>deep</strong> (<em>boolean</em><em>, </em><em>optional</em>) – If True, will return the parameters for this estimator and
-contained subobjects that are estimators.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p><strong>params</strong> – Parameter names mapped to their values.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>mapping of string to any</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.AbstractCalibration.load_model">
-<code class="sig-name descname">load_model</code><span class="sig-paren">(</span><em class="sig-param">filename</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.AbstractCalibration.load_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Load model from saved torch dump.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Instance of a child class of <cite>AbstractCalibration</cite>.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p><a class="reference internal" href="#netcal.AbstractCalibration" title="netcal.AbstractCalibration">AbstractCalibration</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.AbstractCalibration.save_model">
-<code class="sig-name descname">save_model</code><span class="sig-paren">(</span><em class="sig-param">filename: str</em><span class="sig-paren">)</span><a class="headerlink" href="#netcal.AbstractCalibration.save_model" title="Permalink to this definition">¶</a></dt>
-<dd><p>Save model instance as with torch’s save function as this is safer for torch tensors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>filename</strong> (<em>str</em>) – String with filename.</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.AbstractCalibration.set_params">
-<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">**params</em><span class="sig-paren">)</span> &#x2192; netcal.AbstractCalibration.AbstractCalibration<a class="headerlink" href="#netcal.AbstractCalibration.set_params" title="Permalink to this definition">¶</a></dt>
-<dd><p>Set the parameters of this estimator.</p>
-<p>The method works on simple estimators as well as on nested objects
-(such as pipelines). The latter have parameters of the form
-<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
-component of a nested object.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
-<dd class="field-odd"><p></p>
-</dd>
-<dt class="field-even">Return type</dt>
-<dd class="field-even"><p>self</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="method">
-<dt id="netcal.AbstractCalibration.squeeze_generic">
-<em class="property">classmethod </em><code class="sig-name descname">squeeze_generic</code><span class="sig-paren">(</span><em class="sig-param">a: numpy.ndarray, axes_to_keep: Union[int, Iterable[int]]</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.AbstractCalibration.squeeze_generic" title="Permalink to this definition">¶</a></dt>
-<dd><p>Squeeze input array a but keep axes defined by parameter ‘axes_to_keep’ even if the dimension is
-of size 1.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<em>np.ndarray</em>) – NumPy array that should be squeezed.</p></li>
-<li><p><strong>axes_to_keep</strong> (<em>int</em><em> or </em><em>iterable</em>) – Axes that should be kept even if they have a size of 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>Squeezed array.</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray</p>
-</dd>
-</dl>
 </dd></dl>
 
-<dl class="method">
-<dt id="netcal.AbstractCalibration.transform">
-<em class="property">abstract </em><code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">X: numpy.ndarray</em><span class="sig-paren">)</span> &#x2192; numpy.ndarray<a class="headerlink" href="#netcal.AbstractCalibration.transform" title="Permalink to this definition">¶</a></dt>
-<dd><p>Abstract function. After model calibration, this function is used to get calibrated outputs of uncalibrated
-confidence estimates.
-This function performs several checks and returns the improved X.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
-<dd class="field-odd"><p><strong>X</strong> (<em>np.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_classes</em><em>]</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>[</em><em>n_box_features</em><em>]</em><em>)</em>) – NumPy array with confidence values for each prediction on classification with shapes
-1-D for binary classification, 2-D for multi class (softmax).
-On detection, this array must have 2 dimensions with number of additional box features in last dim.</p>
-</dd>
-<dt class="field-even">Returns</dt>
-<dd class="field-even"><p>NumPy array with uncalibrated but checked confidence estimates.
-1-D for binary classification, 2-D for multi class (softmax).</p>
-</dd>
-<dt class="field-odd">Return type</dt>
-<dd class="field-odd"><p>np.ndarray, shape=(n_samples, [n_classes])</p>
-</dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><ul class="simple">
-<li><p><strong>RuntimeError</strong> – If method is called before ‘fit’.</p></li>
-<li><p><strong>AttributeError</strong> – <ul>
-<li><p>If model was built for multi class but 2nd dimension of ‘X’ does not match to number of classes.
-    - If ‘X’ has more than 2 dimensions</p></li>
-</ul>
-</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-</div>
+</section>
 
 
+                </div>
+              </div>
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diff --git a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.BBQ.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.BBQ.rst.txt
index 922c214..7472d94 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.BBQ.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.BBQ.rst.txt
@@ -20,7 +20,6 @@ netcal.binning.BBQ
       ~BBQ.load_model
       ~BBQ.save_model
       ~BBQ.set_params
-      ~BBQ.squeeze_generic
       ~BBQ.transform
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.ENIR.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.ENIR.rst.txt
index 7df5db2..73f0187 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.ENIR.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.ENIR.rst.txt
@@ -20,7 +20,6 @@ netcal.binning.ENIR
       ~ENIR.load_model
       ~ENIR.save_model
       ~ENIR.set_params
-      ~ENIR.squeeze_generic
       ~ENIR.transform
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.rst.txt
index fa4b86d..9ec7a3b 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.rst.txt
@@ -21,7 +21,6 @@ netcal.binning.HistogramBinning
       ~HistogramBinning.load_model
       ~HistogramBinning.save_model
       ~HistogramBinning.set_params
-      ~HistogramBinning.squeeze_generic
       ~HistogramBinning.transform
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.rst.txt
index 7fe4da8..25cea4e 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.rst.txt
@@ -20,7 +20,6 @@ netcal.binning.IsotonicRegression
       ~IsotonicRegression.load_model
       ~IsotonicRegression.save_model
       ~IsotonicRegression.set_params
-      ~IsotonicRegression.squeeze_generic
       ~IsotonicRegression.transform
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ACE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ACE.rst.txt
index 9e2f3d5..098d408 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ACE.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ACE.rst.txt
@@ -14,10 +14,10 @@ netcal.metrics.ACE
    
       ~ACE.__init__
       ~ACE.binning
+      ~ACE.frequency
       ~ACE.measure
       ~ACE.prepare
       ~ACE.process
       ~ACE.reduce
-      ~ACE.squeeze_generic
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ECE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ECE.rst.txt
index d9344b3..51bddb2 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ECE.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ECE.rst.txt
@@ -14,10 +14,10 @@ netcal.metrics.ECE
    
       ~ECE.__init__
       ~ECE.binning
+      ~ECE.frequency
       ~ECE.measure
       ~ECE.prepare
       ~ECE.process
       ~ECE.reduce
-      ~ECE.squeeze_generic
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ENCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ENCE.rst.txt
new file mode 100644
index 0000000..783aadb
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.ENCE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.ENCE
+===================
+
+.. currentmodule:: netcal.metrics
+
+.. autoclass:: ENCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ENCE.__init__
+      ~ENCE.binning
+      ~ENCE.frequency
+      ~ENCE.measure
+      ~ENCE.prepare
+      ~ENCE.process
+      ~ENCE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.MCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.MCE.rst.txt
index f2a508a..c289630 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.MCE.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.MCE.rst.txt
@@ -14,10 +14,10 @@ netcal.metrics.MCE
    
       ~MCE.__init__
       ~MCE.binning
+      ~MCE.frequency
       ~MCE.measure
       ~MCE.prepare
       ~MCE.process
       ~MCE.reduce
-      ~MCE.squeeze_generic
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.NLL.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.NLL.rst.txt
new file mode 100644
index 0000000..f479ac8
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.NLL.rst.txt
@@ -0,0 +1,18 @@
+netcal.metrics.NLL
+==================
+
+.. currentmodule:: netcal.metrics
+
+.. autoclass:: NLL
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~NLL.__init__
+      ~NLL.measure
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.PICP.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.PICP.rst.txt
index a369dcd..5f87553 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.PICP.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.PICP.rst.txt
@@ -13,12 +13,11 @@ netcal.metrics.PICP
    .. autosummary::
    
       ~PICP.__init__
-      ~PICP.accuracy
       ~PICP.binning
+      ~PICP.frequency
       ~PICP.measure
       ~PICP.prepare
       ~PICP.process
       ~PICP.reduce
-      ~PICP.squeeze_generic
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.PinballLoss.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.PinballLoss.rst.txt
new file mode 100644
index 0000000..6b064d9
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.PinballLoss.rst.txt
@@ -0,0 +1,18 @@
+netcal.metrics.PinballLoss
+==========================
+
+.. currentmodule:: netcal.metrics
+
+.. autoclass:: PinballLoss
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~PinballLoss.__init__
+      ~PinballLoss.measure
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.QCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.QCE.rst.txt
new file mode 100644
index 0000000..604137f
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.QCE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.QCE
+==================
+
+.. currentmodule:: netcal.metrics
+
+.. autoclass:: QCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~QCE.__init__
+      ~QCE.binning
+      ~QCE.frequency
+      ~QCE.measure
+      ~QCE.prepare
+      ~QCE.process
+      ~QCE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.QuantileLoss.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.QuantileLoss.rst.txt
new file mode 100644
index 0000000..e66dc63
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.QuantileLoss.rst.txt
@@ -0,0 +1,18 @@
+netcal.metrics.QuantileLoss
+===========================
+
+.. currentmodule:: netcal.metrics
+
+.. autoclass:: QuantileLoss
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~QuantileLoss.__init__
+      ~QuantileLoss.measure
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.UCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.UCE.rst.txt
new file mode 100644
index 0000000..276919b
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric/netcal.metrics.UCE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.UCE
+==================
+
+.. currentmodule:: netcal.metrics
+
+.. autoclass:: UCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~UCE.__init__
+      ~UCE.binning
+      ~UCE.frequency
+      ~UCE.measure
+      ~UCE.prepare
+      ~UCE.process
+      ~UCE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ACE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ACE.rst.txt
new file mode 100644
index 0000000..ab7a86b
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ACE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.confidence.ACE
+=============================
+
+.. currentmodule:: netcal.metrics.confidence
+
+.. autoclass:: ACE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ACE.__init__
+      ~ACE.binning
+      ~ACE.frequency
+      ~ACE.measure
+      ~ACE.prepare
+      ~ACE.process
+      ~ACE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.rst.txt
new file mode 100644
index 0000000..5f4136c
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.confidence.ECE
+=============================
+
+.. currentmodule:: netcal.metrics.confidence
+
+.. autoclass:: ECE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ECE.__init__
+      ~ECE.binning
+      ~ECE.frequency
+      ~ECE.measure
+      ~ECE.prepare
+      ~ECE.process
+      ~ECE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MCE.rst.txt
new file mode 100644
index 0000000..03ce28d
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MCE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.confidence.MCE
+=============================
+
+.. currentmodule:: netcal.metrics.confidence
+
+.. autoclass:: MCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~MCE.__init__
+      ~MCE.binning
+      ~MCE.frequency
+      ~MCE.measure
+      ~MCE.prepare
+      ~MCE.process
+      ~MCE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MMCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MMCE.rst.txt
new file mode 100644
index 0000000..7b3e174
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MMCE.rst.txt
@@ -0,0 +1,18 @@
+netcal.metrics.confidence.MMCE
+==============================
+
+.. currentmodule:: netcal.metrics.confidence
+
+.. autoclass:: MMCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~MMCE.__init__
+      ~MMCE.measure
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.ENCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.ENCE.rst.txt
new file mode 100644
index 0000000..0160905
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.ENCE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.regression.ENCE
+==============================
+
+.. currentmodule:: netcal.metrics.regression
+
+.. autoclass:: ENCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ENCE.__init__
+      ~ENCE.binning
+      ~ENCE.frequency
+      ~ENCE.measure
+      ~ENCE.prepare
+      ~ENCE.process
+      ~ENCE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.NLL.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.NLL.rst.txt
new file mode 100644
index 0000000..5b84062
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.NLL.rst.txt
@@ -0,0 +1,18 @@
+netcal.metrics.regression.NLL
+=============================
+
+.. currentmodule:: netcal.metrics.regression
+
+.. autoclass:: NLL
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~NLL.__init__
+      ~NLL.measure
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PICP.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PICP.rst.txt
new file mode 100644
index 0000000..5bfb600
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PICP.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.regression.PICP
+==============================
+
+.. currentmodule:: netcal.metrics.regression
+
+.. autoclass:: PICP
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~PICP.__init__
+      ~PICP.binning
+      ~PICP.frequency
+      ~PICP.measure
+      ~PICP.prepare
+      ~PICP.process
+      ~PICP.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PinballLoss.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PinballLoss.rst.txt
new file mode 100644
index 0000000..9938631
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PinballLoss.rst.txt
@@ -0,0 +1,18 @@
+netcal.metrics.regression.PinballLoss
+=====================================
+
+.. currentmodule:: netcal.metrics.regression
+
+.. autoclass:: PinballLoss
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~PinballLoss.__init__
+      ~PinballLoss.measure
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QCE.rst.txt
new file mode 100644
index 0000000..d0b453d
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QCE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.regression.QCE
+=============================
+
+.. currentmodule:: netcal.metrics.regression
+
+.. autoclass:: QCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~QCE.__init__
+      ~QCE.binning
+      ~QCE.frequency
+      ~QCE.measure
+      ~QCE.prepare
+      ~QCE.process
+      ~QCE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QuantileLoss.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QuantileLoss.rst.txt
new file mode 100644
index 0000000..4cf060b
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QuantileLoss.rst.txt
@@ -0,0 +1,18 @@
+netcal.metrics.regression.QuantileLoss
+======================================
+
+.. currentmodule:: netcal.metrics.regression
+
+.. autoclass:: QuantileLoss
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~QuantileLoss.__init__
+      ~QuantileLoss.measure
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.UCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.UCE.rst.txt
new file mode 100644
index 0000000..341c8da
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.UCE.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.regression.UCE
+=============================
+
+.. currentmodule:: netcal.metrics.regression
+
+.. autoclass:: UCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~UCE.__init__
+      ~UCE.binning
+      ~UCE.frequency
+      ~UCE.measure
+      ~UCE.prepare
+      ~UCE.process
+      ~UCE.reduce
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/netcal.metrics.confidence.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/netcal.metrics.confidence.rst.txt
new file mode 100644
index 0000000..facff71
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/netcal.metrics.confidence.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.confidence
+=========================
+
+.. automodule:: netcal.metrics.confidence
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.rst.txt
new file mode 100644
index 0000000..afa6dd8
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.rst.txt
@@ -0,0 +1,23 @@
+netcal.metrics.regression
+=========================
+
+.. automodule:: netcal.metrics.regression
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityQCE.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityQCE.rst.txt
new file mode 100644
index 0000000..5979157
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityQCE.rst.txt
@@ -0,0 +1,18 @@
+netcal.presentation.ReliabilityQCE
+==================================
+
+.. currentmodule:: netcal.presentation
+
+.. autoclass:: ReliabilityQCE
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ReliabilityQCE.__init__
+      ~ReliabilityQCE.plot
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityRegression.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityRegression.rst.txt
new file mode 100644
index 0000000..16df9f6
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityRegression.rst.txt
@@ -0,0 +1,18 @@
+netcal.presentation.ReliabilityRegression
+=========================================
+
+.. currentmodule:: netcal.presentation
+
+.. autoclass:: ReliabilityRegression
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ReliabilityRegression.__init__
+      ~ReliabilityRegression.plot
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPBeta.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPBeta.rst.txt
new file mode 100644
index 0000000..880990e
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPBeta.rst.txt
@@ -0,0 +1,95 @@
+netcal.regression.GPBeta
+========================
+
+.. currentmodule:: netcal.regression
+
+.. autoclass:: GPBeta
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~GPBeta.__init__
+      ~GPBeta.add_module
+      ~GPBeta.added_loss_terms
+      ~GPBeta.apply
+      ~GPBeta.bfloat16
+      ~GPBeta.buffers
+      ~GPBeta.children
+      ~GPBeta.clear
+      ~GPBeta.constraint_for_parameter_name
+      ~GPBeta.constraints
+      ~GPBeta.cpu
+      ~GPBeta.cuda
+      ~GPBeta.double
+      ~GPBeta.eval
+      ~GPBeta.extra_repr
+      ~GPBeta.fit
+      ~GPBeta.fit_transform
+      ~GPBeta.float
+      ~GPBeta.forward
+      ~GPBeta.get_buffer
+      ~GPBeta.get_extra_state
+      ~GPBeta.get_fantasy_model
+      ~GPBeta.get_parameter
+      ~GPBeta.get_params
+      ~GPBeta.get_submodule
+      ~GPBeta.guide
+      ~GPBeta.half
+      ~GPBeta.hyperparameters
+      ~GPBeta.initialize
+      ~GPBeta.ipu
+      ~GPBeta.load_model
+      ~GPBeta.load_state_dict
+      ~GPBeta.load_strict_shapes
+      ~GPBeta.local_load_samples
+      ~GPBeta.model
+      ~GPBeta.modules
+      ~GPBeta.named_added_loss_terms
+      ~GPBeta.named_buffers
+      ~GPBeta.named_children
+      ~GPBeta.named_constraints
+      ~GPBeta.named_hyperparameters
+      ~GPBeta.named_modules
+      ~GPBeta.named_parameters
+      ~GPBeta.named_parameters_and_constraints
+      ~GPBeta.named_priors
+      ~GPBeta.named_variational_parameters
+      ~GPBeta.parameters
+      ~GPBeta.pyro_guide
+      ~GPBeta.pyro_load_from_samples
+      ~GPBeta.pyro_model
+      ~GPBeta.pyro_sample_from_prior
+      ~GPBeta.register_added_loss_term
+      ~GPBeta.register_backward_hook
+      ~GPBeta.register_buffer
+      ~GPBeta.register_constraint
+      ~GPBeta.register_forward_hook
+      ~GPBeta.register_forward_pre_hook
+      ~GPBeta.register_full_backward_hook
+      ~GPBeta.register_load_state_dict_post_hook
+      ~GPBeta.register_module
+      ~GPBeta.register_parameter
+      ~GPBeta.register_prior
+      ~GPBeta.requires_grad_
+      ~GPBeta.sample_from_prior
+      ~GPBeta.save_model
+      ~GPBeta.set_extra_state
+      ~GPBeta.set_params
+      ~GPBeta.share_memory
+      ~GPBeta.state_dict
+      ~GPBeta.to
+      ~GPBeta.to_empty
+      ~GPBeta.to_pyro_random_module
+      ~GPBeta.train
+      ~GPBeta.transform
+      ~GPBeta.type
+      ~GPBeta.update_added_loss_term
+      ~GPBeta.variational_parameters
+      ~GPBeta.xpu
+      ~GPBeta.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPCauchy.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPCauchy.rst.txt
new file mode 100644
index 0000000..5479f1a
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPCauchy.rst.txt
@@ -0,0 +1,95 @@
+netcal.regression.GPCauchy
+==========================
+
+.. currentmodule:: netcal.regression
+
+.. autoclass:: GPCauchy
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~GPCauchy.__init__
+      ~GPCauchy.add_module
+      ~GPCauchy.added_loss_terms
+      ~GPCauchy.apply
+      ~GPCauchy.bfloat16
+      ~GPCauchy.buffers
+      ~GPCauchy.children
+      ~GPCauchy.clear
+      ~GPCauchy.constraint_for_parameter_name
+      ~GPCauchy.constraints
+      ~GPCauchy.cpu
+      ~GPCauchy.cuda
+      ~GPCauchy.double
+      ~GPCauchy.eval
+      ~GPCauchy.extra_repr
+      ~GPCauchy.fit
+      ~GPCauchy.fit_transform
+      ~GPCauchy.float
+      ~GPCauchy.forward
+      ~GPCauchy.get_buffer
+      ~GPCauchy.get_extra_state
+      ~GPCauchy.get_fantasy_model
+      ~GPCauchy.get_parameter
+      ~GPCauchy.get_params
+      ~GPCauchy.get_submodule
+      ~GPCauchy.guide
+      ~GPCauchy.half
+      ~GPCauchy.hyperparameters
+      ~GPCauchy.initialize
+      ~GPCauchy.ipu
+      ~GPCauchy.load_model
+      ~GPCauchy.load_state_dict
+      ~GPCauchy.load_strict_shapes
+      ~GPCauchy.local_load_samples
+      ~GPCauchy.model
+      ~GPCauchy.modules
+      ~GPCauchy.named_added_loss_terms
+      ~GPCauchy.named_buffers
+      ~GPCauchy.named_children
+      ~GPCauchy.named_constraints
+      ~GPCauchy.named_hyperparameters
+      ~GPCauchy.named_modules
+      ~GPCauchy.named_parameters
+      ~GPCauchy.named_parameters_and_constraints
+      ~GPCauchy.named_priors
+      ~GPCauchy.named_variational_parameters
+      ~GPCauchy.parameters
+      ~GPCauchy.pyro_guide
+      ~GPCauchy.pyro_load_from_samples
+      ~GPCauchy.pyro_model
+      ~GPCauchy.pyro_sample_from_prior
+      ~GPCauchy.register_added_loss_term
+      ~GPCauchy.register_backward_hook
+      ~GPCauchy.register_buffer
+      ~GPCauchy.register_constraint
+      ~GPCauchy.register_forward_hook
+      ~GPCauchy.register_forward_pre_hook
+      ~GPCauchy.register_full_backward_hook
+      ~GPCauchy.register_load_state_dict_post_hook
+      ~GPCauchy.register_module
+      ~GPCauchy.register_parameter
+      ~GPCauchy.register_prior
+      ~GPCauchy.requires_grad_
+      ~GPCauchy.sample_from_prior
+      ~GPCauchy.save_model
+      ~GPCauchy.set_extra_state
+      ~GPCauchy.set_params
+      ~GPCauchy.share_memory
+      ~GPCauchy.state_dict
+      ~GPCauchy.to
+      ~GPCauchy.to_empty
+      ~GPCauchy.to_pyro_random_module
+      ~GPCauchy.train
+      ~GPCauchy.transform
+      ~GPCauchy.type
+      ~GPCauchy.update_added_loss_term
+      ~GPCauchy.variational_parameters
+      ~GPCauchy.xpu
+      ~GPCauchy.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPNormal.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPNormal.rst.txt
new file mode 100644
index 0000000..97f6c80
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.GPNormal.rst.txt
@@ -0,0 +1,95 @@
+netcal.regression.GPNormal
+==========================
+
+.. currentmodule:: netcal.regression
+
+.. autoclass:: GPNormal
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~GPNormal.__init__
+      ~GPNormal.add_module
+      ~GPNormal.added_loss_terms
+      ~GPNormal.apply
+      ~GPNormal.bfloat16
+      ~GPNormal.buffers
+      ~GPNormal.children
+      ~GPNormal.clear
+      ~GPNormal.constraint_for_parameter_name
+      ~GPNormal.constraints
+      ~GPNormal.cpu
+      ~GPNormal.cuda
+      ~GPNormal.double
+      ~GPNormal.eval
+      ~GPNormal.extra_repr
+      ~GPNormal.fit
+      ~GPNormal.fit_transform
+      ~GPNormal.float
+      ~GPNormal.forward
+      ~GPNormal.get_buffer
+      ~GPNormal.get_extra_state
+      ~GPNormal.get_fantasy_model
+      ~GPNormal.get_parameter
+      ~GPNormal.get_params
+      ~GPNormal.get_submodule
+      ~GPNormal.guide
+      ~GPNormal.half
+      ~GPNormal.hyperparameters
+      ~GPNormal.initialize
+      ~GPNormal.ipu
+      ~GPNormal.load_model
+      ~GPNormal.load_state_dict
+      ~GPNormal.load_strict_shapes
+      ~GPNormal.local_load_samples
+      ~GPNormal.model
+      ~GPNormal.modules
+      ~GPNormal.named_added_loss_terms
+      ~GPNormal.named_buffers
+      ~GPNormal.named_children
+      ~GPNormal.named_constraints
+      ~GPNormal.named_hyperparameters
+      ~GPNormal.named_modules
+      ~GPNormal.named_parameters
+      ~GPNormal.named_parameters_and_constraints
+      ~GPNormal.named_priors
+      ~GPNormal.named_variational_parameters
+      ~GPNormal.parameters
+      ~GPNormal.pyro_guide
+      ~GPNormal.pyro_load_from_samples
+      ~GPNormal.pyro_model
+      ~GPNormal.pyro_sample_from_prior
+      ~GPNormal.register_added_loss_term
+      ~GPNormal.register_backward_hook
+      ~GPNormal.register_buffer
+      ~GPNormal.register_constraint
+      ~GPNormal.register_forward_hook
+      ~GPNormal.register_forward_pre_hook
+      ~GPNormal.register_full_backward_hook
+      ~GPNormal.register_load_state_dict_post_hook
+      ~GPNormal.register_module
+      ~GPNormal.register_parameter
+      ~GPNormal.register_prior
+      ~GPNormal.requires_grad_
+      ~GPNormal.sample_from_prior
+      ~GPNormal.save_model
+      ~GPNormal.set_extra_state
+      ~GPNormal.set_params
+      ~GPNormal.share_memory
+      ~GPNormal.state_dict
+      ~GPNormal.to
+      ~GPNormal.to_empty
+      ~GPNormal.to_pyro_random_module
+      ~GPNormal.train
+      ~GPNormal.transform
+      ~GPNormal.type
+      ~GPNormal.update_added_loss_term
+      ~GPNormal.variational_parameters
+      ~GPNormal.xpu
+      ~GPNormal.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.IsotonicRegression.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.IsotonicRegression.rst.txt
new file mode 100644
index 0000000..2def620
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.IsotonicRegression.rst.txt
@@ -0,0 +1,25 @@
+netcal.regression.IsotonicRegression
+====================================
+
+.. currentmodule:: netcal.regression
+
+.. autoclass:: IsotonicRegression
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~IsotonicRegression.__init__
+      ~IsotonicRegression.clear
+      ~IsotonicRegression.fit
+      ~IsotonicRegression.fit_transform
+      ~IsotonicRegression.get_params
+      ~IsotonicRegression.load_model
+      ~IsotonicRegression.save_model
+      ~IsotonicRegression.set_params
+      ~IsotonicRegression.transform
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.VarianceScaling.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.VarianceScaling.rst.txt
new file mode 100644
index 0000000..26e3eb1
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression/netcal.regression.VarianceScaling.rst.txt
@@ -0,0 +1,25 @@
+netcal.regression.VarianceScaling
+=================================
+
+.. currentmodule:: netcal.regression
+
+.. autoclass:: VarianceScaling
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~VarianceScaling.__init__
+      ~VarianceScaling.clear
+      ~VarianceScaling.fit
+      ~VarianceScaling.fit_transform
+      ~VarianceScaling.get_params
+      ~VarianceScaling.load_model
+      ~VarianceScaling.save_model
+      ~VarianceScaling.set_params
+      ~VarianceScaling.transform
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.AbstractGP.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.AbstractGP.rst.txt
new file mode 100644
index 0000000..f9f3f32
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.AbstractGP.rst.txt
@@ -0,0 +1,95 @@
+netcal.regression.gp.AbstractGP
+===============================
+
+.. currentmodule:: netcal.regression.gp
+
+.. autoclass:: AbstractGP
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~AbstractGP.__init__
+      ~AbstractGP.add_module
+      ~AbstractGP.added_loss_terms
+      ~AbstractGP.apply
+      ~AbstractGP.bfloat16
+      ~AbstractGP.buffers
+      ~AbstractGP.children
+      ~AbstractGP.clear
+      ~AbstractGP.constraint_for_parameter_name
+      ~AbstractGP.constraints
+      ~AbstractGP.cpu
+      ~AbstractGP.cuda
+      ~AbstractGP.double
+      ~AbstractGP.eval
+      ~AbstractGP.extra_repr
+      ~AbstractGP.fit
+      ~AbstractGP.fit_transform
+      ~AbstractGP.float
+      ~AbstractGP.forward
+      ~AbstractGP.get_buffer
+      ~AbstractGP.get_extra_state
+      ~AbstractGP.get_fantasy_model
+      ~AbstractGP.get_parameter
+      ~AbstractGP.get_params
+      ~AbstractGP.get_submodule
+      ~AbstractGP.guide
+      ~AbstractGP.half
+      ~AbstractGP.hyperparameters
+      ~AbstractGP.initialize
+      ~AbstractGP.ipu
+      ~AbstractGP.load_model
+      ~AbstractGP.load_state_dict
+      ~AbstractGP.load_strict_shapes
+      ~AbstractGP.local_load_samples
+      ~AbstractGP.model
+      ~AbstractGP.modules
+      ~AbstractGP.named_added_loss_terms
+      ~AbstractGP.named_buffers
+      ~AbstractGP.named_children
+      ~AbstractGP.named_constraints
+      ~AbstractGP.named_hyperparameters
+      ~AbstractGP.named_modules
+      ~AbstractGP.named_parameters
+      ~AbstractGP.named_parameters_and_constraints
+      ~AbstractGP.named_priors
+      ~AbstractGP.named_variational_parameters
+      ~AbstractGP.parameters
+      ~AbstractGP.pyro_guide
+      ~AbstractGP.pyro_load_from_samples
+      ~AbstractGP.pyro_model
+      ~AbstractGP.pyro_sample_from_prior
+      ~AbstractGP.register_added_loss_term
+      ~AbstractGP.register_backward_hook
+      ~AbstractGP.register_buffer
+      ~AbstractGP.register_constraint
+      ~AbstractGP.register_forward_hook
+      ~AbstractGP.register_forward_pre_hook
+      ~AbstractGP.register_full_backward_hook
+      ~AbstractGP.register_load_state_dict_post_hook
+      ~AbstractGP.register_module
+      ~AbstractGP.register_parameter
+      ~AbstractGP.register_prior
+      ~AbstractGP.requires_grad_
+      ~AbstractGP.sample_from_prior
+      ~AbstractGP.save_model
+      ~AbstractGP.set_extra_state
+      ~AbstractGP.set_params
+      ~AbstractGP.share_memory
+      ~AbstractGP.state_dict
+      ~AbstractGP.to
+      ~AbstractGP.to_empty
+      ~AbstractGP.to_pyro_random_module
+      ~AbstractGP.train
+      ~AbstractGP.transform
+      ~AbstractGP.type
+      ~AbstractGP.update_added_loss_term
+      ~AbstractGP.variational_parameters
+      ~AbstractGP.xpu
+      ~AbstractGP.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPBeta.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPBeta.rst.txt
new file mode 100644
index 0000000..fec0533
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPBeta.rst.txt
@@ -0,0 +1,95 @@
+netcal.regression.gp.GPBeta
+===========================
+
+.. currentmodule:: netcal.regression.gp
+
+.. autoclass:: GPBeta
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~GPBeta.__init__
+      ~GPBeta.add_module
+      ~GPBeta.added_loss_terms
+      ~GPBeta.apply
+      ~GPBeta.bfloat16
+      ~GPBeta.buffers
+      ~GPBeta.children
+      ~GPBeta.clear
+      ~GPBeta.constraint_for_parameter_name
+      ~GPBeta.constraints
+      ~GPBeta.cpu
+      ~GPBeta.cuda
+      ~GPBeta.double
+      ~GPBeta.eval
+      ~GPBeta.extra_repr
+      ~GPBeta.fit
+      ~GPBeta.fit_transform
+      ~GPBeta.float
+      ~GPBeta.forward
+      ~GPBeta.get_buffer
+      ~GPBeta.get_extra_state
+      ~GPBeta.get_fantasy_model
+      ~GPBeta.get_parameter
+      ~GPBeta.get_params
+      ~GPBeta.get_submodule
+      ~GPBeta.guide
+      ~GPBeta.half
+      ~GPBeta.hyperparameters
+      ~GPBeta.initialize
+      ~GPBeta.ipu
+      ~GPBeta.load_model
+      ~GPBeta.load_state_dict
+      ~GPBeta.load_strict_shapes
+      ~GPBeta.local_load_samples
+      ~GPBeta.model
+      ~GPBeta.modules
+      ~GPBeta.named_added_loss_terms
+      ~GPBeta.named_buffers
+      ~GPBeta.named_children
+      ~GPBeta.named_constraints
+      ~GPBeta.named_hyperparameters
+      ~GPBeta.named_modules
+      ~GPBeta.named_parameters
+      ~GPBeta.named_parameters_and_constraints
+      ~GPBeta.named_priors
+      ~GPBeta.named_variational_parameters
+      ~GPBeta.parameters
+      ~GPBeta.pyro_guide
+      ~GPBeta.pyro_load_from_samples
+      ~GPBeta.pyro_model
+      ~GPBeta.pyro_sample_from_prior
+      ~GPBeta.register_added_loss_term
+      ~GPBeta.register_backward_hook
+      ~GPBeta.register_buffer
+      ~GPBeta.register_constraint
+      ~GPBeta.register_forward_hook
+      ~GPBeta.register_forward_pre_hook
+      ~GPBeta.register_full_backward_hook
+      ~GPBeta.register_load_state_dict_post_hook
+      ~GPBeta.register_module
+      ~GPBeta.register_parameter
+      ~GPBeta.register_prior
+      ~GPBeta.requires_grad_
+      ~GPBeta.sample_from_prior
+      ~GPBeta.save_model
+      ~GPBeta.set_extra_state
+      ~GPBeta.set_params
+      ~GPBeta.share_memory
+      ~GPBeta.state_dict
+      ~GPBeta.to
+      ~GPBeta.to_empty
+      ~GPBeta.to_pyro_random_module
+      ~GPBeta.train
+      ~GPBeta.transform
+      ~GPBeta.type
+      ~GPBeta.update_added_loss_term
+      ~GPBeta.variational_parameters
+      ~GPBeta.xpu
+      ~GPBeta.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPCauchy.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPCauchy.rst.txt
new file mode 100644
index 0000000..ee88992
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPCauchy.rst.txt
@@ -0,0 +1,95 @@
+netcal.regression.gp.GPCauchy
+=============================
+
+.. currentmodule:: netcal.regression.gp
+
+.. autoclass:: GPCauchy
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~GPCauchy.__init__
+      ~GPCauchy.add_module
+      ~GPCauchy.added_loss_terms
+      ~GPCauchy.apply
+      ~GPCauchy.bfloat16
+      ~GPCauchy.buffers
+      ~GPCauchy.children
+      ~GPCauchy.clear
+      ~GPCauchy.constraint_for_parameter_name
+      ~GPCauchy.constraints
+      ~GPCauchy.cpu
+      ~GPCauchy.cuda
+      ~GPCauchy.double
+      ~GPCauchy.eval
+      ~GPCauchy.extra_repr
+      ~GPCauchy.fit
+      ~GPCauchy.fit_transform
+      ~GPCauchy.float
+      ~GPCauchy.forward
+      ~GPCauchy.get_buffer
+      ~GPCauchy.get_extra_state
+      ~GPCauchy.get_fantasy_model
+      ~GPCauchy.get_parameter
+      ~GPCauchy.get_params
+      ~GPCauchy.get_submodule
+      ~GPCauchy.guide
+      ~GPCauchy.half
+      ~GPCauchy.hyperparameters
+      ~GPCauchy.initialize
+      ~GPCauchy.ipu
+      ~GPCauchy.load_model
+      ~GPCauchy.load_state_dict
+      ~GPCauchy.load_strict_shapes
+      ~GPCauchy.local_load_samples
+      ~GPCauchy.model
+      ~GPCauchy.modules
+      ~GPCauchy.named_added_loss_terms
+      ~GPCauchy.named_buffers
+      ~GPCauchy.named_children
+      ~GPCauchy.named_constraints
+      ~GPCauchy.named_hyperparameters
+      ~GPCauchy.named_modules
+      ~GPCauchy.named_parameters
+      ~GPCauchy.named_parameters_and_constraints
+      ~GPCauchy.named_priors
+      ~GPCauchy.named_variational_parameters
+      ~GPCauchy.parameters
+      ~GPCauchy.pyro_guide
+      ~GPCauchy.pyro_load_from_samples
+      ~GPCauchy.pyro_model
+      ~GPCauchy.pyro_sample_from_prior
+      ~GPCauchy.register_added_loss_term
+      ~GPCauchy.register_backward_hook
+      ~GPCauchy.register_buffer
+      ~GPCauchy.register_constraint
+      ~GPCauchy.register_forward_hook
+      ~GPCauchy.register_forward_pre_hook
+      ~GPCauchy.register_full_backward_hook
+      ~GPCauchy.register_load_state_dict_post_hook
+      ~GPCauchy.register_module
+      ~GPCauchy.register_parameter
+      ~GPCauchy.register_prior
+      ~GPCauchy.requires_grad_
+      ~GPCauchy.sample_from_prior
+      ~GPCauchy.save_model
+      ~GPCauchy.set_extra_state
+      ~GPCauchy.set_params
+      ~GPCauchy.share_memory
+      ~GPCauchy.state_dict
+      ~GPCauchy.to
+      ~GPCauchy.to_empty
+      ~GPCauchy.to_pyro_random_module
+      ~GPCauchy.train
+      ~GPCauchy.transform
+      ~GPCauchy.type
+      ~GPCauchy.update_added_loss_term
+      ~GPCauchy.variational_parameters
+      ~GPCauchy.xpu
+      ~GPCauchy.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPNormal.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPNormal.rst.txt
new file mode 100644
index 0000000..1b86972
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPNormal.rst.txt
@@ -0,0 +1,95 @@
+netcal.regression.gp.GPNormal
+=============================
+
+.. currentmodule:: netcal.regression.gp
+
+.. autoclass:: GPNormal
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~GPNormal.__init__
+      ~GPNormal.add_module
+      ~GPNormal.added_loss_terms
+      ~GPNormal.apply
+      ~GPNormal.bfloat16
+      ~GPNormal.buffers
+      ~GPNormal.children
+      ~GPNormal.clear
+      ~GPNormal.constraint_for_parameter_name
+      ~GPNormal.constraints
+      ~GPNormal.cpu
+      ~GPNormal.cuda
+      ~GPNormal.double
+      ~GPNormal.eval
+      ~GPNormal.extra_repr
+      ~GPNormal.fit
+      ~GPNormal.fit_transform
+      ~GPNormal.float
+      ~GPNormal.forward
+      ~GPNormal.get_buffer
+      ~GPNormal.get_extra_state
+      ~GPNormal.get_fantasy_model
+      ~GPNormal.get_parameter
+      ~GPNormal.get_params
+      ~GPNormal.get_submodule
+      ~GPNormal.guide
+      ~GPNormal.half
+      ~GPNormal.hyperparameters
+      ~GPNormal.initialize
+      ~GPNormal.ipu
+      ~GPNormal.load_model
+      ~GPNormal.load_state_dict
+      ~GPNormal.load_strict_shapes
+      ~GPNormal.local_load_samples
+      ~GPNormal.model
+      ~GPNormal.modules
+      ~GPNormal.named_added_loss_terms
+      ~GPNormal.named_buffers
+      ~GPNormal.named_children
+      ~GPNormal.named_constraints
+      ~GPNormal.named_hyperparameters
+      ~GPNormal.named_modules
+      ~GPNormal.named_parameters
+      ~GPNormal.named_parameters_and_constraints
+      ~GPNormal.named_priors
+      ~GPNormal.named_variational_parameters
+      ~GPNormal.parameters
+      ~GPNormal.pyro_guide
+      ~GPNormal.pyro_load_from_samples
+      ~GPNormal.pyro_model
+      ~GPNormal.pyro_sample_from_prior
+      ~GPNormal.register_added_loss_term
+      ~GPNormal.register_backward_hook
+      ~GPNormal.register_buffer
+      ~GPNormal.register_constraint
+      ~GPNormal.register_forward_hook
+      ~GPNormal.register_forward_pre_hook
+      ~GPNormal.register_full_backward_hook
+      ~GPNormal.register_load_state_dict_post_hook
+      ~GPNormal.register_module
+      ~GPNormal.register_parameter
+      ~GPNormal.register_prior
+      ~GPNormal.requires_grad_
+      ~GPNormal.sample_from_prior
+      ~GPNormal.save_model
+      ~GPNormal.set_extra_state
+      ~GPNormal.set_params
+      ~GPNormal.share_memory
+      ~GPNormal.state_dict
+      ~GPNormal.to
+      ~GPNormal.to_empty
+      ~GPNormal.to_pyro_random_module
+      ~GPNormal.train
+      ~GPNormal.transform
+      ~GPNormal.type
+      ~GPNormal.update_added_loss_term
+      ~GPNormal.variational_parameters
+      ~GPNormal.xpu
+      ~GPNormal.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_kernel/netcal.regression.gp.kernel.GaussianRBFKernel.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_kernel/netcal.regression.gp.kernel.GaussianRBFKernel.rst.txt
new file mode 100644
index 0000000..319c4e5
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_kernel/netcal.regression.gp.kernel.GaussianRBFKernel.rst.txt
@@ -0,0 +1,87 @@
+netcal.regression.gp.kernel.GaussianRBFKernel
+=============================================
+
+.. currentmodule:: netcal.regression.gp.kernel
+
+.. autoclass:: GaussianRBFKernel
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~GaussianRBFKernel.__init__
+      ~GaussianRBFKernel.add_module
+      ~GaussianRBFKernel.added_loss_terms
+      ~GaussianRBFKernel.apply
+      ~GaussianRBFKernel.bfloat16
+      ~GaussianRBFKernel.buffers
+      ~GaussianRBFKernel.children
+      ~GaussianRBFKernel.constraint_for_parameter_name
+      ~GaussianRBFKernel.constraints
+      ~GaussianRBFKernel.covar_dist
+      ~GaussianRBFKernel.cpu
+      ~GaussianRBFKernel.cuda
+      ~GaussianRBFKernel.double
+      ~GaussianRBFKernel.eval
+      ~GaussianRBFKernel.extra_repr
+      ~GaussianRBFKernel.float
+      ~GaussianRBFKernel.forward
+      ~GaussianRBFKernel.get_buffer
+      ~GaussianRBFKernel.get_extra_state
+      ~GaussianRBFKernel.get_parameter
+      ~GaussianRBFKernel.get_submodule
+      ~GaussianRBFKernel.half
+      ~GaussianRBFKernel.hyperparameters
+      ~GaussianRBFKernel.initialize
+      ~GaussianRBFKernel.ipu
+      ~GaussianRBFKernel.load_state_dict
+      ~GaussianRBFKernel.load_strict_shapes
+      ~GaussianRBFKernel.local_load_samples
+      ~GaussianRBFKernel.modules
+      ~GaussianRBFKernel.named_added_loss_terms
+      ~GaussianRBFKernel.named_buffers
+      ~GaussianRBFKernel.named_children
+      ~GaussianRBFKernel.named_constraints
+      ~GaussianRBFKernel.named_hyperparameters
+      ~GaussianRBFKernel.named_modules
+      ~GaussianRBFKernel.named_parameters
+      ~GaussianRBFKernel.named_parameters_and_constraints
+      ~GaussianRBFKernel.named_priors
+      ~GaussianRBFKernel.named_sub_kernels
+      ~GaussianRBFKernel.named_variational_parameters
+      ~GaussianRBFKernel.num_outputs_per_input
+      ~GaussianRBFKernel.parameters
+      ~GaussianRBFKernel.prediction_strategy
+      ~GaussianRBFKernel.pyro_load_from_samples
+      ~GaussianRBFKernel.pyro_sample_from_prior
+      ~GaussianRBFKernel.register_added_loss_term
+      ~GaussianRBFKernel.register_backward_hook
+      ~GaussianRBFKernel.register_buffer
+      ~GaussianRBFKernel.register_constraint
+      ~GaussianRBFKernel.register_forward_hook
+      ~GaussianRBFKernel.register_forward_pre_hook
+      ~GaussianRBFKernel.register_full_backward_hook
+      ~GaussianRBFKernel.register_load_state_dict_post_hook
+      ~GaussianRBFKernel.register_module
+      ~GaussianRBFKernel.register_parameter
+      ~GaussianRBFKernel.register_prior
+      ~GaussianRBFKernel.requires_grad_
+      ~GaussianRBFKernel.sample_from_prior
+      ~GaussianRBFKernel.set_extra_state
+      ~GaussianRBFKernel.share_memory
+      ~GaussianRBFKernel.state_dict
+      ~GaussianRBFKernel.sub_kernels
+      ~GaussianRBFKernel.to
+      ~GaussianRBFKernel.to_empty
+      ~GaussianRBFKernel.to_pyro_random_module
+      ~GaussianRBFKernel.train
+      ~GaussianRBFKernel.type
+      ~GaussianRBFKernel.update_added_loss_term
+      ~GaussianRBFKernel.variational_parameters
+      ~GaussianRBFKernel.xpu
+      ~GaussianRBFKernel.zero_grad
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.BetaLikelihood.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.BetaLikelihood.rst.txt
new file mode 100644
index 0000000..f29c7c0
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.BetaLikelihood.rst.txt
@@ -0,0 +1,38 @@
+netcal.regression.gp.likelihood.BetaLikelihood
+==============================================
+
+.. currentmodule:: netcal.regression.gp.likelihood
+
+.. autoclass:: BetaLikelihood
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~BetaLikelihood.__init__
+      ~BetaLikelihood.cdf
+      ~BetaLikelihood.conjugate_update
+      ~BetaLikelihood.entropy
+      ~BetaLikelihood.enumerate_support
+      ~BetaLikelihood.expand
+      ~BetaLikelihood.expand_by
+      ~BetaLikelihood.has_rsample_
+      ~BetaLikelihood.icdf
+      ~BetaLikelihood.independent
+      ~BetaLikelihood.infer_shapes
+      ~BetaLikelihood.log_prob
+      ~BetaLikelihood.mask
+      ~BetaLikelihood.perplexity
+      ~BetaLikelihood.reshape
+      ~BetaLikelihood.rsample
+      ~BetaLikelihood.sample
+      ~BetaLikelihood.sample_n
+      ~BetaLikelihood.score_parts
+      ~BetaLikelihood.set_default_validate_args
+      ~BetaLikelihood.shape
+      ~BetaLikelihood.to_event
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.CauchyLikelihood.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.CauchyLikelihood.rst.txt
new file mode 100644
index 0000000..699d9bb
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.CauchyLikelihood.rst.txt
@@ -0,0 +1,38 @@
+netcal.regression.gp.likelihood.CauchyLikelihood
+================================================
+
+.. currentmodule:: netcal.regression.gp.likelihood
+
+.. autoclass:: CauchyLikelihood
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~CauchyLikelihood.__init__
+      ~CauchyLikelihood.cdf
+      ~CauchyLikelihood.conjugate_update
+      ~CauchyLikelihood.entropy
+      ~CauchyLikelihood.enumerate_support
+      ~CauchyLikelihood.expand
+      ~CauchyLikelihood.expand_by
+      ~CauchyLikelihood.has_rsample_
+      ~CauchyLikelihood.icdf
+      ~CauchyLikelihood.independent
+      ~CauchyLikelihood.infer_shapes
+      ~CauchyLikelihood.log_prob
+      ~CauchyLikelihood.mask
+      ~CauchyLikelihood.perplexity
+      ~CauchyLikelihood.reshape
+      ~CauchyLikelihood.rsample
+      ~CauchyLikelihood.sample
+      ~CauchyLikelihood.sample_n
+      ~CauchyLikelihood.score_parts
+      ~CauchyLikelihood.set_default_validate_args
+      ~CauchyLikelihood.shape
+      ~CauchyLikelihood.to_event
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood.rst.txt
new file mode 100644
index 0000000..d0ea290
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood.rst.txt
@@ -0,0 +1,40 @@
+netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood
+==================================================================
+
+.. currentmodule:: netcal.regression.gp.likelihood
+
+.. autoclass:: ScaledMultivariateNormalLikelihood
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ScaledMultivariateNormalLikelihood.__init__
+      ~ScaledMultivariateNormalLikelihood.cdf
+      ~ScaledMultivariateNormalLikelihood.conjugate_update
+      ~ScaledMultivariateNormalLikelihood.entropy
+      ~ScaledMultivariateNormalLikelihood.enumerate_support
+      ~ScaledMultivariateNormalLikelihood.expand
+      ~ScaledMultivariateNormalLikelihood.expand_by
+      ~ScaledMultivariateNormalLikelihood.has_rsample_
+      ~ScaledMultivariateNormalLikelihood.icdf
+      ~ScaledMultivariateNormalLikelihood.independent
+      ~ScaledMultivariateNormalLikelihood.infer_shapes
+      ~ScaledMultivariateNormalLikelihood.log_prob
+      ~ScaledMultivariateNormalLikelihood.mask
+      ~ScaledMultivariateNormalLikelihood.perplexity
+      ~ScaledMultivariateNormalLikelihood.reconstruct
+      ~ScaledMultivariateNormalLikelihood.rescale
+      ~ScaledMultivariateNormalLikelihood.reshape
+      ~ScaledMultivariateNormalLikelihood.rsample
+      ~ScaledMultivariateNormalLikelihood.sample
+      ~ScaledMultivariateNormalLikelihood.sample_n
+      ~ScaledMultivariateNormalLikelihood.score_parts
+      ~ScaledMultivariateNormalLikelihood.set_default_validate_args
+      ~ScaledMultivariateNormalLikelihood.shape
+      ~ScaledMultivariateNormalLikelihood.to_event
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledNormalLikelihood.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledNormalLikelihood.rst.txt
new file mode 100644
index 0000000..2feae3b
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledNormalLikelihood.rst.txt
@@ -0,0 +1,38 @@
+netcal.regression.gp.likelihood.ScaledNormalLikelihood
+======================================================
+
+.. currentmodule:: netcal.regression.gp.likelihood
+
+.. autoclass:: ScaledNormalLikelihood
+   :no-private-members:
+
+   
+   
+   .. rubric:: Methods
+
+   .. autosummary::
+   
+      ~ScaledNormalLikelihood.__init__
+      ~ScaledNormalLikelihood.cdf
+      ~ScaledNormalLikelihood.conjugate_update
+      ~ScaledNormalLikelihood.entropy
+      ~ScaledNormalLikelihood.enumerate_support
+      ~ScaledNormalLikelihood.expand
+      ~ScaledNormalLikelihood.expand_by
+      ~ScaledNormalLikelihood.has_rsample_
+      ~ScaledNormalLikelihood.icdf
+      ~ScaledNormalLikelihood.independent
+      ~ScaledNormalLikelihood.infer_shapes
+      ~ScaledNormalLikelihood.log_prob
+      ~ScaledNormalLikelihood.mask
+      ~ScaledNormalLikelihood.perplexity
+      ~ScaledNormalLikelihood.reshape
+      ~ScaledNormalLikelihood.rsample
+      ~ScaledNormalLikelihood.sample
+      ~ScaledNormalLikelihood.sample_n
+      ~ScaledNormalLikelihood.score_parts
+      ~ScaledNormalLikelihood.set_default_validate_args
+      ~ScaledNormalLikelihood.shape
+      ~ScaledNormalLikelihood.to_event
+   
+   
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.rst.txt
new file mode 100644
index 0000000..d439596
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.rst.txt
@@ -0,0 +1,23 @@
+netcal.regression.gp.kernel
+===========================
+
+.. automodule:: netcal.regression.gp.kernel
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.likelihood.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.likelihood.rst.txt
new file mode 100644
index 0000000..83999d3
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.likelihood.rst.txt
@@ -0,0 +1,23 @@
+netcal.regression.gp.likelihood
+===============================
+
+.. automodule:: netcal.regression.gp.likelihood
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/netcal.regression.gp.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/netcal.regression.gp.rst.txt
new file mode 100644
index 0000000..46290d1
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regression_gp/netcal.regression.gp.rst.txt
@@ -0,0 +1,23 @@
+netcal.regression.gp
+====================
+
+.. automodule:: netcal.regression.gp
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.rst.txt
index b3683ee..8e32dac 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.rst.txt
@@ -22,11 +22,17 @@ netcal.regularization.ConfidencePenalty
       ~ConfidencePenalty.cpu
       ~ConfidencePenalty.cuda
       ~ConfidencePenalty.double
+      ~ConfidencePenalty.entropy
       ~ConfidencePenalty.eval
       ~ConfidencePenalty.extra_repr
       ~ConfidencePenalty.float
       ~ConfidencePenalty.forward
+      ~ConfidencePenalty.get_buffer
+      ~ConfidencePenalty.get_extra_state
+      ~ConfidencePenalty.get_parameter
+      ~ConfidencePenalty.get_submodule
       ~ConfidencePenalty.half
+      ~ConfidencePenalty.ipu
       ~ConfidencePenalty.load_state_dict
       ~ConfidencePenalty.modules
       ~ConfidencePenalty.named_buffers
@@ -38,13 +44,19 @@ netcal.regularization.ConfidencePenalty
       ~ConfidencePenalty.register_buffer
       ~ConfidencePenalty.register_forward_hook
       ~ConfidencePenalty.register_forward_pre_hook
+      ~ConfidencePenalty.register_full_backward_hook
+      ~ConfidencePenalty.register_load_state_dict_post_hook
+      ~ConfidencePenalty.register_module
       ~ConfidencePenalty.register_parameter
       ~ConfidencePenalty.requires_grad_
+      ~ConfidencePenalty.set_extra_state
       ~ConfidencePenalty.share_memory
       ~ConfidencePenalty.state_dict
       ~ConfidencePenalty.to
+      ~ConfidencePenalty.to_empty
       ~ConfidencePenalty.train
       ~ConfidencePenalty.type
+      ~ConfidencePenalty.xpu
       ~ConfidencePenalty.zero_grad
    
    
@@ -55,7 +67,10 @@ netcal.regularization.ConfidencePenalty
 
    .. autosummary::
    
+      ~ConfidencePenalty.T_destination
       ~ConfidencePenalty.dump_patches
       ~ConfidencePenalty.epsilon
+      ~ConfidencePenalty.reduction
+      ~ConfidencePenalty.training
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.rst.txt
index adae756..9899c1b 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.rst.txt
@@ -26,7 +26,12 @@ netcal.regularization.DCAPenalty
       ~DCAPenalty.extra_repr
       ~DCAPenalty.float
       ~DCAPenalty.forward
+      ~DCAPenalty.get_buffer
+      ~DCAPenalty.get_extra_state
+      ~DCAPenalty.get_parameter
+      ~DCAPenalty.get_submodule
       ~DCAPenalty.half
+      ~DCAPenalty.ipu
       ~DCAPenalty.load_state_dict
       ~DCAPenalty.modules
       ~DCAPenalty.named_buffers
@@ -38,13 +43,19 @@ netcal.regularization.DCAPenalty
       ~DCAPenalty.register_buffer
       ~DCAPenalty.register_forward_hook
       ~DCAPenalty.register_forward_pre_hook
+      ~DCAPenalty.register_full_backward_hook
+      ~DCAPenalty.register_load_state_dict_post_hook
+      ~DCAPenalty.register_module
       ~DCAPenalty.register_parameter
       ~DCAPenalty.requires_grad_
+      ~DCAPenalty.set_extra_state
       ~DCAPenalty.share_memory
       ~DCAPenalty.state_dict
       ~DCAPenalty.to
+      ~DCAPenalty.to_empty
       ~DCAPenalty.train
       ~DCAPenalty.type
+      ~DCAPenalty.xpu
       ~DCAPenalty.zero_grad
    
    
@@ -55,6 +66,9 @@ netcal.regularization.DCAPenalty
 
    .. autosummary::
    
+      ~DCAPenalty.T_destination
       ~DCAPenalty.dump_patches
+      ~DCAPenalty.reduction
+      ~DCAPenalty.training
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.rst.txt
index 0dbd163..8e92323 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.rst.txt
@@ -26,7 +26,12 @@ netcal.regularization.MMCEPenalty
       ~MMCEPenalty.extra_repr
       ~MMCEPenalty.float
       ~MMCEPenalty.forward
+      ~MMCEPenalty.get_buffer
+      ~MMCEPenalty.get_extra_state
+      ~MMCEPenalty.get_parameter
+      ~MMCEPenalty.get_submodule
       ~MMCEPenalty.half
+      ~MMCEPenalty.ipu
       ~MMCEPenalty.kernel
       ~MMCEPenalty.load_state_dict
       ~MMCEPenalty.modules
@@ -39,13 +44,19 @@ netcal.regularization.MMCEPenalty
       ~MMCEPenalty.register_buffer
       ~MMCEPenalty.register_forward_hook
       ~MMCEPenalty.register_forward_pre_hook
+      ~MMCEPenalty.register_full_backward_hook
+      ~MMCEPenalty.register_load_state_dict_post_hook
+      ~MMCEPenalty.register_module
       ~MMCEPenalty.register_parameter
       ~MMCEPenalty.requires_grad_
+      ~MMCEPenalty.set_extra_state
       ~MMCEPenalty.share_memory
       ~MMCEPenalty.state_dict
       ~MMCEPenalty.to
+      ~MMCEPenalty.to_empty
       ~MMCEPenalty.train
       ~MMCEPenalty.type
+      ~MMCEPenalty.xpu
       ~MMCEPenalty.zero_grad
    
    
@@ -56,7 +67,10 @@ netcal.regularization.MMCEPenalty
 
    .. autosummary::
    
+      ~MMCEPenalty.T_destination
       ~MMCEPenalty.dump_patches
       ~MMCEPenalty.epsilon
+      ~MMCEPenalty.reduction
+      ~MMCEPenalty.training
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.rst.txt
index d955507..91be3ea 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.rst.txt
@@ -28,7 +28,6 @@ netcal.scaling.AbstractLogisticRegression
       ~AbstractLogisticRegression.prior
       ~AbstractLogisticRegression.save_model
       ~AbstractLogisticRegression.set_params
-      ~AbstractLogisticRegression.squeeze_generic
       ~AbstractLogisticRegression.to
       ~AbstractLogisticRegression.transform
       ~AbstractLogisticRegression.variational
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.rst.txt
index b7baa15..4fe4929 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.rst.txt
@@ -28,7 +28,6 @@ netcal.scaling.BetaCalibration
       ~BetaCalibration.prior
       ~BetaCalibration.save_model
       ~BetaCalibration.set_params
-      ~BetaCalibration.squeeze_generic
       ~BetaCalibration.to
       ~BetaCalibration.transform
       ~BetaCalibration.variational
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.rst.txt
index c7f3a91..cc256b3 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.rst.txt
@@ -28,7 +28,6 @@ netcal.scaling.BetaCalibrationDependent
       ~BetaCalibrationDependent.prior
       ~BetaCalibrationDependent.save_model
       ~BetaCalibrationDependent.set_params
-      ~BetaCalibrationDependent.squeeze_generic
       ~BetaCalibrationDependent.to
       ~BetaCalibrationDependent.transform
       ~BetaCalibrationDependent.variational
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.rst.txt
index c2fddda..fc7b1ae 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.rst.txt
@@ -28,7 +28,6 @@ netcal.scaling.LogisticCalibration
       ~LogisticCalibration.prior
       ~LogisticCalibration.save_model
       ~LogisticCalibration.set_params
-      ~LogisticCalibration.squeeze_generic
       ~LogisticCalibration.to
       ~LogisticCalibration.transform
       ~LogisticCalibration.variational
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.rst.txt
index c690a1e..15e499a 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.rst.txt
@@ -28,7 +28,6 @@ netcal.scaling.LogisticCalibrationDependent
       ~LogisticCalibrationDependent.prior
       ~LogisticCalibrationDependent.save_model
       ~LogisticCalibrationDependent.set_params
-      ~LogisticCalibrationDependent.squeeze_generic
       ~LogisticCalibrationDependent.to
       ~LogisticCalibrationDependent.transform
       ~LogisticCalibrationDependent.variational
diff --git a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.rst.txt b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.rst.txt
index 7a1f47e..cfce02a 100644
--- a/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.rst.txt
+++ b/docs/build/html/_sources/_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.rst.txt
@@ -28,7 +28,6 @@ netcal.scaling.TemperatureScaling
       ~TemperatureScaling.prior
       ~TemperatureScaling.save_model
       ~TemperatureScaling.set_params
-      ~TemperatureScaling.squeeze_generic
       ~TemperatureScaling.to
       ~TemperatureScaling.transform
       ~TemperatureScaling.variational
diff --git a/docs/build/html/_sources/_autosummary/netcal.binning.rst.txt b/docs/build/html/_sources/_autosummary/netcal.binning.rst.txt
index 3496a8e..2af16bb 100644
--- a/docs/build/html/_sources/_autosummary/netcal.binning.rst.txt
+++ b/docs/build/html/_sources/_autosummary/netcal.binning.rst.txt
@@ -1,4 +1,4 @@
-netcal.binning
+netcal.binning
 ==============
 
 .. automodule:: netcal.binning
@@ -13,4 +13,11 @@ netcal.binning
 
    
    
-   
\ No newline at end of file
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/netcal.metrics.rst.txt b/docs/build/html/_sources/_autosummary/netcal.metrics.rst.txt
index 728937d..a7dcdae 100644
--- a/docs/build/html/_sources/_autosummary/netcal.metrics.rst.txt
+++ b/docs/build/html/_sources/_autosummary/netcal.metrics.rst.txt
@@ -1,4 +1,4 @@
-netcal.metrics
+netcal.metrics
 ==============
 
 .. automodule:: netcal.metrics
@@ -13,4 +13,11 @@ netcal.metrics
 
    
    
-   
\ No newline at end of file
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/netcal.presentation.rst.txt b/docs/build/html/_sources/_autosummary/netcal.presentation.rst.txt
index 128b063..4fb4661 100644
--- a/docs/build/html/_sources/_autosummary/netcal.presentation.rst.txt
+++ b/docs/build/html/_sources/_autosummary/netcal.presentation.rst.txt
@@ -1,4 +1,4 @@
-netcal.presentation
+netcal.presentation
 ===================
 
 .. automodule:: netcal.presentation
@@ -13,4 +13,11 @@ netcal.presentation
 
    
    
-   
\ No newline at end of file
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/netcal.regression.rst.txt b/docs/build/html/_sources/_autosummary/netcal.regression.rst.txt
new file mode 100644
index 0000000..4f39629
--- /dev/null
+++ b/docs/build/html/_sources/_autosummary/netcal.regression.rst.txt
@@ -0,0 +1,23 @@
+netcal.regression
+=================
+
+.. automodule:: netcal.regression
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/netcal.regularization.rst.txt b/docs/build/html/_sources/_autosummary/netcal.regularization.rst.txt
index 594dca3..6202e5b 100644
--- a/docs/build/html/_sources/_autosummary/netcal.regularization.rst.txt
+++ b/docs/build/html/_sources/_autosummary/netcal.regularization.rst.txt
@@ -1,4 +1,4 @@
-netcal.regularization
+netcal.regularization
 =====================
 
 .. automodule:: netcal.regularization
@@ -13,4 +13,11 @@ netcal.regularization
 
    
    
-   
\ No newline at end of file
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary/netcal.scaling.rst.txt b/docs/build/html/_sources/_autosummary/netcal.scaling.rst.txt
index 4827e4c..fe60d9c 100644
--- a/docs/build/html/_sources/_autosummary/netcal.scaling.rst.txt
+++ b/docs/build/html/_sources/_autosummary/netcal.scaling.rst.txt
@@ -1,4 +1,4 @@
-netcal.scaling
+netcal.scaling
 ==============
 
 .. automodule:: netcal.scaling
@@ -13,4 +13,11 @@ netcal.scaling
 
    
    
-   
\ No newline at end of file
+   
+
+   
+   
+   
+
+
+
diff --git a/docs/build/html/_sources/_autosummary_abstract_calibration/netcal.AbstractCalibration.rst.txt b/docs/build/html/_sources/_autosummary_abstract_calibration/netcal.AbstractCalibration.rst.txt
index cd99eb1..f0860f1 100644
--- a/docs/build/html/_sources/_autosummary_abstract_calibration/netcal.AbstractCalibration.rst.txt
+++ b/docs/build/html/_sources/_autosummary_abstract_calibration/netcal.AbstractCalibration.rst.txt
@@ -1,4 +1,4 @@
-netcal.AbstractCalibration
+netcal.AbstractCalibration
 ==========================
 
 .. currentmodule:: netcal
@@ -20,7 +20,6 @@ netcal.AbstractCalibration
       ~AbstractCalibration.load_model
       ~AbstractCalibration.save_model
       ~AbstractCalibration.set_params
-      ~AbstractCalibration.squeeze_generic
       ~AbstractCalibration.transform
    
    
\ No newline at end of file
diff --git a/docs/build/html/_sources/index.rst.txt b/docs/build/html/_sources/index.rst.txt
index ef93093..a57659f 100644
--- a/docs/build/html/_sources/index.rst.txt
+++ b/docs/build/html/_sources/index.rst.txt
@@ -1,5 +1,6 @@
 .. automodule:: netcal
-.. include:: ../../README.rst
+.. include:: /../../README.md
+   :parser: myst_parser.sphinx_
 
 
 
diff --git a/docs/build/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/build/html/_static/_sphinx_javascript_frameworks_compat.js
new file mode 100644
index 0000000..8549469
--- /dev/null
+++ b/docs/build/html/_static/_sphinx_javascript_frameworks_compat.js
@@ -0,0 +1,134 @@
+/*
+ * _sphinx_javascript_frameworks_compat.js
+ * ~~~~~~~~~~
+ *
+ * Compatability shim for jQuery and underscores.js.
+ *
+ * WILL BE REMOVED IN Sphinx 6.0
+ * xref RemovedInSphinx60Warning
+ *
+ */
+
+/**
+ * select a different prefix for underscore
+ */
+$u = _.noConflict();
+
+
+/**
+ * small helper function to urldecode strings
+ *
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
+ */
+jQuery.urldecode = function(x) {
+    if (!x) {
+        return x
+    }
+    return decodeURIComponent(x.replace(/\+/g, ' '));
+};
+
+/**
+ * small helper function to urlencode strings
+ */
+jQuery.urlencode = encodeURIComponent;
+
+/**
+ * This function returns the parsed url parameters of the
+ * current request. Multiple values per key are supported,
+ * it will always return arrays of strings for the value parts.
+ */
+jQuery.getQueryParameters = function(s) {
+    if (typeof s === 'undefined')
+        s = document.location.search;
+    var parts = s.substr(s.indexOf('?') + 1).split('&');
+    var result = {};
+    for (var i = 0; i < parts.length; i++) {
+        var tmp = parts[i].split('=', 2);
+        var key = jQuery.urldecode(tmp[0]);
+        var value = jQuery.urldecode(tmp[1]);
+        if (key in result)
+            result[key].push(value);
+        else
+            result[key] = [value];
+    }
+    return result;
+};
+
+/**
+ * highlight a given string on a jquery object by wrapping it in
+ * span elements with the given class name.
+ */
+jQuery.fn.highlightText = function(text, className) {
+    function highlight(node, addItems) {
+        if (node.nodeType === 3) {
+            var val = node.nodeValue;
+            var pos = val.toLowerCase().indexOf(text);
+            if (pos >= 0 &&
+                !jQuery(node.parentNode).hasClass(className) &&
+                !jQuery(node.parentNode).hasClass("nohighlight")) {
+                var span;
+                var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
+                if (isInSVG) {
+                    span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+                } else {
+                    span = document.createElement("span");
+                    span.className = className;
+                }
+                span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+                node.parentNode.insertBefore(span, node.parentNode.insertBefore(
+                    document.createTextNode(val.substr(pos + text.length)),
+                    node.nextSibling));
+                node.nodeValue = val.substr(0, pos);
+                if (isInSVG) {
+                    var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
+                    var bbox = node.parentElement.getBBox();
+                    rect.x.baseVal.value = bbox.x;
+                    rect.y.baseVal.value = bbox.y;
+                    rect.width.baseVal.value = bbox.width;
+                    rect.height.baseVal.value = bbox.height;
+                    rect.setAttribute('class', className);
+                    addItems.push({
+                        "parent": node.parentNode,
+                        "target": rect});
+                }
+            }
+        }
+        else if (!jQuery(node).is("button, select, textarea")) {
+            jQuery.each(node.childNodes, function() {
+                highlight(this, addItems);
+            });
+        }
+    }
+    var addItems = [];
+    var result = this.each(function() {
+        highlight(this, addItems);
+    });
+    for (var i = 0; i < addItems.length; ++i) {
+        jQuery(addItems[i].parent).before(addItems[i].target);
+    }
+    return result;
+};
+
+/*
+ * backward compatibility for jQuery.browser
+ * This will be supported until firefox bug is fixed.
+ */
+if (!jQuery.browser) {
+    jQuery.uaMatch = function(ua) {
+        ua = ua.toLowerCase();
+
+        var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
+            /(webkit)[ \/]([\w.]+)/.exec(ua) ||
+            /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
+            /(msie) ([\w.]+)/.exec(ua) ||
+            ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
+            [];
+
+        return {
+            browser: match[ 1 ] || "",
+            version: match[ 2 ] || "0"
+        };
+    };
+    jQuery.browser = {};
+    jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
+}
diff --git a/docs/build/html/_static/basic.css b/docs/build/html/_static/basic.css
index 0119285..4e9a9f1 100644
--- a/docs/build/html/_static/basic.css
+++ b/docs/build/html/_static/basic.css
@@ -4,7 +4,7 @@
  *
  * Sphinx stylesheet -- basic theme.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -15,6 +15,12 @@ div.clearer {
     clear: both;
 }
 
+div.section::after {
+    display: block;
+    content: '';
+    clear: left;
+}
+
 /* -- relbar ---------------------------------------------------------------- */
 
 div.related {
@@ -124,7 +130,7 @@ ul.search li a {
     font-weight: bold;
 }
 
-ul.search li div.context {
+ul.search li p.context {
     color: #888;
     margin: 2px 0 0 30px;
     text-align: left;
@@ -216,7 +222,7 @@ table.modindextable td {
 /* -- general body styles --------------------------------------------------- */
 
 div.body {
-    min-width: 450px;
+    min-width: 360px;
     max-width: 800px;
 }
 
@@ -231,16 +237,6 @@ a.headerlink {
     visibility: hidden;
 }
 
-a.brackets:before,
-span.brackets > a:before{
-    content: "[";
-}
-
-a.brackets:after,
-span.brackets > a:after {
-    content: "]";
-}
-
 h1:hover > a.headerlink,
 h2:hover > a.headerlink,
 h3:hover > a.headerlink,
@@ -271,25 +267,25 @@ p.rubric {
     font-weight: bold;
 }
 
-img.align-left, .figure.align-left, object.align-left {
+img.align-left, figure.align-left, .figure.align-left, object.align-left {
     clear: left;
     float: left;
     margin-right: 1em;
 }
 
-img.align-right, .figure.align-right, object.align-right {
+img.align-right, figure.align-right, .figure.align-right, object.align-right {
     clear: right;
     float: right;
     margin-left: 1em;
 }
 
-img.align-center, .figure.align-center, object.align-center {
+img.align-center, figure.align-center, .figure.align-center, object.align-center {
   display: block;
   margin-left: auto;
   margin-right: auto;
 }
 
-img.align-default, .figure.align-default {
+img.align-default, figure.align-default, .figure.align-default {
   display: block;
   margin-left: auto;
   margin-right: auto;
@@ -313,24 +309,33 @@ img.align-default, .figure.align-default {
 
 /* -- sidebars -------------------------------------------------------------- */
 
-div.sidebar {
+div.sidebar,
+aside.sidebar {
     margin: 0 0 0.5em 1em;
     border: 1px solid #ddb;
-    padding: 7px 7px 0 7px;
+    padding: 7px;
     background-color: #ffe;
     width: 40%;
     float: right;
+    clear: right;
+    overflow-x: auto;
 }
 
 p.sidebar-title {
     font-weight: bold;
 }
+nav.contents,
+aside.topic,
+div.admonition, div.topic, blockquote {
+    clear: left;
+}
 
 /* -- topics ---------------------------------------------------------------- */
-
+nav.contents,
+aside.topic,
 div.topic {
     border: 1px solid #ccc;
-    padding: 7px 7px 0 7px;
+    padding: 7px;
     margin: 10px 0 10px 0;
 }
 
@@ -352,10 +357,6 @@ div.admonition dt {
     font-weight: bold;
 }
 
-div.admonition dl {
-    margin-bottom: 0;
-}
-
 p.admonition-title {
     margin: 0px 10px 5px 0px;
     font-weight: bold;
@@ -366,9 +367,34 @@ div.body p.centered {
     margin-top: 25px;
 }
 
+/* -- content of sidebars/topics/admonitions -------------------------------- */
+
+div.sidebar > :last-child,
+aside.sidebar > :last-child,
+nav.contents > :last-child,
+aside.topic > :last-child,
+div.topic > :last-child,
+div.admonition > :last-child {
+    margin-bottom: 0;
+}
+
+div.sidebar::after,
+aside.sidebar::after,
+nav.contents::after,
+aside.topic::after,
+div.topic::after,
+div.admonition::after,
+blockquote::after {
+    display: block;
+    content: '';
+    clear: both;
+}
+
 /* -- tables ---------------------------------------------------------------- */
 
 table.docutils {
+    margin-top: 10px;
+    margin-bottom: 10px;
     border: 0;
     border-collapse: collapse;
 }
@@ -398,10 +424,6 @@ table.docutils td, table.docutils th {
     border-bottom: 1px solid #aaa;
 }
 
-table.footnote td, table.footnote th {
-    border: 0 !important;
-}
-
 th {
     text-align: left;
     padding-right: 5px;
@@ -416,32 +438,34 @@ table.citation td {
     border-bottom: none;
 }
 
-th > p:first-child,
-td > p:first-child {
+th > :first-child,
+td > :first-child {
     margin-top: 0px;
 }
 
-th > p:last-child,
-td > p:last-child {
+th > :last-child,
+td > :last-child {
     margin-bottom: 0px;
 }
 
 /* -- figures --------------------------------------------------------------- */
 
-div.figure {
+div.figure, figure {
     margin: 0.5em;
     padding: 0.5em;
 }
 
-div.figure p.caption {
+div.figure p.caption, figcaption {
     padding: 0.3em;
 }
 
-div.figure p.caption span.caption-number {
+div.figure p.caption span.caption-number,
+figcaption span.caption-number {
     font-style: italic;
 }
 
-div.figure p.caption span.caption-text {
+div.figure p.caption span.caption-text,
+figcaption span.caption-text {
 }
 
 /* -- field list styles ----------------------------------------------------- */
@@ -468,10 +492,71 @@ table.field-list td, table.field-list th {
 
 /* -- hlist styles ---------------------------------------------------------- */
 
+table.hlist {
+    margin: 1em 0;
+}
+
 table.hlist td {
     vertical-align: top;
 }
 
+/* -- object description styles --------------------------------------------- */
+
+.sig {
+	font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
+}
+
+.sig-name, code.descname {
+    background-color: transparent;
+    font-weight: bold;
+}
+
+.sig-name {
+	font-size: 1.1em;
+}
+
+code.descname {
+    font-size: 1.2em;
+}
+
+.sig-prename, code.descclassname {
+    background-color: transparent;
+}
+
+.optional {
+    font-size: 1.3em;
+}
+
+.sig-paren {
+    font-size: larger;
+}
+
+.sig-param.n {
+	font-style: italic;
+}
+
+/* C++ specific styling */
+
+.sig-inline.c-texpr,
+.sig-inline.cpp-texpr {
+	font-family: unset;
+}
+
+.sig.c   .k, .sig.c   .kt,
+.sig.cpp .k, .sig.cpp .kt {
+	color: #0033B3;
+}
+
+.sig.c   .m,
+.sig.cpp .m {
+	color: #1750EB;
+}
+
+.sig.c   .s, .sig.c   .sc,
+.sig.cpp .s, .sig.cpp .sc {
+	color: #067D17;
+}
+
 
 /* -- other body styles ----------------------------------------------------- */
 
@@ -495,26 +580,52 @@ ol.upperroman {
     list-style: upper-roman;
 }
 
-li > p:first-child {
+:not(li) > ol > li:first-child > :first-child,
+:not(li) > ul > li:first-child > :first-child {
     margin-top: 0px;
 }
 
-li > p:last-child {
+:not(li) > ol > li:last-child > :last-child,
+:not(li) > ul > li:last-child > :last-child {
     margin-bottom: 0px;
 }
 
-dl.footnote > dt,
-dl.citation > dt {
-    float: left;
+ol.simple ol p,
+ol.simple ul p,
+ul.simple ol p,
+ul.simple ul p {
+    margin-top: 0;
 }
 
-dl.footnote > dd,
-dl.citation > dd {
-    margin-bottom: 0em;
+ol.simple > li:not(:first-child) > p,
+ul.simple > li:not(:first-child) > p {
+    margin-top: 0;
 }
 
-dl.footnote > dd:after,
-dl.citation > dd:after {
+ol.simple p,
+ul.simple p {
+    margin-bottom: 0;
+}
+aside.footnote > span,
+div.citation > span {
+    float: left;
+}
+aside.footnote > span:last-of-type,
+div.citation > span:last-of-type {
+  padding-right: 0.5em;
+}
+aside.footnote > p {
+  margin-left: 2em;
+}
+div.citation > p {
+  margin-left: 4em;
+}
+aside.footnote > p:last-of-type,
+div.citation > p:last-of-type {
+    margin-bottom: 0em;
+}
+aside.footnote > p:last-of-type:after,
+div.citation > p:last-of-type:after {
     content: "";
     clear: both;
 }
@@ -531,10 +642,6 @@ dl.field-list > dt {
     padding-right: 5px;
 }
 
-dl.field-list > dt:after {
-    content: ":";
-}
-
 dl.field-list > dd {
     padding-left: 0.5em;
     margin-top: 0em;
@@ -546,7 +653,7 @@ dl {
     margin-bottom: 15px;
 }
 
-dd > p:first-child {
+dd > :first-child {
     margin-top: 0px;
 }
 
@@ -560,6 +667,11 @@ dd {
     margin-left: 30px;
 }
 
+dl > dd:last-child,
+dl > dd:last-child > :last-child {
+    margin-bottom: 0;
+}
+
 dt:target, span.highlighted {
     background-color: #fbe54e;
 }
@@ -573,14 +685,6 @@ dl.glossary dt {
     font-size: 1.1em;
 }
 
-.optional {
-    font-size: 1.3em;
-}
-
-.sig-paren {
-    font-size: larger;
-}
-
 .versionmodified {
     font-style: italic;
 }
@@ -621,8 +725,9 @@ dl.glossary dt {
 
 .classifier:before {
     font-style: normal;
-    margin: 0.5em;
+    margin: 0 0.5em;
     content: ":";
+    display: inline-block;
 }
 
 abbr, acronym {
@@ -637,29 +742,69 @@ pre {
     overflow-y: hidden;  /* fixes display issues on Chrome browsers */
 }
 
+pre, div[class*="highlight-"] {
+    clear: both;
+}
+
 span.pre {
     -moz-hyphens: none;
     -ms-hyphens: none;
     -webkit-hyphens: none;
     hyphens: none;
+    white-space: nowrap;
+}
+
+div[class*="highlight-"] {
+    margin: 1em 0;
 }
 
 td.linenos pre {
-    padding: 5px 0px;
     border: 0;
     background-color: transparent;
     color: #aaa;
 }
 
 table.highlighttable {
-    margin-left: 0.5em;
+    display: block;
+}
+
+table.highlighttable tbody {
+    display: block;
+}
+
+table.highlighttable tr {
+    display: flex;
 }
 
 table.highlighttable td {
-    padding: 0 0.5em 0 0.5em;
+    margin: 0;
+    padding: 0;
+}
+
+table.highlighttable td.linenos {
+    padding-right: 0.5em;
+}
+
+table.highlighttable td.code {
+    flex: 1;
+    overflow: hidden;
+}
+
+.highlight .hll {
+    display: block;
+}
+
+div.highlight pre,
+table.highlighttable pre {
+    margin: 0;
+}
+
+div.code-block-caption + div {
+    margin-top: 0;
 }
 
 div.code-block-caption {
+    margin-top: 1em;
     padding: 2px 5px;
     font-size: small;
 }
@@ -668,12 +813,14 @@ div.code-block-caption code {
     background-color: transparent;
 }
 
-div.code-block-caption + div > div.highlight > pre {
-    margin-top: 0;
-}
-
-div.doctest > div.highlight span.gp {  /* gp: Generic.Prompt */
-    user-select: none;
+table.highlighttable td.linenos,
+span.linenos,
+div.highlight span.gp {  /* gp: Generic.Prompt */
+  user-select: none;
+  -webkit-user-select: text; /* Safari fallback only */
+  -webkit-user-select: none; /* Chrome/Safari */
+  -moz-user-select: none; /* Firefox */
+  -ms-user-select: none; /* IE10+ */
 }
 
 div.code-block-caption span.caption-number {
@@ -685,21 +832,7 @@ div.code-block-caption span.caption-text {
 }
 
 div.literal-block-wrapper {
-    padding: 1em 1em 0;
-}
-
-div.literal-block-wrapper div.highlight {
-    margin: 0;
-}
-
-code.descname {
-    background-color: transparent;
-    font-weight: bold;
-    font-size: 1.2em;
-}
-
-code.descclassname {
-    background-color: transparent;
+    margin: 1em 0;
 }
 
 code.xref, a code {
@@ -740,8 +873,7 @@ span.eqno {
 }
 
 span.eqno a.headerlink {
-    position: relative;
-    left: 0px;
+    position: absolute;
     z-index: 1;
 }
 
diff --git a/docs/build/html/_static/classic.css b/docs/build/html/_static/classic.css
deleted file mode 100644
index b4fd80f..0000000
--- a/docs/build/html/_static/classic.css
+++ /dev/null
@@ -1,266 +0,0 @@
-/*
- * classic.css_t
- * ~~~~~~~~~~~~~
- *
- * Sphinx stylesheet -- classic theme.
- *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
- * :license: BSD, see LICENSE for details.
- *
- */
-
-@import url("basic.css");
-
-/* -- page layout ----------------------------------------------------------- */
-
-html {
-    /* CSS hack for macOS's scrollbar (see #1125) */
-    background-color: #FFFFFF;
-}
-
-body {
-    font-family: sans-serif;
-    font-size: 100%;
-    background-color: #11303d;
-    color: #000;
-    margin: 0;
-    padding: 0;
-}
-
-div.document {
-    background-color: #1c4e63;
-}
-
-div.documentwrapper {
-    float: left;
-    width: 100%;
-}
-
-div.bodywrapper {
-    margin: 0 0 0 230px;
-}
-
-div.body {
-    background-color: #ffffff;
-    color: #000000;
-    padding: 0 20px 30px 20px;
-}
-
-div.footer {
-    color: #ffffff;
-    width: 100%;
-    padding: 9px 0 9px 0;
-    text-align: center;
-    font-size: 75%;
-}
-
-div.footer a {
-    color: #ffffff;
-    text-decoration: underline;
-}
-
-div.related {
-    background-color: #133f52;
-    line-height: 30px;
-    color: #ffffff;
-}
-
-div.related a {
-    color: #ffffff;
-}
-
-div.sphinxsidebar {
-}
-
-div.sphinxsidebar h3 {
-    font-family: 'Trebuchet MS', sans-serif;
-    color: #ffffff;
-    font-size: 1.4em;
-    font-weight: normal;
-    margin: 0;
-    padding: 0;
-}
-
-div.sphinxsidebar h3 a {
-    color: #ffffff;
-}
-
-div.sphinxsidebar h4 {
-    font-family: 'Trebuchet MS', sans-serif;
-    color: #ffffff;
-    font-size: 1.3em;
-    font-weight: normal;
-    margin: 5px 0 0 0;
-    padding: 0;
-}
-
-div.sphinxsidebar p {
-    color: #ffffff;
-}
-
-div.sphinxsidebar p.topless {
-    margin: 5px 10px 10px 10px;
-}
-
-div.sphinxsidebar ul {
-    margin: 10px;
-    padding: 0;
-    color: #ffffff;
-}
-
-div.sphinxsidebar a {
-    color: #98dbcc;
-}
-
-div.sphinxsidebar input {
-    border: 1px solid #98dbcc;
-    font-family: sans-serif;
-    font-size: 1em;
-}
-
-
-
-/* -- hyperlink styles ------------------------------------------------------ */
-
-a {
-    color: #355f7c;
-    text-decoration: none;
-}
-
-a:visited {
-    color: #355f7c;
-    text-decoration: none;
-}
-
-a:hover {
-    text-decoration: underline;
-}
-
-
-
-/* -- body styles ----------------------------------------------------------- */
-
-div.body h1,
-div.body h2,
-div.body h3,
-div.body h4,
-div.body h5,
-div.body h6 {
-    font-family: 'Trebuchet MS', sans-serif;
-    background-color: #f2f2f2;
-    font-weight: normal;
-    color: #20435c;
-    border-bottom: 1px solid #ccc;
-    margin: 20px -20px 10px -20px;
-    padding: 3px 0 3px 10px;
-}
-
-div.body h1 { margin-top: 0; font-size: 200%; }
-div.body h2 { font-size: 160%; }
-div.body h3 { font-size: 140%; }
-div.body h4 { font-size: 120%; }
-div.body h5 { font-size: 110%; }
-div.body h6 { font-size: 100%; }
-
-a.headerlink {
-    color: #c60f0f;
-    font-size: 0.8em;
-    padding: 0 4px 0 4px;
-    text-decoration: none;
-}
-
-a.headerlink:hover {
-    background-color: #c60f0f;
-    color: white;
-}
-
-div.body p, div.body dd, div.body li, div.body blockquote {
-    text-align: justify;
-    line-height: 130%;
-}
-
-div.admonition p.admonition-title + p {
-    display: inline;
-}
-
-div.admonition p {
-    margin-bottom: 5px;
-}
-
-div.admonition pre {
-    margin-bottom: 5px;
-}
-
-div.admonition ul, div.admonition ol {
-    margin-bottom: 5px;
-}
-
-div.note {
-    background-color: #eee;
-    border: 1px solid #ccc;
-}
-
-div.seealso {
-    background-color: #ffc;
-    border: 1px solid #ff6;
-}
-
-div.topic {
-    background-color: #eee;
-}
-
-div.warning {
-    background-color: #ffe4e4;
-    border: 1px solid #f66;
-}
-
-p.admonition-title {
-    display: inline;
-}
-
-p.admonition-title:after {
-    content: ":";
-}
-
-pre {
-    padding: 5px;
-    background-color: #eeffcc;
-    color: #333333;
-    line-height: 120%;
-    border: 1px solid #ac9;
-    border-left: none;
-    border-right: none;
-}
-
-code {
-    background-color: #ecf0f3;
-    padding: 0 1px 0 1px;
-    font-size: 0.95em;
-}
-
-th, dl.field-list > dt {
-    background-color: #ede;
-}
-
-.warning code {
-    background: #efc2c2;
-}
-
-.note code {
-    background: #d6d6d6;
-}
-
-.viewcode-back {
-    font-family: sans-serif;
-}
-
-div.viewcode-block:target {
-    background-color: #f4debf;
-    border-top: 1px solid #ac9;
-    border-bottom: 1px solid #ac9;
-}
-
-div.code-block-caption {
-    color: #efefef;
-    background-color: #1c4e63;
-}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/_common_adjust.css b/docs/build/html/_static/css/adjust_theme/_common_adjust.css
new file mode 100644
index 0000000..974e930
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/_common_adjust.css
@@ -0,0 +1,71 @@
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: {{ table_border_color }};
+}
+table.docutils tr {
+  color: {{ table_color }};
+  background-color: {{ table_background_color }} ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: {{ table_border_color }};
+}
+table.docutils tbody + tbody {
+  border-color: {{ table_border_color }};
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: {{ table_border_color }};
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: {{ warning_color }};
+  background-color: {{ warning_background_color }};
+  border-color: {{ warning_border_color }};
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: {{ danger_color }};
+  background-color: {{ danger_background_color }};
+  border-color: {{ danger_border_color }};
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: {{ warning_color }};
+  background-color: {{ warning_background_color }};
+  border-color: {{ warning_border_color }};
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: {{ note_color }};
+  background-color: {{ note_background_color }};
+  border-color: {{ note_border_color }};
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: {{ hint_color }};
+  background-color: {{ hint_background_color }};
+  border-color: {{ hint_border_color }};
+}
+
+div.topic {
+  background-color: {{ table_oddrow_color }};
+  border-color: {{ table_border_color }};
+}
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-amelia.css b/docs/build/html/_static/css/adjust_theme/bootswatch-amelia.css
new file mode 100644
index 0000000..155ad25
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-amelia.css
@@ -0,0 +1,134 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #357279;
+}
+table.docutils tr {
+  color: #fff;
+  background-color: #108a93 ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #357279;
+}
+table.docutils tbody + tbody {
+  border-color: #357279;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #357279;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #df6e1e;
+  border-color: #df6e1e;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #d5b321;
+  border-color: #d5b321;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #df6e1e;
+  border-color: #df6e1e;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #48ca3b;
+  border-color: #48ca3b;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #4d3a7d;
+  border-color: #4d3a7d;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #357279;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #00747d !important;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #00747d;
+  border: none;
+  box-shadow: none;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #00747d;
+ border-top: 1px solid #00747d;
+ border-bottom: 1px solid #00747d;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: #d92432;
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: #e5c953;
+   color: #ffffff;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-cerulean.css b/docs/build/html/_static/css/adjust_theme/bootswatch-cerulean.css
new file mode 100644
index 0000000..e9b91e6
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-cerulean.css
@@ -0,0 +1,118 @@
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #555;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: ;
+  background-color: ;
+  border-color: ;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: ;
+  background-color: ;
+  border-color: ;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: ;
+  background-color: ;
+  border-color: ;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: ;
+  background-color: ;
+  border-color: ;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: ;
+  background-color: ;
+  border-color: ;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #eeeeee !important;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #eeeeee;
+  border: 1px solid #eeeeee;
+  box-shadow: none;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #eeeeee;
+ border-top: 1px solid #eeeeee;
+ border-bottom: 1px solid #eeeeee;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: #178acc;
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: #022f5a;
+   color: #ffffff;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-cosmo.css b/docs/build/html/_static/css/adjust_theme/bootswatch-cosmo.css
new file mode 100644
index 0000000..5fa8833
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-cosmo.css
@@ -0,0 +1,135 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #333;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #ff7518;
+  border-color: transparent;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #ff0039;
+  border-color: transparent;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #ff7518;
+  border-color: transparent;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #3fb618;
+  border-color: #transparent;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #9954bb;
+  border-color: transparent;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #e6e6e6 !important;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #e6e6e6;
+  border: 1px solid #e6e6e6;
+  box-shadow: none;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #e6e6e6;
+ border-top: 1px solid #e6e6e6;
+ border-bottom: 1px solid #e6e6e6;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: #090909;
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: #0066cc;
+   color: #ffffff;
+}
+
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-cyborg.css b/docs/build/html/_static/css/adjust_theme/bootswatch-cyborg.css
new file mode 100644
index 0000000..b32cde3
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-cyborg.css
@@ -0,0 +1,145 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #222222;
+}
+table.docutils tr {
+  color: #888;
+  background-color: #060606 ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #222222;
+}
+table.docutils tbody + tbody {
+  border-color: #222222;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #222222;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #eeeeee;
+  background-color: #666666;
+  border-color: transparent;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #eeeeee;
+  background-color: #cc0000;
+  border-color: transparent;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #eeeeee;
+  background-color: #666666;
+  border-color: transparent;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #eeeeee;
+  background-color: #5c8a00;
+  border-color: #transparent;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #007399;
+  border-color: transparent;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #222222;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #282828 !important;
+}
+
+/* Field-list
+   ---------------------------------------------------------*/
+
+table.field-list {
+  background-color: #060606;
+}
+
+/* Citation
+   ---------------------------------------------------------*/
+
+table.citation{
+  background-color: #060606;
+}
+
+/* Footnote
+   ---------------------------------------------------------*/
+
+table.footnote {
+  background-color: #060606;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #222222;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #282828;
+ border-top: 1px solid #282828;
+ border-bottom: 1px solid #282828;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-darkly.css b/docs/build/html/_static/css/adjust_theme/bootswatch-darkly.css
new file mode 100644
index 0000000..0db84dd
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-darkly.css
@@ -0,0 +1,132 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #464545;
+}
+table.docutils tr {
+  color: #fff;
+  background-color: #222 ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #464545;
+}
+table.docutils tbody + tbody {
+  border-color: #464545;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #464545;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #f59d00;
+  border-color: #f59d00;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #e94b35;
+  border-color: #e94b35;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #f59d00;
+  border-color: #f59d00;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #00bd8b;
+  border-color: #00bd8b;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #2c97de;
+  border-color: #2c97de;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #464545;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #464545 !important;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #464545;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #464545;
+ border-top: 1px solid #464545;
+ border-bottom: 1px solid #464545;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: transparent;
+   color: #00bc8c;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: transparent;
+   color: #375a7f;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-flatly.css b/docs/build/html/_static/css/adjust_theme/bootswatch-flatly.css
new file mode 100644
index 0000000..b94f76d
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-flatly.css
@@ -0,0 +1,126 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #ecf0f1;
+}
+table.docutils tr {
+  color: #2c3e50;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #ecf0f1;
+}
+table.docutils tbody + tbody {
+  border-color: #ecf0f1;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #ecf0f1;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #ec9B00;
+  border-color: #ec9B00;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #dd4838;
+  border-color: #dd4838;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #ec9B00;
+  border-color: #ec9B00;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #40bc9c;
+  border-color: #40bc9c;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #4b99dc;
+  border-color: #4b99dc;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #ecf0f1;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #ecf0f1 !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #ecf0f1;
+ border-top: 1px solid #ecf0f1;
+ border-bottom: 1px solid #ecf0f1;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: transparent;
+   color: #00bc8c;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: transparent;
+   color: #2c3e50;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-journal.css b/docs/build/html/_static/css/adjust_theme/bootswatch-journal.css
new file mode 100644
index 0000000..e9f55e9
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-journal.css
@@ -0,0 +1,141 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #777777;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #f77400;
+  border-color: #f77400;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #ed6761;
+  border-color: #ed6761;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #f77400;
+  border-color: #f77400;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #11b446;
+  border-color: #11b446;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #306598;
+  border-color: #306598;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #eeeeee !important;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+ background-color: #eeeeee;
+ border-color: #eeeeee;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #eeeeee;
+ border-top: 1px solid #eeeeee;
+ border-bottom: 1px solid #eeeeee;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #000000;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: #eeeeee;
+   color: #000000;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: #e74b47;
+   color: #ffffff;
+}
+
+/* Etc
+   ---------------------------------------------------------*/
+
+div.navbar-inner ul.pull-right li a{
+    font-size: 15px;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-lumen.css b/docs/build/html/_static/css/adjust_theme/bootswatch-lumen.css
new file mode 100644
index 0000000..d40f583
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-lumen.css
@@ -0,0 +1,133 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #555;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #ff8500;
+  border-color: #ff8500;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #ff3f2c;
+  border-color: #ff3f2c;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #ff8500;
+  border-color: #ff8500;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #18B81D;
+  border-color: #18B81D;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #71CAED;
+  border-color: #71CAED;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #eeeeee !important;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #fafafa;
+  border-color: #eeeeee;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #eeeeee;
+ border-top: 1px solid #eeeeee;
+ border-bottom: 1px solid #eeeeee;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #999999;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: transparent;
+   color: #333333;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #999999;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: transparent;
+   color: #333333;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-paper.css b/docs/build/html/_static/css/adjust_theme/bootswatch-paper.css
new file mode 100644
index 0000000..6a2bcc6
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-paper.css
@@ -0,0 +1,91 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #666;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #f19842;
+  border-color: #f19842;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #d23f3c;
+  border-color: #d23f3c;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #f19842;
+  border-color: #f19842;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #69a858;
+  border-color: #69a858;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #8e45ab;
+  border-color: #8e45ab;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-readable.css b/docs/build/html/_static/css/adjust_theme/bootswatch-readable.css
new file mode 100644
index 0000000..e7847c1
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-readable.css
@@ -0,0 +1,145 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #333;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #f2ae43;
+  border-color: #f2ae43;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #db524b;
+  border-color: #db524b;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #f2ae43;
+  border-color: #f2ae43;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #39af40;
+  border-color: #39af40;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #56C0E0;
+  border-color: #56C0E0;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #eeeeee !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #eeeeee;
+ border-top: 1px solid #eeeeee;
+ border-bottom: 1px solid #eeeeee;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #f7f7f7;
+  border-color: #eeeeee;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   margin-left: 7px;
+   margin-right: 7px;
+   border: 1px solid transparent;
+   border-radius: 4px;
+   color: #4582ec;
+}
+ul.sp-localtoc ul a:hover{
+   border-color: #dddddd;
+   color: #4582ec;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #333333;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #333333;
+}
+
+
+/* Etc
+   ---------------------------------------------------------*/
+
+div.navbar-inner ul.pull-right li a{
+    font-size: 15px;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-sandstone.css b/docs/build/html/_static/css/adjust_theme/bootswatch-sandstone.css
new file mode 100644
index 0000000..470db3d
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-sandstone.css
@@ -0,0 +1,91 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #3e3f3a;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #e48353;
+  border-color: #e48353;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #c9605a;
+  border-color: #c9605a;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #e48353;
+  border-color: #e48353;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #9fbe5b;
+  border-color: #9fbe5b;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #55abda;
+  border-color: #55abda;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-simplex.css b/docs/build/html/_static/css/adjust_theme/bootswatch-simplex.css
new file mode 100644
index 0000000..6acc691
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-simplex.css
@@ -0,0 +1,133 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #777;
+  background-color: #fcfcfc ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #9c43a1;
+  border-color: #9c43a1;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #d88400;
+  border-color: #d88400;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #9c43a1;
+  border-color: #9c43a1;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #439500;
+  border-color: #439500;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #0099d1;
+  border-color: #0099d1;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #dddddd !important;
+}
+ 
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #dddddd;
+ border-top: 1px solid #dddddd;
+ border-bottom: 1px solid #dddddd;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #f4f4f4;
+  border: none;
+  box-shadow: none;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #333333;
+}
+ul.sp-localtoc ul a:hover{
+   color: #d9230f;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #fac0ba;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-slate.css b/docs/build/html/_static/css/adjust_theme/bootswatch-slate.css
new file mode 100644
index 0000000..665e09d
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-slate.css
@@ -0,0 +1,155 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #1c1e22;
+}
+table.docutils tr {
+  color: #c8c8c8;
+  background-color: #272b30 ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #1c1e22;
+}
+table.docutils tbody + tbody {
+  border-color: #1c1e22;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #1c1e22;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #fa9500;
+  border-color: #eb6500;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #f05e57;
+  border-color: #ef4b60;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #fa9500;
+  border-color: #eb6500;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #468847;
+  border-color: #5ec65d;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #56C0E0;
+  border-color: #31ced9;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #1c1e22;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #1c1e22 !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #1c1e22;
+ border-top: 1px solid #1c1e22;
+ border-bottom: 1px solid #1c1e22;
+}
+
+
+/* Field-list
+   ---------------------------------------------------------*/
+
+table.field-list {
+  background-color: #272B30;
+}
+
+/* Citation
+   ---------------------------------------------------------*/
+
+table.citation{
+  background-color: #272B30;
+}
+
+/* Footnote
+   ---------------------------------------------------------*/
+
+table.footnote {
+  background-color: #272B30;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #1c1e22;
+  border-color: #0b0b0d;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #c8c8c8;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: #272b2e;
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #c8c8c8;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: #272b2e;
+   color: #ffffff;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-solar.css b/docs/build/html/_static/css/adjust_theme/bootswatch-solar.css
new file mode 100644
index 0000000..a70279b
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-solar.css
@@ -0,0 +1,155 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #1c1e22;
+}
+table.docutils tr {
+  color: #839496;
+  background-color: #002b36 ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #1c1e22;
+}
+table.docutils tbody + tbody {
+  border-color: #1c1e22;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #1c1e22;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #fa9500;
+  border-color: #eb6500;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #f05e57;
+  border-color: #ef4b60;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #fa9500;
+  border-color: #eb6500;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #468847;
+  border-color: #5ec65d;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: rgba(255, 255, 255, 0.9);
+  background-color: #56C0E0;
+  border-color: #31ced9;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #1c1e22;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #1c1e22 !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #1c1e22;
+ border-top: 1px solid #1c1e22;
+ border-bottom: 1px solid #1c1e22;
+}
+
+
+/* Field-list
+   ---------------------------------------------------------*/
+
+table.field-list {
+  background-color: #272B30;
+}
+
+/* Citation
+   ---------------------------------------------------------*/
+
+table.citation{
+  background-color: #272B30;
+}
+
+/* Footnote
+   ---------------------------------------------------------*/
+
+table.footnote {
+  background-color: #272B30;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #1c1e22;
+  border-color: #0b0b0d;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #c8c8c8;
+}
+ul.sp-localtoc ul a:hover{
+   background-color: #272b2e;
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #c8c8c8;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   background-color: #272b2e;
+   color: #ffffff;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-spacelab.css b/docs/build/html/_static/css/adjust_theme/bootswatch-spacelab.css
new file mode 100644
index 0000000..969df6e
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-spacelab.css
@@ -0,0 +1,144 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #666;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #d47500;
+  border-color: #c54c00;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #cd0200;
+  border-color: #be001e;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #d47500;
+  border-color: #c54c00;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #3cb521;
+  border-color: #4b9f1d;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #3399f3;
+  border-color: #11adf1;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #eeeeee !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #eeeeee;
+ border-top: 1px solid #eeeeee;
+ border-bottom: 1px solid #eeeeee;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #eeeeee;
+  border: none;
+  box-shadow: none;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #777777;
+}
+ul.sp-localtoc ul a:hover{
+   color: #3399f3;
+   -webkit-transition: color ease-in-out .2s;
+   transition: color ease-in-out .2s;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #c8c8c8;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+   -webkit-transition: color ease-in-out .2s;
+   transition: color ease-in-out .2s;
+}
+
+/* Etc
+   ---------------------------------------------------------*/
+
+div.navbar-inner ul.pull-right li a{
+    font-size: 12px;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-spruce.css b/docs/build/html/_static/css/adjust_theme/bootswatch-spruce.css
new file mode 100644
index 0000000..dd840b0
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-spruce.css
@@ -0,0 +1,108 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+div.navbar-inner ul.pull-right li a{
+    font-size: 15px;
+}
+
+@media (max-width: 480px) {
+    a.brand {
+        line-height: 25px;
+    }
+}
+
+table.docutils th.head {
+    background-color: #015b4e;
+color: #fff;
+}
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #999999;
+}
+table.docutils tr {
+  color: #555;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #999999;
+}
+table.docutils tbody + tbody {
+  border-color: #999999;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #999999;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #f26522;
+  border-color: #f13614;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #d14432;
+  border-color: #c72d35;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #f26522;
+  border-color: #f13614;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #24c00b;
+  border-color: #3aa80a;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #185af9;
+  border-color: #066ee7;
+}
+
+div.topic {
+  background-color: #eaeaea;;
+  border-color: #999999;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-superhero.css b/docs/build/html/_static/css/adjust_theme/bootswatch-superhero.css
new file mode 100644
index 0000000..f400aee
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-superhero.css
@@ -0,0 +1,194 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #4d5d6d;
+}
+table.docutils tr {
+  color: #ebebeb;
+  background-color: #2b3e50 ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #4d5d6d;
+}
+table.docutils tbody + tbody {
+  border-color: #4d5d6d;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #4d5d6d;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #f2ae43;
+  border-color: #f2ae43;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #db524b;
+  border-color: #db524b;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #f2ae43;
+  border-color: #f2ae43;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #58b957;
+  border-color: #58b957;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #56c0e0;
+  border-color: #56c0e0;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #4d5d6d;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #4d5d6d !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #4d5d6d;
+ border-top: 1px solid #4d5d6d;
+ border-bottom: 1px solid #4d5d6d;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #4d5d6d;
+  border: none;
+  box-shadow: none;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   font-size: 12px;
+   color: #ebebeb;
+}
+ul.sp-localtoc ul a:hover{
+   color: #ebebeb;
+   background-color: #485563;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ebebeb;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #ebebeb;
+   background-color: #c85e17;
+}
+
+/* Code
+   ---------------------------------------------------------*/
+
+code, pre {
+    padding:0 3px 2px;
+    font-family:Menlo,Monaco,Consolas,"Courier New",monospace;
+    font-size:12px;
+    color:#3a3f44;
+    -webkit-border-radius:3px;
+    -moz-border-radius:3px;
+    border-radius:3px;
+}
+code{
+    padding:2px 4px;
+    color:#d14;
+    background-color:#f7f7f9;
+    border:1px solid #e1e1e8;
+    white-space:nowrap;
+}
+pre{
+    display:block;
+    padding:10px;
+    margin:0 0 10.5px;
+    font-size:13px;
+    line-height:21px;
+    word-break:break-all;
+    word-wrap:break-word;
+    white-space:pre;
+    white-space:pre-wrap;
+    background-color:#f5f5f5;
+    border:1px solid #ccc;
+    border:1px solid rgba(0, 0, 0, 0.15);
+    -webkit-border-radius:4px;
+    -moz-border-radius:4px;
+    border-radius:4px;
+}
+pre.prettyprint{
+    margin-bottom:21px;
+}
+pre code{
+    padding:0;
+    color:inherit;
+    white-space:pre;
+    white-space:pre-wrap;
+    background-color:transparent;
+    border:0;
+}
+
+div.navbar-inner ul.pull-right li a{
+    font-size: 15px;
+}
+
+
+@media (max-width: 480px) {
+  a.brand {
+      line-height: 30px;
+  }
+}
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-united.css b/docs/build/html/_static/css/adjust_theme/bootswatch-united.css
new file mode 100644
index 0000000..a269fc1
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-united.css
@@ -0,0 +1,134 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #333;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #f0b82d;
+  border-color: #f0b82d;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #e13622;
+  border-color: #e13622;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #f0b82d;
+  border-color: #f0b82d;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #30b644;
+  border-color: #30b644;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #782753;
+  border-color: #782753;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #eeeeee !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #eeeeee;
+ border-top: 1px solid #eeeeee;
+ border-bottom: 1px solid #eeeeee;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #eeeeee;
+  border: none;
+  box-shadow: none;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+   background-color: #97310e;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+   background-color: #3e152b;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/bootswatch-yeti.css b/docs/build/html/_static/css/adjust_theme/bootswatch-yeti.css
new file mode 100644
index 0000000..3ffc9fb
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/bootswatch-yeti.css
@@ -0,0 +1,134 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #dddddd;
+}
+table.docutils tr {
+  color: #222;
+  background-color: #fff ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #dddddd;
+}
+table.docutils tbody + tbody {
+  border-color: #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #dddddd;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #ffffff;
+  background-color: #eb9100;
+  border-color: #d28100;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #f33f13;
+  border-color: #ed2c00;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #ffffff;
+  background-color: #eb9100;
+  border-color: #d28100;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #3ead68;
+  border-color: #379b5d;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #ffffff;
+  background-color: #56c0e0;
+  border-color: #3ab5da;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #dddddd;
+}
+
+/* Heading
+   ---------------------------------------------------------*/
+
+h2, h3, h4, h5, h6 {
+ border-bottom: 1px solid #dddddd !important;
+}
+
+/* Genindex
+   ---------------------------------------------------------*/
+
+div.genindex-jumpbox {
+ color: #dddddd;
+ border-top: 1px solid #dddddd;
+ border-bottom: 1px solid #dddddd;
+}
+
+/* Contents
+   ---------------------------------------------------------*/
+
+div.contents {
+  background-color: #fafafa;
+  border: none;
+  box-shadow: none;
+}
+
+/* Smartphone Local Toc
+   ---------------------------------------------------------*/
+
+ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+   background-color: #272727;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #ffffff;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+   background-color: #006687;
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/css/adjust_theme/geo-bootstrap.css b/docs/build/html/_static/css/adjust_theme/geo-bootstrap.css
new file mode 100644
index 0000000..26d833d
--- /dev/null
+++ b/docs/build/html/_static/css/adjust_theme/geo-bootstrap.css
@@ -0,0 +1,105 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table.docutils {
+  border-color: #228000;
+}
+table.docutils tr {
+  color: ;
+  background-color:  ;
+}
+table.docutils th,
+table.docutils td
+{
+  border-color: #228000;
+}
+table.docutils tbody + tbody {
+  border-color: #228000;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-color: #228000;
+}
+
+/* -- admonition -- */
+div.admonition {
+  color: #000000;
+  background-color: #fcfe00;
+  border-color: #f40000;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #ffffff;
+  background-color: #f40000;
+  border-color: #a20000;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+  color: #000000;
+  background-color: #fcfe00;
+  border-color: #f40000;
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #ffffff;
+  background-color: #228000;
+  border-color: #2faa00;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #000000;
+  background-color: #57ffff;
+  border-color: #a8a900;
+}
+
+div.topic {
+  background-color: ;
+  border-color: #228000;
+}
+
+table.docutils {
+  -webkit-border-radius: 0px;
+  -moz-border-radius: 0px;
+  border-radius: 0px;
+}
+
+div.admonition {
+  -webkit-border-radius: 0px;
+  -moz-border-radius: 0px;
+  border-radius: 0px;
+}
+
+div.topic {
+  background: url("../../img/stars.gif") !important;
+}
diff --git a/docs/build/html/_static/css/basicstrap-base.css b/docs/build/html/_static/css/basicstrap-base.css
new file mode 100644
index 0000000..81f8a7d
--- /dev/null
+++ b/docs/build/html/_static/css/basicstrap-base.css
@@ -0,0 +1,381 @@
+@import url("../basic.css");
+
+
+/* Table
+   ---------------------------------------------------------*/
+
+table {
+  border: 0;
+  max-width: 100%;
+  background-color: transparent;
+  border-collapse: collapse;
+  border-spacing: 0 !important;
+}
+
+table.docutils {
+  width: 100%;
+  margin-bottom: 20px;
+  border: 1px solid #dddddd;
+  border-collapse: separate;
+  *border-collapse: collapse;
+  border-left: 0;
+  border-right: 0;
+}
+
+table.docutils tr {
+  color: #333;
+  background-color: #fff;
+}
+
+table.docutils th {
+  font-weight: bold;
+}
+table.docutils th,
+table.docutils td
+{
+  padding: 8px;
+  line-height: 20px;
+  text-align: left;
+  vertical-align: top;
+  border: none;
+  border-spacing: 0 !important;
+  border-collapse: none;
+  border-top: 1px solid #dddddd;
+}
+table.docutils caption + thead tr:first-child th,
+table.docutils caption + tbody tr:first-child th,
+table.docutils caption + tbody tr:first-child td,
+table.docutils colgroup + thead tr:first-child th,
+table.docutils colgroup + tbody tr:first-child th,
+table.docutils colgroup + tbody tr:first-child td,
+table.docutils thead:first-child tr:first-child th,
+table.docutils tbody:first-child tr:first-child th,
+table.docutils tbody:first-child tr:first-child td {
+  border-top: 0;
+}
+table.docutils thead th {
+  vertical-align: bottom;
+}
+table.docutils tbody + tbody {
+  border-top: 2px solid #dddddd;
+}
+
+/* Table-bordered
+   ---------------------------------------------------------*/
+
+table.table-bordered {
+  border-top: 1px solid #dddddd;
+  border-left: 1px solid #dddddd;
+  border-right: none;
+}
+table.table-bordered > thead > tr > th,
+table.table-bordered > tbody > tr > th,
+table.table-bordered > tfoot > tr > th,
+table.table-bordered > thead > tr > td,
+table.table-bordered > tbody > tr > td,
+table.table-bordered > tfoot > tr > td {
+  border-left: none;
+  border-bottom-width: 0;
+}
+
+/* Highlight Table
+   ---------------------------------------------------------*/
+
+.highlighttable {
+  width: 100%;
+}
+
+.highlighttable .code pre {
+  font-size: 12px;
+}
+
+.highlighttable .code {
+  max-width: 0;
+}
+
+.highlighttable .linenos {
+    width: 1%;
+}
+.highlighttable .linenos pre {
+    word-break: normal;
+    font-size: 12px;
+}
+
+.literal-block-wrapper {
+ padding: 0;
+}
+
+
+div.highlight {
+  background: none;
+}
+
+/* Field-list
+   ---------------------------------------------------------*/
+
+table.field-list {
+  width: auto;
+  border: none;
+}
+
+/* Citation
+   ---------------------------------------------------------*/
+
+table.citation{
+    width: auto;
+    margin-bottom: 0;
+    border: none;
+}
+table.citation td.label {
+  font-size: 100%;
+  display: block;
+  line-height: normal;
+  background: inherit;
+}
+
+/* Footnote
+   ---------------------------------------------------------*/
+
+a.footnote-reference {
+  vertical-align: super;
+  font-size: 75%;
+}
+
+table.footnote td.label {
+  font-size: 100%;
+  display: block;
+  line-height: normal;
+  background: inherit;
+}
+
+table.footnote {
+  width: auto;
+  margin-bottom: 0px;
+  border: none;
+}
+
+
+/* Footer
+   ---------------------------------------------------------*/
+
+footer {
+  width: 100%;
+  margin: 0;
+  text-align: center;
+  padding: 0px;
+  padding-left: auto;
+  padding-right: auto;
+}
+
+/*  Sidebar
+    ------------------------------------------------------- */
+div.sidebar {
+  border: none;
+  margin: 0;
+  padding: 0;
+  background: none;
+  width: 100%;
+  float: none;
+}
+
+div.sidebar ul:second-child {
+  color: red;
+  background-color: #000 !important;
+  list-style: none !important;
+}
+
+/* Definition lists
+   ----------------------------------------------------------- */
+
+dl dd {
+ padding-left: 1em;
+}
+
+/* Admonition styles
+   ----------------------------------------------------------- */
+div.admonition {
+  padding: 0.5em 2.5em 0.5em 1em;
+  margin-bottom: 20px;
+  color: #c09853;
+  text-shadow: 0 1px 0 rgba(255, 255, 255, 0.5);
+  background-color: #fcf8e3;
+  border: 1px solid #fbeed5;
+  -webkit-border-radius: 4px;
+     -moz-border-radius: 4px;
+          border-radius: 4px;
+}
+
+div.admonition p {
+  padding: 0;
+}
+
+div.admonition p.admonition-title {
+  margin: 0;
+  padding: 0.1em 0 0.1em 0;
+  font-weight: bold;
+}
+
+div.admonition ul, div.admonition ol {
+  padding: 0.1em 0.5em 0.5em 2em;
+}
+
+/* -- danger, error -- */
+div.danger,
+div.error {
+  color: #b94a48;
+  background-color: #f2dede;
+  border-color: #eed3d7;
+}
+
+/* -- warning, caution, attention -- */
+div.warning,
+div.caution,
+div.attention {
+}
+
+div.warning table.docutils,
+div.warning table.docutils th,
+div.warning table.docutils td,
+div.caution table.docutils,
+div.caution table.docutils th,
+div.caution table.docutils td,
+div.attention table.docutils,
+div.attention table.docutils th,
+div.attention table.docutils td {
+}
+
+div.warning blockquote,
+div.caution blockquote,
+div.attention blockquote {
+}
+
+/* -- note, important -- */
+div.note,
+div.important {
+  color: #468847;
+  background-color: #dff0d8;
+  border-color: #d6e9c6;
+}
+
+/* -- hint, tip -- */
+div.hint,
+div.tip {
+  color: #3a87ad;
+  background-color: #d9edf7;
+  border-color: #bce8f1;
+}
+
+
+
+/* Etc
+   ----------------------------------------------------------- */
+
+div.figure-round img {
+  -webkit-border-radius: 6px;
+     -moz-border-radius: 6px;
+          border-radius: 6px;
+}
+
+div.figure-polaroid img{
+  padding: 4px;
+  background-color: #fff;
+  border: 1px solid #ccc;
+  border: 1px solid rgba(0, 0, 0, 0.2);
+  -webkit-box-shadow: 0 1px 3px rgba(0, 0, 0, 0.1);
+     -moz-box-shadow: 0 1px 3px rgba(0, 0, 0, 0.1);
+          box-shadow: 0 1px 3px rgba(0, 0, 0, 0.1);
+}
+
+div.figure-circle img {
+  -webkit-border-radius: 500px;
+     -moz-border-radius: 500px;
+          border-radius: 500px;
+}
+
+a.headerlink {
+ font-size: 60% !important;
+ padding-left: 5px;
+}
+
+/*
+#searchbox .search-query {
+  width: 60%;
+}
+*/
+
+div.topic {
+  min-height: 20px;
+  padding: 9px;
+  margin-bottom: 20px;
+
+  background-color: #f5f5f5;
+  border: 1px solid #e3e3e3;
+
+  -webkit-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
+     -moz-box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
+          box-shadow: inset 0 1px 1px rgba(0, 0, 0, 0.05);
+  -webkit-border-radius: 3px;
+     -moz-border-radius: 3px;
+          border-radius: 3px;
+}
+
+ul.sp-localtoc {
+   list-style: none;
+   padding: 0;
+}
+ul.sp-localtoc ul{
+   list-style: none;
+   padding-left: 0;
+}
+ul.sp-localtoc ul a{
+   padding-left: 15px;
+   padding-top:7px;
+   padding-bottom:7px;
+   display: block;
+   text-decoration: none;
+   color: #777777;
+}
+ul.sp-localtoc ul a:hover{
+   color: #555555;
+}
+ul.sp-localtoc ul ul{
+   list-style: none;
+}
+ul.sp-localtoc ul ul a{
+   padding-left: 25px;
+}
+ul.sp-localtoc ul ul ul a{
+   padding-left: 35px;
+}
+ul.sp-localtoc ul ul ul ul a{
+   padding-left: 45px;
+}
+ul.sp-localtoc ul ul ul ul ul a{
+   padding-left: 55px;
+}
+ul.sp-localtoc ul ul ul ul ul a{
+   padding-left: 65px;
+}
+div.navbar-inverse ul.sp-localtoc ul a{
+   color: #999999;
+}
+div.navbar-inverse ul.sp-localtoc ul a:hover{
+   color: #ffffff;
+}
+
+
+div.footer-relbar {
+  margin-top:10px;
+}
+
+div.sidebar ul {
+    list-style: none;
+    padding-left: 10px;
+}
+div.sidebar ul ul {
+    list-style: initial;
+    padding-left: 40px;
+}
+div.sidebar p.topless {
+    padding-left: 10px;
+}
diff --git a/docs/build/html/_static/css/basicstrap.css b/docs/build/html/_static/css/basicstrap.css
new file mode 100644
index 0000000..8bac6bb
--- /dev/null
+++ b/docs/build/html/_static/css/basicstrap.css
@@ -0,0 +1,91 @@
+/*  Bootstrap
+    ------------------------------------------------------- */
+
+/*  apply font awesome
+    ------------------------------------------------------- */
+
+div.danger p.admonition-title:before,
+div.error p.admonition-title:before,
+div.warning p.admonition-title:before,
+div.caution p.admonition-title:before,
+div.attention p.admonition-title:before,
+div.important p.admonition-title:before,
+div.note p.admonition-title:before,
+div.hint p.admonition-title:before,
+div.tip p.admonition-title:before
+{
+  display: inline-block;
+  font-family: FontAwesome;
+  font-style: normal;
+  font-weight: normal;
+  line-height: 1;
+  -webkit-font-smoothing: antialiased;
+  -moz-osx-font-smoothing: grayscale;
+}
+
+div.danger p.admonition-title:before,
+div.error p.admonition-title:before {
+  content: "\f06a\00a0";
+}
+div.warning p.admonition-title:before,
+div.caution p.admonition-title:before,
+div.attention p.admonition-title:before {
+  content: "\f071\00a0";
+}
+div.important p.admonition-title:before,
+div.note p.admonition-title:before {
+  content: "\f05a\00a0";
+}
+div.hint p.admonition-title:before,
+div.tip p.admonition-title:before {
+  content: "\f0eb\00a0";
+}
+
+h2, h3, h4, h5, h6 {
+ padding-bottom: 10px;
+ border-bottom: 1px solid #d0d0d0;
+}
+
+
+/* for tablet */
+@media (max-width: 767px) {
+  form.sp-searchbox div.input-append {
+    margin-top: 10px;
+    margin-left: 12px;
+  }
+  form.sp-searchbox div.input-append {
+    width: 90%;
+    
+  }
+  form.sp-searchbox input.search-query {
+    width: 100%;
+  }
+}
+
+/* for smartphone */
+@media (max-width: 480px) {
+  a.brand {
+    width: 80%;
+  }
+  a.navbar-brand {
+    width: 80%;
+    height: 100%;
+  }
+  .searchbox .search-query {
+    width: 90%;
+  }
+}
+
+/* for desktop */
+@media (min-width: 768px) {
+  
+  .navbar-inner div.container {
+    width: 900px;
+  }
+  
+  
+  div.container {
+    width: 900px;
+  }
+  
+}
diff --git a/docs/build/html/_static/css/bootstrap2/bootstrap-responsive.min.css b/docs/build/html/_static/css/bootstrap2/bootstrap-responsive.min.css
new file mode 100644
index 0000000..f4ede63
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootstrap-responsive.min.css
@@ -0,0 +1,9 @@
+/*!
+ * Bootstrap Responsive v2.3.2
+ *
+ * Copyright 2012 Twitter, Inc
+ * Licensed under the Apache License v2.0
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Designed and built with all the love in the world @twitter by @mdo and @fat.
+ */.clearfix{*zoom:1}.clearfix:before,.clearfix:after{display:table;line-height:0;content:""}.clearfix:after{clear:both}.hide-text{font:0/0 a;color:transparent;text-shadow:none;background-color:transparent;border:0}.input-block-level{display:block;width:100%;min-height:30px;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}@-ms-viewport{width:device-width}.hidden{display:none;visibility:hidden}.visible-phone{display:none!important}.visible-tablet{display:none!important}.hidden-desktop{display:none!important}.visible-desktop{display:inherit!important}@media(min-width:768px) and 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[class*="span"]:first-child{margin-left:0}.row-fluid .controls-row [class*="span"]+[class*="span"]{margin-left:2.564102564102564%}.row-fluid .span12{width:100%;*width:99.94680851063829%}.row-fluid .span11{width:91.45299145299145%;*width:91.39979996362975%}.row-fluid .span10{width:82.90598290598291%;*width:82.8527914166212%}.row-fluid .span9{width:74.35897435897436%;*width:74.30578286961266%}.row-fluid .span8{width:65.81196581196582%;*width:65.75877432260411%}.row-fluid .span7{width:57.26495726495726%;*width:57.21176577559556%}.row-fluid .span6{width:48.717948717948715%;*width:48.664757228587014%}.row-fluid .span5{width:40.17094017094017%;*width:40.11774868157847%}.row-fluid .span4{width:31.623931623931625%;*width:31.570740134569924%}.row-fluid .span3{width:23.076923076923077%;*width:23.023731587561375%}.row-fluid .span2{width:14.52991452991453%;*width:14.476723040552828%}.row-fluid .span1{width:5.982905982905983%;*width:5.929714493544281%}.row-fluid 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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-amelia.css b/docs/build/html/_static/css/bootstrap2/bootswatch-amelia.css
new file mode 100644
index 0000000..cc2e477
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-amelia.css
@@ -0,0 +1,9 @@
+@import url('//fonts.googleapis.com/css?family=Lobster|Cabin:400,700');/*!
+ * Bootstrap v2.3.2
+ *
+ * Copyright 2013 Twitter, Inc
+ * Licensed under the Apache License v2.0
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Designed and built with all the love in the world by @mdo and @fat.
+ */.clearfix{*zoom:1}.clearfix:before,.clearfix:after{display:table;line-height:0;content:""}.clearfix:after{clear:both}.hide-text{font:0/0 a;color:transparent;text-shadow:none;background-color:transparent;border:0}.input-block-level{display:block;width:100%;min-height:30px;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}article,aside,details,figcaption,figure,footer,header,hgroup,nav,section{display:block}audio,canvas,video{display:inline-block;*display:inline;*zoom:1}audio:not([controls]){display:none}html{font-size:100%;-webkit-text-size-adjust:100%;-ms-text-size-adjust:100%}a:focus{outline:thin dotted #333;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}a:hover,a:active{outline:0}sub,sup{position:relative;font-size:75%;line-height:0;vertical-align:baseline}sup{top:-0.5em}sub{bottom:-0.25em}img{width:auto\9;height:auto;max-width:100%;vertical-align:middle;border:0;-ms-interpolation-mode:bicubic}#map_canvas img,.google-maps 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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-cerulean.css b/docs/build/html/_static/css/bootstrap2/bootswatch-cerulean.css
new file mode 100644
index 0000000..9740c15
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-cerulean.css
@@ -0,0 +1,9 @@
+@import url(//fonts.googleapis.com/css?family=Telex);/*!
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+ * Licensed under the Apache License v2.0
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+ *
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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-cosmo.css b/docs/build/html/_static/css/bootstrap2/bootswatch-cosmo.css
new file mode 100644
index 0000000..1ca451d
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-cosmo.css
@@ -0,0 +1,9 @@
+@import url('//fonts.googleapis.com/css?family=Open+Sans:400italic,700italic,400,700');/*!
+ * Bootstrap v2.3.2
+ *
+ * Copyright 2013 Twitter, Inc
+ * Licensed under the Apache License v2.0
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Designed and built with all the love in the world by @mdo and @fat.
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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-cyborg.css b/docs/build/html/_static/css/bootstrap2/bootswatch-cyborg.css
new file mode 100644
index 0000000..dbaf2d5
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-cyborg.css
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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-flatly.css b/docs/build/html/_static/css/bootstrap2/bootswatch-flatly.css
new file mode 100644
index 0000000..c6923a9
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-flatly.css
@@ -0,0 +1,9 @@
+@import url("//fonts.googleapis.com/css?family=Lato:400,700,900,400italic");/*!
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+ *
+ * Copyright 2013 Twitter, Inc
+ * Licensed under the Apache License v2.0
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+ *
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new file mode 100644
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new file mode 100644
index 0000000..0efc48f
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-readable.css
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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-simplex.css b/docs/build/html/_static/css/bootstrap2/bootswatch-simplex.css
new file mode 100644
index 0000000..a3e828f
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-simplex.css
@@ -0,0 +1,9 @@
+@import url('//fonts.googleapis.com/css?family=Josefin+Sans:300,400,700');/*!
+ * Bootstrap v2.3.2
+ *
+ * Copyright 2012 Twitter, Inc
+ * Licensed under the Apache License v2.0
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Designed and built with all the love in the world @twitter by @mdo and @fat.
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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-slate.css b/docs/build/html/_static/css/bootstrap2/bootswatch-slate.css
new file mode 100644
index 0000000..40746a2
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-slate.css
@@ -0,0 +1,9 @@
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+ *
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diff --git a/docs/build/html/_static/css/bootstrap2/bootswatch-spacelab.css b/docs/build/html/_static/css/bootstrap2/bootswatch-spacelab.css
new file mode 100644
index 0000000..1075a46
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/bootswatch-spacelab.css
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new file mode 100644
index 0000000..6d5279c
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new file mode 100644
index 0000000..29cb6b6
--- /dev/null
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diff --git a/docs/build/html/_static/css/bootstrap2/geo-bootstrap.css b/docs/build/html/_static/css/bootstrap2/geo-bootstrap.css
new file mode 100644
index 0000000..4348685
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap2/geo-bootstrap.css
@@ -0,0 +1,9 @@
+/*!
+ * Bootstrap v2.3.1
+ *
+ * Copyright 2012 Twitter, Inc
+ * Licensed under the Apache License v2.0
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Designed and built with all the love in the world @twitter by @mdo and @fat.
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diff --git a/docs/build/html/_static/css/bootstrap3/bootstrap-non-responsive.css b/docs/build/html/_static/css/bootstrap3/bootstrap-non-responsive.css
new file mode 100644
index 0000000..9311ee6
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootstrap-non-responsive.css
@@ -0,0 +1,82 @@
+/* Template-specific stuff
+ *
+ * Customizations just for the template; these are not necessary for anything
+ * with disabling the responsiveness.
+ */
+
+/* Account for fixed navbar */
+body {
+  min-width: 970px;
+}
+
+/* Finesse the page header spacing */
+.page-header {
+  margin-bottom: 30px;
+}
+.page-header .lead {
+  margin-bottom: 10px;
+}
+
+
+/* Non-responsive overrides
+ *
+ * Utilitze the following CSS to disable the responsive-ness of the container,
+ * grid system, and navbar.
+ */
+/* Reset the container */
+.container {
+  width: 970px;
+  max-width: none !important;
+}
+
+/* Demonstrate the grids */
+.col-xs-3 {
+}
+
+.container .navbar-header,
+.container .navbar-collapse {
+  margin-right: 0;
+  margin-left: 0;
+}
+
+/* Always float the navbar header */
+.navbar-header {
+  float: left;
+}
+
+/* Undo the collapsing navbar */
+.navbar-collapse {
+  display: block !important;
+  height: auto !important;
+  padding-bottom: 0;
+  overflow: visible !important;
+}
+.navbar-toggle {
+  display: none;
+}
+.navbar-collapse {
+  border-top: 0;
+}
+.navbar-brand {
+  margin-left: -15px;
+}
+/* Always apply the floated nav */
+.navbar-nav {
+  float: left;
+  margin: 0;
+}
+.navbar-nav > li {
+  float: left;
+}
+.navbar-nav > li > a {
+  padding: 15px;
+}
+/* Redeclare since we override the float above */
+.navbar-nav.navbar-right {
+  float: right;
+}
+/* Undo custom dropdowns */
+.navbar .navbar-nav .open .dropdown-menu {
+  position: absolute;
+  float: left;
+}
diff --git a/docs/build/html/_static/css/bootstrap3/bootstrap-theme.min.css b/docs/build/html/_static/css/bootstrap3/bootstrap-theme.min.css
new file mode 100644
index 0000000..cefa3d1
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootstrap-theme.min.css
@@ -0,0 +1,5 @@
+/*!
+ * Bootstrap v3.3.4 (http://getbootstrap.com)
+ * Copyright 2011-2015 Twitter, Inc.
+ * Licensed under MIT (https://github.com/twbs/bootstrap/blob/master/LICENSE)
+ */.btn-danger,.btn-default,.btn-info,.btn-primary,.btn-success,.btn-warning{text-shadow:0 -1px 0 rgba(0,0,0,.2);-webkit-box-shadow:inset 0 1px 0 rgba(255,255,255,.15),0 1px 1px rgba(0,0,0,.075);box-shadow:inset 0 1px 0 rgba(255,255,255,.15),0 1px 1px rgba(0,0,0,.075)}.btn-danger.active,.btn-danger:active,.btn-default.active,.btn-default:active,.btn-info.active,.btn-info:active,.btn-primary.active,.btn-primary:active,.btn-success.active,.btn-success:active,.btn-warning.active,.btn-warning:active{-webkit-box-shadow:inset 0 3px 5px rgba(0,0,0,.125);box-shadow:inset 0 3px 5px rgba(0,0,0,.125)}.btn-danger .badge,.btn-default .badge,.btn-info .badge,.btn-primary .badge,.btn-success .badge,.btn-warning .badge{text-shadow:none}.btn.active,.btn:active{background-image:none}.btn-default{text-shadow:0 1px 0 #fff;background-image:-webkit-linear-gradient(top,#fff 0,#e0e0e0 100%);background-image:-o-linear-gradient(top,#fff 0,#e0e0e0 100%);background-image:-webkit-gradient(linear,left top,left 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diff --git a/docs/build/html/_static/css/bootstrap3/bootstrap.min.css b/docs/build/html/_static/css/bootstrap3/bootstrap.min.css
new file mode 100644
index 0000000..4c5fdc4
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootstrap.min.css
@@ -0,0 +1,5 @@
+/*!
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+ * Copyright 2011-2015 Twitter, Inc.
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-amelia.css b/docs/build/html/_static/css/bootstrap3/bootswatch-amelia.css
new file mode 100644
index 0000000..2a8b2ec
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-amelia.css
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+@import url("//fonts.googleapis.com/css?family=Lobster|Cabin:400,700");/*!
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+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2014 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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new file mode 100644
index 0000000..9dce50c
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-cosmo.css b/docs/build/html/_static/css/bootstrap3/bootswatch-cosmo.css
new file mode 100644
index 0000000..68aac11
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-cosmo.css
@@ -0,0 +1,7 @@
+@import url("https://fonts.googleapis.com/css?family=Source+Sans+Pro:300,400,700");/*!
+ * bootswatch v3.3.4+1
+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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new file mode 100644
index 0000000..07dd707
--- /dev/null
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new file mode 100644
index 0000000..e3d8bfb
--- /dev/null
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-flatly.css b/docs/build/html/_static/css/bootstrap3/bootswatch-flatly.css
new file mode 100644
index 0000000..57fb3b6
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-flatly.css
@@ -0,0 +1,7 @@
+@import url("https://fonts.googleapis.com/css?family=Lato:400,700,400italic");/*!
+ * bootswatch v3.3.4+1
+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-journal.css b/docs/build/html/_static/css/bootstrap3/bootswatch-journal.css
new file mode 100644
index 0000000..ddf7331
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-journal.css
@@ -0,0 +1,7 @@
+@import url("https://fonts.googleapis.com/css?family=News+Cycle:400,700");/*!
+ * bootswatch v3.3.4+1
+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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new file mode 100644
index 0000000..7f6a4cd
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new file mode 100644
index 0000000..4802bb4
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-paper.css
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+ * Licensed under MIT
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-readable.css b/docs/build/html/_static/css/bootstrap3/bootswatch-readable.css
new file mode 100644
index 0000000..79d1030
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-readable.css
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+@import url("https://fonts.googleapis.com/css?family=Raleway:400,700");/*!
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+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-sandstone.css b/docs/build/html/_static/css/bootstrap3/bootswatch-sandstone.css
new file mode 100644
index 0000000..cf81ab9
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-sandstone.css
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new file mode 100644
index 0000000..3f12ee2
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-simplex.css
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-slate.css b/docs/build/html/_static/css/bootstrap3/bootswatch-slate.css
new file mode 100644
index 0000000..5cc28b0
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-slate.css
@@ -0,0 +1,7 @@
+/*!
+ * bootswatch v3.3.4+1
+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-solar.css b/docs/build/html/_static/css/bootstrap3/bootswatch-solar.css
new file mode 100644
index 0000000..42ab992
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-solar.css
@@ -0,0 +1,11 @@
+@import url("https://fonts.googleapis.com/css?family=Source+Sans+Pro:300,400,700");/*!
+ * bootswatch v3.3.7
+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2017 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
+*//*!
+ * Bootstrap v3.3.7 (http://getbootstrap.com)
+ * Copyright 2011-2016 Twitter, Inc.
+ * Licensed under MIT (https://github.com/twbs/bootstrap/blob/master/LICENSE)
+ *//*! normalize.css v3.0.3 | MIT License | github.com/necolas/normalize.css */html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}body{margin:0}article,aside,details,figcaption,figure,footer,header,hgroup,main,menu,nav,section,summary{display:block}audio,canvas,progress,video{display:inline-block;vertical-align:baseline}audio:not([controls]){display:none;height:0}[hidden],template{display:none}a{background-color:transparent}a:active,a:hover{outline:0}abbr[title]{border-bottom:1px dotted}b,strong{font-weight:bold}dfn{font-style:italic}h1{font-size:2em;margin:0.67em 0}mark{background:#ff0;color:#000}small{font-size:80%}sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}sup{top:-0.5em}sub{bottom:-0.25em}img{border:0}svg:not(:root){overflow:hidden}figure{margin:1em 40px}hr{-webkit-box-sizing:content-box;-moz-box-sizing:content-box;box-sizing:content-box;height:0}pre{overflow:auto}code,kbd,pre,samp{font-family:monospace, monospace;font-size:1em}button,input,optgroup,select,textarea{color:inherit;font:inherit;margin:0}button{overflow:visible}button,select{text-transform:none}button,html input[type="button"],input[type="reset"],input[type="submit"]{-webkit-appearance:button;cursor:pointer}button[disabled],html input[disabled]{cursor:default}button::-moz-focus-inner,input::-moz-focus-inner{border:0;padding:0}input{line-height:normal}input[type="checkbox"],input[type="radio"]{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box;padding:0}input[type="number"]::-webkit-inner-spin-button,input[type="number"]::-webkit-outer-spin-button{height:auto}input[type="search"]{-webkit-appearance:textfield;-webkit-box-sizing:content-box;-moz-box-sizing:content-box;box-sizing:content-box}input[type="search"]::-webkit-search-cancel-button,input[type="search"]::-webkit-search-decoration{-webkit-appearance:none}fieldset{border:1px solid #c0c0c0;margin:0 2px;padding:0.35em 0.625em 0.75em}legend{border:0;padding:0}textarea{overflow:auto}optgroup{font-weight:bold}table{border-collapse:collapse;border-spacing:0}td,th{padding:0}/*! 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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-spacelab.css b/docs/build/html/_static/css/bootstrap3/bootswatch-spacelab.css
new file mode 100644
index 0000000..22154b6
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-spacelab.css
@@ -0,0 +1,7 @@
+@import url("https://fonts.googleapis.com/css?family=Open+Sans:400italic,700italic,400,700");/*!
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+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-superhero.css b/docs/build/html/_static/css/bootstrap3/bootswatch-superhero.css
new file mode 100644
index 0000000..92c8279
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-superhero.css
@@ -0,0 +1,7 @@
+@import url("https://fonts.googleapis.com/css?family=Lato:300,400,700");/*!
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+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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new file mode 100644
index 0000000..c1a8f51
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-united.css
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+@import url("https://fonts.googleapis.com/css?family=Ubuntu");/*!
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+ * Homepage: http://bootswatch.com
+ * Copyright 2012-2015 Thomas Park
+ * Licensed under MIT
+ * Based on Bootstrap
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diff --git a/docs/build/html/_static/css/bootstrap3/bootswatch-yeti.css b/docs/build/html/_static/css/bootstrap3/bootswatch-yeti.css
new file mode 100644
index 0000000..3c8d090
--- /dev/null
+++ b/docs/build/html/_static/css/bootstrap3/bootswatch-yeti.css
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new file mode 100644
index 0000000..d3dae63
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+.icon-th{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf00a;');}
+.icon-th-list{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf00b;');}
+.icon-ok{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf00c;');}
+.icon-remove{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf00d;');}
+.icon-zoom-in{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf00e;');}
+.icon-zoom-out{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf010;');}
+.icon-off{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf011;');}
+.icon-power-off{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf011;');}
+.icon-signal{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf012;');}
+.icon-cog{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf013;');}
+.icon-gear{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf013;');}
+.icon-trash{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf014;');}
+.icon-home{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf015;');}
+.icon-file-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf016;');}
+.icon-time{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf017;');}
+.icon-road{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf018;');}
+.icon-download-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf019;');}
+.icon-download{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf01a;');}
+.icon-upload{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf01b;');}
+.icon-inbox{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf01c;');}
+.icon-play-circle{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf01d;');}
+.icon-repeat{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf01e;');}
+.icon-rotate-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf01e;');}
+.icon-refresh{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf021;');}
+.icon-list-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf022;');}
+.icon-lock{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf023;');}
+.icon-flag{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf024;');}
+.icon-headphones{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf025;');}
+.icon-volume-off{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf026;');}
+.icon-volume-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf027;');}
+.icon-volume-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf028;');}
+.icon-qrcode{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf029;');}
+.icon-barcode{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf02a;');}
+.icon-tag{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf02b;');}
+.icon-tags{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf02c;');}
+.icon-book{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf02d;');}
+.icon-bookmark{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf02e;');}
+.icon-print{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf02f;');}
+.icon-camera{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf030;');}
+.icon-font{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf031;');}
+.icon-bold{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf032;');}
+.icon-italic{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf033;');}
+.icon-text-height{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf034;');}
+.icon-text-width{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf035;');}
+.icon-align-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf036;');}
+.icon-align-center{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf037;');}
+.icon-align-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf038;');}
+.icon-align-justify{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf039;');}
+.icon-list{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf03a;');}
+.icon-indent-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf03b;');}
+.icon-indent-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf03c;');}
+.icon-facetime-video{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf03d;');}
+.icon-picture{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf03e;');}
+.icon-pencil{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf040;');}
+.icon-map-marker{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf041;');}
+.icon-adjust{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf042;');}
+.icon-tint{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf043;');}
+.icon-edit{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf044;');}
+.icon-share{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf045;');}
+.icon-check{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf046;');}
+.icon-move{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf047;');}
+.icon-step-backward{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf048;');}
+.icon-fast-backward{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf049;');}
+.icon-backward{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf04a;');}
+.icon-play{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf04b;');}
+.icon-pause{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf04c;');}
+.icon-stop{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf04d;');}
+.icon-forward{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf04e;');}
+.icon-fast-forward{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf050;');}
+.icon-step-forward{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf051;');}
+.icon-eject{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf052;');}
+.icon-chevron-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf053;');}
+.icon-chevron-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf054;');}
+.icon-plus-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf055;');}
+.icon-minus-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf056;');}
+.icon-remove-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf057;');}
+.icon-ok-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf058;');}
+.icon-question-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf059;');}
+.icon-info-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf05a;');}
+.icon-screenshot{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf05b;');}
+.icon-remove-circle{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf05c;');}
+.icon-ok-circle{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf05d;');}
+.icon-ban-circle{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf05e;');}
+.icon-arrow-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf060;');}
+.icon-arrow-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf061;');}
+.icon-arrow-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf062;');}
+.icon-arrow-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf063;');}
+.icon-share-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf064;');}
+.icon-mail-forward{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf064;');}
+.icon-resize-full{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf065;');}
+.icon-resize-small{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf066;');}
+.icon-plus{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf067;');}
+.icon-minus{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf068;');}
+.icon-asterisk{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf069;');}
+.icon-exclamation-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf06a;');}
+.icon-gift{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf06b;');}
+.icon-leaf{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf06c;');}
+.icon-fire{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf06d;');}
+.icon-eye-open{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf06e;');}
+.icon-eye-close{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf070;');}
+.icon-warning-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf071;');}
+.icon-plane{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf072;');}
+.icon-calendar{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf073;');}
+.icon-random{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf074;');}
+.icon-comment{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf075;');}
+.icon-magnet{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf076;');}
+.icon-chevron-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf077;');}
+.icon-chevron-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf078;');}
+.icon-retweet{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf079;');}
+.icon-shopping-cart{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf07a;');}
+.icon-folder-close{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf07b;');}
+.icon-folder-open{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf07c;');}
+.icon-resize-vertical{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf07d;');}
+.icon-resize-horizontal{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf07e;');}
+.icon-bar-chart{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf080;');}
+.icon-twitter-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf081;');}
+.icon-facebook-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf082;');}
+.icon-camera-retro{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf083;');}
+.icon-key{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf084;');}
+.icon-cogs{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf085;');}
+.icon-gears{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf085;');}
+.icon-comments{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf086;');}
+.icon-thumbs-up-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf087;');}
+.icon-thumbs-down-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf088;');}
+.icon-star-half{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf089;');}
+.icon-heart-empty{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf08a;');}
+.icon-signout{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf08b;');}
+.icon-linkedin-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf08c;');}
+.icon-pushpin{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf08d;');}
+.icon-external-link{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf08e;');}
+.icon-signin{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf090;');}
+.icon-trophy{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf091;');}
+.icon-github-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf092;');}
+.icon-upload-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf093;');}
+.icon-lemon{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf094;');}
+.icon-phone{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf095;');}
+.icon-check-empty{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf096;');}
+.icon-unchecked{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf096;');}
+.icon-bookmark-empty{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf097;');}
+.icon-phone-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf098;');}
+.icon-twitter{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf099;');}
+.icon-facebook{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf09a;');}
+.icon-github{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf09b;');}
+.icon-unlock{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf09c;');}
+.icon-credit-card{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf09d;');}
+.icon-rss{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf09e;');}
+.icon-hdd{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a0;');}
+.icon-bullhorn{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a1;');}
+.icon-bell{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a2;');}
+.icon-certificate{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a3;');}
+.icon-hand-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a4;');}
+.icon-hand-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a5;');}
+.icon-hand-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a6;');}
+.icon-hand-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a7;');}
+.icon-circle-arrow-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a8;');}
+.icon-circle-arrow-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0a9;');}
+.icon-circle-arrow-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0aa;');}
+.icon-circle-arrow-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ab;');}
+.icon-globe{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ac;');}
+.icon-wrench{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ad;');}
+.icon-tasks{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ae;');}
+.icon-filter{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0b0;');}
+.icon-briefcase{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0b1;');}
+.icon-fullscreen{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0b2;');}
+.icon-group{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c0;');}
+.icon-link{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c1;');}
+.icon-cloud{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c2;');}
+.icon-beaker{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c3;');}
+.icon-cut{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c4;');}
+.icon-copy{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c5;');}
+.icon-paper-clip{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c6;');}
+.icon-paperclip{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c6;');}
+.icon-save{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c7;');}
+.icon-sign-blank{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c8;');}
+.icon-reorder{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0c9;');}
+.icon-list-ul{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ca;');}
+.icon-list-ol{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0cb;');}
+.icon-strikethrough{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0cc;');}
+.icon-underline{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0cd;');}
+.icon-table{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ce;');}
+.icon-magic{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d0;');}
+.icon-truck{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d1;');}
+.icon-pinterest{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d2;');}
+.icon-pinterest-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d3;');}
+.icon-google-plus-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d4;');}
+.icon-google-plus{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d5;');}
+.icon-money{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d6;');}
+.icon-caret-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d7;');}
+.icon-caret-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d8;');}
+.icon-caret-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0d9;');}
+.icon-caret-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0da;');}
+.icon-columns{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0db;');}
+.icon-sort{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0dc;');}
+.icon-sort-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0dd;');}
+.icon-sort-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0de;');}
+.icon-envelope{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e0;');}
+.icon-linkedin{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e1;');}
+.icon-undo{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e2;');}
+.icon-rotate-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e2;');}
+.icon-legal{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e3;');}
+.icon-dashboard{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e4;');}
+.icon-comment-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e5;');}
+.icon-comments-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e6;');}
+.icon-bolt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e7;');}
+.icon-sitemap{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e8;');}
+.icon-umbrella{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0e9;');}
+.icon-paste{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ea;');}
+.icon-lightbulb{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0eb;');}
+.icon-exchange{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ec;');}
+.icon-cloud-download{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ed;');}
+.icon-cloud-upload{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0ee;');}
+.icon-user-md{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f0;');}
+.icon-stethoscope{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f1;');}
+.icon-suitcase{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f2;');}
+.icon-bell-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f3;');}
+.icon-coffee{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f4;');}
+.icon-food{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f5;');}
+.icon-file-text-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f6;');}
+.icon-building{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f7;');}
+.icon-hospital{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f8;');}
+.icon-ambulance{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0f9;');}
+.icon-medkit{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0fa;');}
+.icon-fighter-jet{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0fb;');}
+.icon-beer{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0fc;');}
+.icon-h-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0fd;');}
+.icon-plus-sign-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf0fe;');}
+.icon-double-angle-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf100;');}
+.icon-double-angle-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf101;');}
+.icon-double-angle-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf102;');}
+.icon-double-angle-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf103;');}
+.icon-angle-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf104;');}
+.icon-angle-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf105;');}
+.icon-angle-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf106;');}
+.icon-angle-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf107;');}
+.icon-desktop{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf108;');}
+.icon-laptop{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf109;');}
+.icon-tablet{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf10a;');}
+.icon-mobile-phone{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf10b;');}
+.icon-circle-blank{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf10c;');}
+.icon-quote-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf10d;');}
+.icon-quote-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf10e;');}
+.icon-spinner{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf110;');}
+.icon-circle{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf111;');}
+.icon-reply{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf112;');}
+.icon-mail-reply{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf112;');}
+.icon-github-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf113;');}
+.icon-folder-close-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf114;');}
+.icon-folder-open-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf115;');}
+.icon-expand-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf116;');}
+.icon-collapse-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf117;');}
+.icon-smile{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf118;');}
+.icon-frown{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf119;');}
+.icon-meh{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf11a;');}
+.icon-gamepad{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf11b;');}
+.icon-keyboard{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf11c;');}
+.icon-flag-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf11d;');}
+.icon-flag-checkered{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf11e;');}
+.icon-terminal{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf120;');}
+.icon-code{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf121;');}
+.icon-reply-all{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf122;');}
+.icon-mail-reply-all{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf122;');}
+.icon-star-half-empty{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf123;');}
+.icon-star-half-full{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf123;');}
+.icon-location-arrow{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf124;');}
+.icon-crop{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf125;');}
+.icon-code-fork{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf126;');}
+.icon-unlink{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf127;');}
+.icon-question{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf128;');}
+.icon-info{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf129;');}
+.icon-exclamation{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf12a;');}
+.icon-superscript{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf12b;');}
+.icon-subscript{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf12c;');}
+.icon-eraser{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf12d;');}
+.icon-puzzle-piece{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf12e;');}
+.icon-microphone{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf130;');}
+.icon-microphone-off{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf131;');}
+.icon-shield{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf132;');}
+.icon-calendar-empty{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf133;');}
+.icon-fire-extinguisher{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf134;');}
+.icon-rocket{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf135;');}
+.icon-maxcdn{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf136;');}
+.icon-chevron-sign-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf137;');}
+.icon-chevron-sign-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf138;');}
+.icon-chevron-sign-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf139;');}
+.icon-chevron-sign-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf13a;');}
+.icon-html5{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf13b;');}
+.icon-css3{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf13c;');}
+.icon-anchor{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf13d;');}
+.icon-unlock-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf13e;');}
+.icon-bullseye{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf140;');}
+.icon-ellipsis-horizontal{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf141;');}
+.icon-ellipsis-vertical{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf142;');}
+.icon-rss-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf143;');}
+.icon-play-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf144;');}
+.icon-ticket{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf145;');}
+.icon-minus-sign-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf146;');}
+.icon-check-minus{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf147;');}
+.icon-level-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf148;');}
+.icon-level-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf149;');}
+.icon-check-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf14a;');}
+.icon-edit-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf14b;');}
+.icon-external-link-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf14c;');}
+.icon-share-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf14d;');}
+.icon-compass{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf14e;');}
+.icon-collapse{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf150;');}
+.icon-collapse-top{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf151;');}
+.icon-expand{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf152;');}
+.icon-eur{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf153;');}
+.icon-euro{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf153;');}
+.icon-gbp{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf154;');}
+.icon-usd{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf155;');}
+.icon-dollar{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf155;');}
+.icon-inr{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf156;');}
+.icon-rupee{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf156;');}
+.icon-jpy{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf157;');}
+.icon-yen{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf157;');}
+.icon-cny{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf158;');}
+.icon-renminbi{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf158;');}
+.icon-krw{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf159;');}
+.icon-won{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf159;');}
+.icon-btc{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf15a;');}
+.icon-bitcoin{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf15a;');}
+.icon-file{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf15b;');}
+.icon-file-text{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf15c;');}
+.icon-sort-by-alphabet{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf15d;');}
+.icon-sort-by-alphabet-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf15e;');}
+.icon-sort-by-attributes{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf160;');}
+.icon-sort-by-attributes-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf161;');}
+.icon-sort-by-order{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf162;');}
+.icon-sort-by-order-alt{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf163;');}
+.icon-thumbs-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf164;');}
+.icon-thumbs-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf165;');}
+.icon-youtube-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf166;');}
+.icon-youtube{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf167;');}
+.icon-xing{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf168;');}
+.icon-xing-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf169;');}
+.icon-youtube-play{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf16a;');}
+.icon-dropbox{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf16b;');}
+.icon-stackexchange{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf16c;');}
+.icon-instagram{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf16d;');}
+.icon-flickr{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf16e;');}
+.icon-adn{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf170;');}
+.icon-bitbucket{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf171;');}
+.icon-bitbucket-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf172;');}
+.icon-tumblr{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf173;');}
+.icon-tumblr-sign{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf174;');}
+.icon-long-arrow-down{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf175;');}
+.icon-long-arrow-up{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf176;');}
+.icon-long-arrow-left{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf177;');}
+.icon-long-arrow-right{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf178;');}
+.icon-apple{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf179;');}
+.icon-windows{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf17a;');}
+.icon-android{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf17b;');}
+.icon-linux{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf17c;');}
+.icon-dribbble{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf17d;');}
+.icon-skype{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf17e;');}
+.icon-foursquare{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf180;');}
+.icon-trello{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf181;');}
+.icon-female{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf182;');}
+.icon-male{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf183;');}
+.icon-gittip{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf184;');}
+.icon-sun{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf185;');}
+.icon-moon{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf186;');}
+.icon-archive{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf187;');}
+.icon-bug{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf188;');}
+.icon-vk{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf189;');}
+.icon-weibo{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf18a;');}
+.icon-renren{*zoom:expression( this.runtimeStyle['zoom'] = '1', this.innerHTML = '&#xf18b;');}
diff --git a/docs/build/html/_static/css/font-awesome.min.css b/docs/build/html/_static/css/font-awesome.min.css
new file mode 100644
index 0000000..24fcc04
--- /dev/null
+++ b/docs/build/html/_static/css/font-awesome.min.css
@@ -0,0 +1,4 @@
+/*!
+ *  Font Awesome 4.3.0 by @davegandy - http://fontawesome.io - @fontawesome
+ *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)
+ */@font-face{font-family:'FontAwesome';src:url('../fonts/fontawesome-webfont.eot?v=4.3.0');src:url('../fonts/fontawesome-webfont.eot?#iefix&v=4.3.0') format('embedded-opentype'),url('../fonts/fontawesome-webfont.woff2?v=4.3.0') format('woff2'),url('../fonts/fontawesome-webfont.woff?v=4.3.0') format('woff'),url('../fonts/fontawesome-webfont.ttf?v=4.3.0') format('truetype'),url('../fonts/fontawesome-webfont.svg?v=4.3.0#fontawesomeregular') format('svg');font-weight:normal;font-style:normal}.fa{display:inline-block;font:normal normal normal 14px/1 FontAwesome;font-size:inherit;text-rendering:auto;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;transform:translate(0, 0)}.fa-lg{font-size:1.33333333em;line-height:.75em;vertical-align:-15%}.fa-2x{font-size:2em}.fa-3x{font-size:3em}.fa-4x{font-size:4em}.fa-5x{font-size:5em}.fa-fw{width:1.28571429em;text-align:center}.fa-ul{padding-left:0;margin-left:2.14285714em;list-style-type:none}.fa-ul>li{position:relative}.fa-li{position:absolute;left:-2.14285714em;width:2.14285714em;top:.14285714em;text-align:center}.fa-li.fa-lg{left:-1.85714286em}.fa-border{padding:.2em .25em .15em;border:solid .08em #eee;border-radius:.1em}.pull-right{float:right}.pull-left{float:left}.fa.pull-left{margin-right:.3em}.fa.pull-right{margin-left:.3em}.fa-spin{-webkit-animation:fa-spin 2s infinite linear;animation:fa-spin 2s infinite linear}.fa-pulse{-webkit-animation:fa-spin 1s infinite steps(8);animation:fa-spin 1s infinite steps(8)}@-webkit-keyframes fa-spin{0%{-webkit-transform:rotate(0deg);transform:rotate(0deg)}100%{-webkit-transform:rotate(359deg);transform:rotate(359deg)}}@keyframes fa-spin{0%{-webkit-transform:rotate(0deg);transform:rotate(0deg)}100%{-webkit-transform:rotate(359deg);transform:rotate(359deg)}}.fa-rotate-90{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=1);-webkit-transform:rotate(90deg);-ms-transform:rotate(90deg);transform:rotate(90deg)}.fa-rotate-180{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=2);-webkit-transform:rotate(180deg);-ms-transform:rotate(180deg);transform:rotate(180deg)}.fa-rotate-270{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=3);-webkit-transform:rotate(270deg);-ms-transform:rotate(270deg);transform:rotate(270deg)}.fa-flip-horizontal{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=0, mirror=1);-webkit-transform:scale(-1, 1);-ms-transform:scale(-1, 1);transform:scale(-1, 1)}.fa-flip-vertical{filter:progid:DXImageTransform.Microsoft.BasicImage(rotation=2, mirror=1);-webkit-transform:scale(1, -1);-ms-transform:scale(1, -1);transform:scale(1, -1)}:root .fa-rotate-90,:root .fa-rotate-180,:root .fa-rotate-270,:root .fa-flip-horizontal,:root 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\ No newline at end of file
diff --git a/docs/build/html/_static/default.css b/docs/build/html/_static/default.css
deleted file mode 100644
index 81b9363..0000000
--- a/docs/build/html/_static/default.css
+++ /dev/null
@@ -1 +0,0 @@
-@import url("classic.css");
diff --git a/docs/build/html/_static/doctools.js b/docs/build/html/_static/doctools.js
index daccd20..527b876 100644
--- a/docs/build/html/_static/doctools.js
+++ b/docs/build/html/_static/doctools.js
@@ -2,314 +2,155 @@
  * doctools.js
  * ~~~~~~~~~~~
  *
- * Sphinx JavaScript utilities for all documentation.
+ * Base JavaScript utilities for all Sphinx HTML documentation.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
-
-/**
- * select a different prefix for underscore
- */
-$u = _.noConflict();
-
-/**
- * make the code below compatible with browsers without
- * an installed firebug like debugger
-if (!window.console || !console.firebug) {
-  var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
-    "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
-    "profile", "profileEnd"];
-  window.console = {};
-  for (var i = 0; i < names.length; ++i)
-    window.console[names[i]] = function() {};
-}
- */
-
-/**
- * small helper function to urldecode strings
- */
-jQuery.urldecode = function(x) {
-  return decodeURIComponent(x).replace(/\+/g, ' ');
-};
-
-/**
- * small helper function to urlencode strings
- */
-jQuery.urlencode = encodeURIComponent;
-
-/**
- * This function returns the parsed url parameters of the
- * current request. Multiple values per key are supported,
- * it will always return arrays of strings for the value parts.
- */
-jQuery.getQueryParameters = function(s) {
-  if (typeof s === 'undefined')
-    s = document.location.search;
-  var parts = s.substr(s.indexOf('?') + 1).split('&');
-  var result = {};
-  for (var i = 0; i < parts.length; i++) {
-    var tmp = parts[i].split('=', 2);
-    var key = jQuery.urldecode(tmp[0]);
-    var value = jQuery.urldecode(tmp[1]);
-    if (key in result)
-      result[key].push(value);
-    else
-      result[key] = [value];
+"use strict";
+
+const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
+  "TEXTAREA",
+  "INPUT",
+  "SELECT",
+  "BUTTON",
+]);
+
+const _ready = (callback) => {
+  if (document.readyState !== "loading") {
+    callback();
+  } else {
+    document.addEventListener("DOMContentLoaded", callback);
   }
-  return result;
 };
 
-/**
- * highlight a given string on a jquery object by wrapping it in
- * span elements with the given class name.
- */
-jQuery.fn.highlightText = function(text, className) {
-  function highlight(node, addItems) {
-    if (node.nodeType === 3) {
-      var val = node.nodeValue;
-      var pos = val.toLowerCase().indexOf(text);
-      if (pos >= 0 &&
-          !jQuery(node.parentNode).hasClass(className) &&
-          !jQuery(node.parentNode).hasClass("nohighlight")) {
-        var span;
-        var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
-        if (isInSVG) {
-          span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
-        } else {
-          span = document.createElement("span");
-          span.className = className;
-        }
-        span.appendChild(document.createTextNode(val.substr(pos, text.length)));
-        node.parentNode.insertBefore(span, node.parentNode.insertBefore(
-          document.createTextNode(val.substr(pos + text.length)),
-          node.nextSibling));
-        node.nodeValue = val.substr(0, pos);
-        if (isInSVG) {
-          var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
-          var bbox = node.parentElement.getBBox();
-          rect.x.baseVal.value = bbox.x;
-          rect.y.baseVal.value = bbox.y;
-          rect.width.baseVal.value = bbox.width;
-          rect.height.baseVal.value = bbox.height;
-          rect.setAttribute('class', className);
-          addItems.push({
-              "parent": node.parentNode,
-              "target": rect});
-        }
-      }
-    }
-    else if (!jQuery(node).is("button, select, textarea")) {
-      jQuery.each(node.childNodes, function() {
-        highlight(this, addItems);
-      });
-    }
-  }
-  var addItems = [];
-  var result = this.each(function() {
-    highlight(this, addItems);
-  });
-  for (var i = 0; i < addItems.length; ++i) {
-    jQuery(addItems[i].parent).before(addItems[i].target);
-  }
-  return result;
-};
-
-/*
- * backward compatibility for jQuery.browser
- * This will be supported until firefox bug is fixed.
- */
-if (!jQuery.browser) {
-  jQuery.uaMatch = function(ua) {
-    ua = ua.toLowerCase();
-
-    var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
-      /(webkit)[ \/]([\w.]+)/.exec(ua) ||
-      /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
-      /(msie) ([\w.]+)/.exec(ua) ||
-      ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
-      [];
-
-    return {
-      browser: match[ 1 ] || "",
-      version: match[ 2 ] || "0"
-    };
-  };
-  jQuery.browser = {};
-  jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
-}
-
 /**
  * Small JavaScript module for the documentation.
  */
-var Documentation = {
-
-  init : function() {
-    this.fixFirefoxAnchorBug();
-    this.highlightSearchWords();
-    this.initIndexTable();
-    if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) {
-      this.initOnKeyListeners();
-    }
+const Documentation = {
+  init: () => {
+    Documentation.initDomainIndexTable();
+    Documentation.initOnKeyListeners();
   },
 
   /**
    * i18n support
    */
-  TRANSLATIONS : {},
-  PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
-  LOCALE : 'unknown',
+  TRANSLATIONS: {},
+  PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
+  LOCALE: "unknown",
 
   // gettext and ngettext don't access this so that the functions
   // can safely bound to a different name (_ = Documentation.gettext)
-  gettext : function(string) {
-    var translated = Documentation.TRANSLATIONS[string];
-    if (typeof translated === 'undefined')
-      return string;
-    return (typeof translated === 'string') ? translated : translated[0];
-  },
-
-  ngettext : function(singular, plural, n) {
-    var translated = Documentation.TRANSLATIONS[singular];
-    if (typeof translated === 'undefined')
-      return (n == 1) ? singular : plural;
-    return translated[Documentation.PLURALEXPR(n)];
+  gettext: (string) => {
+    const translated = Documentation.TRANSLATIONS[string];
+    switch (typeof translated) {
+      case "undefined":
+        return string; // no translation
+      case "string":
+        return translated; // translation exists
+      default:
+        return translated[0]; // (singular, plural) translation tuple exists
+    }
   },
 
-  addTranslations : function(catalog) {
-    for (var key in catalog.messages)
-      this.TRANSLATIONS[key] = catalog.messages[key];
-    this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
-    this.LOCALE = catalog.locale;
+  ngettext: (singular, plural, n) => {
+    const translated = Documentation.TRANSLATIONS[singular];
+    if (typeof translated !== "undefined")
+      return translated[Documentation.PLURAL_EXPR(n)];
+    return n === 1 ? singular : plural;
   },
 
-  /**
-   * add context elements like header anchor links
-   */
-  addContextElements : function() {
-    $('div[id] > :header:first').each(function() {
-      $('<a class="headerlink">\u00B6</a>').
-      attr('href', '#' + this.id).
-      attr('title', _('Permalink to this headline')).
-      appendTo(this);
-    });
-    $('dt[id]').each(function() {
-      $('<a class="headerlink">\u00B6</a>').
-      attr('href', '#' + this.id).
-      attr('title', _('Permalink to this definition')).
-      appendTo(this);
-    });
+  addTranslations: (catalog) => {
+    Object.assign(Documentation.TRANSLATIONS, catalog.messages);
+    Documentation.PLURAL_EXPR = new Function(
+      "n",
+      `return (${catalog.plural_expr})`
+    );
+    Documentation.LOCALE = catalog.locale;
   },
 
   /**
-   * workaround a firefox stupidity
-   * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075
+   * helper function to focus on search bar
    */
-  fixFirefoxAnchorBug : function() {
-    if (document.location.hash && $.browser.mozilla)
-      window.setTimeout(function() {
-        document.location.href += '';
-      }, 10);
+  focusSearchBar: () => {
+    document.querySelectorAll("input[name=q]")[0]?.focus();
   },
 
   /**
-   * highlight the search words provided in the url in the text
+   * Initialise the domain index toggle buttons
    */
-  highlightSearchWords : function() {
-    var params = $.getQueryParameters();
-    var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : [];
-    if (terms.length) {
-      var body = $('div.body');
-      if (!body.length) {
-        body = $('body');
+  initDomainIndexTable: () => {
+    const toggler = (el) => {
+      const idNumber = el.id.substr(7);
+      const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
+      if (el.src.substr(-9) === "minus.png") {
+        el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
+        toggledRows.forEach((el) => (el.style.display = "none"));
+      } else {
+        el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
+        toggledRows.forEach((el) => (el.style.display = ""));
       }
-      window.setTimeout(function() {
-        $.each(terms, function() {
-          body.highlightText(this.toLowerCase(), 'highlighted');
-        });
-      }, 10);
-      $('<p class="highlight-link"><a href="javascript:Documentation.' +
-        'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
-          .appendTo($('#searchbox'));
-    }
-  },
-
-  /**
-   * init the domain index toggle buttons
-   */
-  initIndexTable : function() {
-    var togglers = $('img.toggler').click(function() {
-      var src = $(this).attr('src');
-      var idnum = $(this).attr('id').substr(7);
-      $('tr.cg-' + idnum).toggle();
-      if (src.substr(-9) === 'minus.png')
-        $(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
-      else
-        $(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
-    }).css('display', '');
-    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
-        togglers.click();
-    }
-  },
-
-  /**
-   * helper function to hide the search marks again
-   */
-  hideSearchWords : function() {
-    $('#searchbox .highlight-link').fadeOut(300);
-    $('span.highlighted').removeClass('highlighted');
-  },
-
-  /**
-   * make the url absolute
-   */
-  makeURL : function(relativeURL) {
-    return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
-  },
+    };
 
-  /**
-   * get the current relative url
-   */
-  getCurrentURL : function() {
-    var path = document.location.pathname;
-    var parts = path.split(/\//);
-    $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
-      if (this === '..')
-        parts.pop();
-    });
-    var url = parts.join('/');
-    return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
+    const togglerElements = document.querySelectorAll("img.toggler");
+    togglerElements.forEach((el) =>
+      el.addEventListener("click", (event) => toggler(event.currentTarget))
+    );
+    togglerElements.forEach((el) => (el.style.display = ""));
+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
   },
 
-  initOnKeyListeners: function() {
-    $(document).keydown(function(event) {
-      var activeElementType = document.activeElement.tagName;
-      // don't navigate when in search box or textarea
-      if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
-          && !event.altKey && !event.ctrlKey && !event.metaKey && !event.shiftKey) {
-        switch (event.keyCode) {
-          case 37: // left
-            var prevHref = $('link[rel="prev"]').prop('href');
-            if (prevHref) {
-              window.location.href = prevHref;
-              return false;
+  initOnKeyListeners: () => {
+    // only install a listener if it is really needed
+    if (
+      !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
+      !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
+    )
+      return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.altKey || event.ctrlKey || event.metaKey) return;
+
+      if (!event.shiftKey) {
+        switch (event.key) {
+          case "ArrowLeft":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const prevLink = document.querySelector('link[rel="prev"]');
+            if (prevLink && prevLink.href) {
+              window.location.href = prevLink.href;
+              event.preventDefault();
             }
-          case 39: // right
-            var nextHref = $('link[rel="next"]').prop('href');
-            if (nextHref) {
-              window.location.href = nextHref;
-              return false;
+            break;
+          case "ArrowRight":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const nextLink = document.querySelector('link[rel="next"]');
+            if (nextLink && nextLink.href) {
+              window.location.href = nextLink.href;
+              event.preventDefault();
             }
+            break;
         }
       }
+
+      // some keyboard layouts may need Shift to get /
+      switch (event.key) {
+        case "/":
+          if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+          Documentation.focusSearchBar();
+          event.preventDefault();
+      }
     });
-  }
+  },
 };
 
 // quick alias for translations
-_ = Documentation.gettext;
+const _ = Documentation.gettext;
 
-$(document).ready(function() {
-  Documentation.init();
-});
+_ready(Documentation.init);
diff --git a/docs/build/html/_static/documentation_options.js b/docs/build/html/_static/documentation_options.js
index 895ff1e..46dea9b 100644
--- a/docs/build/html/_static/documentation_options.js
+++ b/docs/build/html/_static/documentation_options.js
@@ -1,11 +1,14 @@
 var DOCUMENTATION_OPTIONS = {
     URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
-    VERSION: '1.2.1',
-    LANGUAGE: 'None',
+    VERSION: '1.3.0',
+    LANGUAGE: 'en',
     COLLAPSE_INDEX: false,
     BUILDER: 'html',
     FILE_SUFFIX: '.html',
+    LINK_SUFFIX: '.html',
     HAS_SOURCE: true,
     SOURCELINK_SUFFIX: '.txt',
-    NAVIGATION_WITH_KEYS: false
+    NAVIGATION_WITH_KEYS: false,
+    SHOW_SEARCH_SUMMARY: true,
+    ENABLE_SEARCH_SHORTCUTS: true,
 };
\ No newline at end of file
diff --git a/docs/build/html/_static/favicon.ico b/docs/build/html/_static/favicon.ico
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diff --git a/docs/build/html/_static/jquery-3.4.1.js b/docs/build/html/_static/jquery-3.6.0.js
similarity index 90%
rename from docs/build/html/_static/jquery-3.4.1.js
rename to docs/build/html/_static/jquery-3.6.0.js
index 773ad95..fc6c299 100644
--- a/docs/build/html/_static/jquery-3.4.1.js
+++ b/docs/build/html/_static/jquery-3.6.0.js
@@ -1,15 +1,15 @@
 /*!
- * jQuery JavaScript Library v3.4.1
+ * jQuery JavaScript Library v3.6.0
  * https://jquery.com/
  *
  * Includes Sizzle.js
  * https://sizzlejs.com/
  *
- * Copyright JS Foundation and other contributors
+ * Copyright OpenJS Foundation and other contributors
  * Released under the MIT license
  * https://jquery.org/license
  *
- * Date: 2019-05-01T21:04Z
+ * Date: 2021-03-02T17:08Z
  */
 ( function( global, factory ) {
 
@@ -47,13 +47,16 @@
 
 var arr = [];
 
-var document = window.document;
-
 var getProto = Object.getPrototypeOf;
 
 var slice = arr.slice;
 
-var concat = arr.concat;
+var flat = arr.flat ? function( array ) {
+	return arr.flat.call( array );
+} : function( array ) {
+	return arr.concat.apply( [], array );
+};
+
 
 var push = arr.push;
 
@@ -73,12 +76,16 @@ var support = {};
 
 var isFunction = function isFunction( obj ) {
 
-      // Support: Chrome <=57, Firefox <=52
-      // In some browsers, typeof returns "function" for HTML <object> elements
-      // (i.e., `typeof document.createElement( "object" ) === "function"`).
-      // We don't want to classify *any* DOM node as a function.
-      return typeof obj === "function" && typeof obj.nodeType !== "number";
-  };
+		// Support: Chrome <=57, Firefox <=52
+		// In some browsers, typeof returns "function" for HTML <object> elements
+		// (i.e., `typeof document.createElement( "object" ) === "function"`).
+		// We don't want to classify *any* DOM node as a function.
+		// Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5
+		// Plus for old WebKit, typeof returns "function" for HTML collections
+		// (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756)
+		return typeof obj === "function" && typeof obj.nodeType !== "number" &&
+			typeof obj.item !== "function";
+	};
 
 
 var isWindow = function isWindow( obj ) {
@@ -86,6 +93,8 @@ var isWindow = function isWindow( obj ) {
 	};
 
 
+var document = window.document;
+
 
 
 	var preservedScriptAttributes = {
@@ -142,7 +151,7 @@ function toType( obj ) {
 
 
 var
-	version = "3.4.1",
+	version = "3.6.0",
 
 	// Define a local copy of jQuery
 	jQuery = function( selector, context ) {
@@ -150,11 +159,7 @@ var
 		// The jQuery object is actually just the init constructor 'enhanced'
 		// Need init if jQuery is called (just allow error to be thrown if not included)
 		return new jQuery.fn.init( selector, context );
-	},
-
-	// Support: Android <=4.0 only
-	// Make sure we trim BOM and NBSP
-	rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
+	};
 
 jQuery.fn = jQuery.prototype = {
 
@@ -220,6 +225,18 @@ jQuery.fn = jQuery.prototype = {
 		return this.eq( -1 );
 	},
 
+	even: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return ( i + 1 ) % 2;
+		} ) );
+	},
+
+	odd: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return i % 2;
+		} ) );
+	},
+
 	eq: function( i ) {
 		var len = this.length,
 			j = +i + ( i < 0 ? len : 0 );
@@ -353,9 +370,10 @@ jQuery.extend( {
 		return true;
 	},
 
-	// Evaluates a script in a global context
-	globalEval: function( code, options ) {
-		DOMEval( code, { nonce: options && options.nonce } );
+	// Evaluates a script in a provided context; falls back to the global one
+	// if not specified.
+	globalEval: function( code, options, doc ) {
+		DOMEval( code, { nonce: options && options.nonce }, doc );
 	},
 
 	each: function( obj, callback ) {
@@ -379,13 +397,6 @@ jQuery.extend( {
 		return obj;
 	},
 
-	// Support: Android <=4.0 only
-	trim: function( text ) {
-		return text == null ?
-			"" :
-			( text + "" ).replace( rtrim, "" );
-	},
-
 	// results is for internal usage only
 	makeArray: function( arr, results ) {
 		var ret = results || [];
@@ -394,7 +405,7 @@ jQuery.extend( {
 			if ( isArrayLike( Object( arr ) ) ) {
 				jQuery.merge( ret,
 					typeof arr === "string" ?
-					[ arr ] : arr
+						[ arr ] : arr
 				);
 			} else {
 				push.call( ret, arr );
@@ -472,7 +483,7 @@ jQuery.extend( {
 		}
 
 		// Flatten any nested arrays
-		return concat.apply( [], ret );
+		return flat( ret );
 	},
 
 	// A global GUID counter for objects
@@ -489,9 +500,9 @@ if ( typeof Symbol === "function" ) {
 
 // Populate the class2type map
 jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
-function( i, name ) {
-	class2type[ "[object " + name + "]" ] = name.toLowerCase();
-} );
+	function( _i, name ) {
+		class2type[ "[object " + name + "]" ] = name.toLowerCase();
+	} );
 
 function isArrayLike( obj ) {
 
@@ -511,17 +522,16 @@ function isArrayLike( obj ) {
 }
 var Sizzle =
 /*!
- * Sizzle CSS Selector Engine v2.3.4
+ * Sizzle CSS Selector Engine v2.3.6
  * https://sizzlejs.com/
  *
  * Copyright JS Foundation and other contributors
  * Released under the MIT license
  * https://js.foundation/
  *
- * Date: 2019-04-08
+ * Date: 2021-02-16
  */
-(function( window ) {
-
+( function( window ) {
 var i,
 	support,
 	Expr,
@@ -561,59 +571,70 @@ var i,
 	},
 
 	// Instance methods
-	hasOwn = ({}).hasOwnProperty,
+	hasOwn = ( {} ).hasOwnProperty,
 	arr = [],
 	pop = arr.pop,
-	push_native = arr.push,
+	pushNative = arr.push,
 	push = arr.push,
 	slice = arr.slice,
+
 	// Use a stripped-down indexOf as it's faster than native
 	// https://jsperf.com/thor-indexof-vs-for/5
 	indexOf = function( list, elem ) {
 		var i = 0,
 			len = list.length;
 		for ( ; i < len; i++ ) {
-			if ( list[i] === elem ) {
+			if ( list[ i ] === elem ) {
 				return i;
 			}
 		}
 		return -1;
 	},
 
-	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",
+	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
+		"ismap|loop|multiple|open|readonly|required|scoped",
 
 	// Regular expressions
 
 	// http://www.w3.org/TR/css3-selectors/#whitespace
 	whitespace = "[\\x20\\t\\r\\n\\f]",
 
-	// http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
-	identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
+	// https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+	identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+		"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
 
 	// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
 	attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
+
 		// Operator (capture 2)
 		"*([*^$|!~]?=)" + whitespace +
-		// "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]"
-		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace +
-		"*\\]",
+
+		// "Attribute values must be CSS identifiers [capture 5]
+		// or strings [capture 3 or capture 4]"
+		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
+		whitespace + "*\\]",
 
 	pseudos = ":(" + identifier + ")(?:\\((" +
+
 		// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
 		// 1. quoted (capture 3; capture 4 or capture 5)
 		"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
+
 		// 2. simple (capture 6)
 		"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
+
 		// 3. anything else (capture 2)
 		".*" +
 		")\\)|)",
 
 	// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
 	rwhitespace = new RegExp( whitespace + "+", "g" ),
-	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ),
+	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
+		whitespace + "+$", "g" ),
 
 	rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
-	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ),
+	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
+		"*" ),
 	rdescend = new RegExp( whitespace + "|>" ),
 
 	rpseudo = new RegExp( pseudos ),
@@ -625,14 +646,16 @@ var i,
 		"TAG": new RegExp( "^(" + identifier + "|[*])" ),
 		"ATTR": new RegExp( "^" + attributes ),
 		"PSEUDO": new RegExp( "^" + pseudos ),
-		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace +
-			"*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace +
-			"*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
+		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
+			whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
+			whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
 		"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
+
 		// For use in libraries implementing .is()
 		// We use this for POS matching in `select`
-		"needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" +
-			whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
+		"needsContext": new RegExp( "^" + whitespace +
+			"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
+			"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
 	},
 
 	rhtml = /HTML$/i,
@@ -648,18 +671,21 @@ var i,
 
 	// CSS escapes
 	// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
-	runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ),
-	funescape = function( _, escaped, escapedWhitespace ) {
-		var high = "0x" + escaped - 0x10000;
-		// NaN means non-codepoint
-		// Support: Firefox<24
-		// Workaround erroneous numeric interpretation of +"0x"
-		return high !== high || escapedWhitespace ?
-			escaped :
+	runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+	funescape = function( escape, nonHex ) {
+		var high = "0x" + escape.slice( 1 ) - 0x10000;
+
+		return nonHex ?
+
+			// Strip the backslash prefix from a non-hex escape sequence
+			nonHex :
+
+			// Replace a hexadecimal escape sequence with the encoded Unicode code point
+			// Support: IE <=11+
+			// For values outside the Basic Multilingual Plane (BMP), manually construct a
+			// surrogate pair
 			high < 0 ?
-				// BMP codepoint
 				String.fromCharCode( high + 0x10000 ) :
-				// Supplemental Plane codepoint (surrogate pair)
 				String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
 	},
 
@@ -675,7 +701,8 @@ var i,
 			}
 
 			// Control characters and (dependent upon position) numbers get escaped as code points
-			return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
+			return ch.slice( 0, -1 ) + "\\" +
+				ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
 		}
 
 		// Other potentially-special ASCII characters get backslash-escaped
@@ -700,18 +727,20 @@ var i,
 // Optimize for push.apply( _, NodeList )
 try {
 	push.apply(
-		(arr = slice.call( preferredDoc.childNodes )),
+		( arr = slice.call( preferredDoc.childNodes ) ),
 		preferredDoc.childNodes
 	);
+
 	// Support: Android<4.0
 	// Detect silently failing push.apply
+	// eslint-disable-next-line no-unused-expressions
 	arr[ preferredDoc.childNodes.length ].nodeType;
 } catch ( e ) {
 	push = { apply: arr.length ?
 
 		// Leverage slice if possible
 		function( target, els ) {
-			push_native.apply( target, slice.call(els) );
+			pushNative.apply( target, slice.call( els ) );
 		} :
 
 		// Support: IE<9
@@ -719,8 +748,9 @@ try {
 		function( target, els ) {
 			var j = target.length,
 				i = 0;
+
 			// Can't trust NodeList.length
-			while ( (target[j++] = els[i++]) ) {}
+			while ( ( target[ j++ ] = els[ i++ ] ) ) {}
 			target.length = j - 1;
 		}
 	};
@@ -744,24 +774,21 @@ function Sizzle( selector, context, results, seed ) {
 
 	// Try to shortcut find operations (as opposed to filters) in HTML documents
 	if ( !seed ) {
-
-		if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
-			setDocument( context );
-		}
+		setDocument( context );
 		context = context || document;
 
 		if ( documentIsHTML ) {
 
 			// If the selector is sufficiently simple, try using a "get*By*" DOM method
 			// (excepting DocumentFragment context, where the methods don't exist)
-			if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) {
+			if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
 
 				// ID selector
-				if ( (m = match[1]) ) {
+				if ( ( m = match[ 1 ] ) ) {
 
 					// Document context
 					if ( nodeType === 9 ) {
-						if ( (elem = context.getElementById( m )) ) {
+						if ( ( elem = context.getElementById( m ) ) ) {
 
 							// Support: IE, Opera, Webkit
 							// TODO: identify versions
@@ -780,7 +807,7 @@ function Sizzle( selector, context, results, seed ) {
 						// Support: IE, Opera, Webkit
 						// TODO: identify versions
 						// getElementById can match elements by name instead of ID
-						if ( newContext && (elem = newContext.getElementById( m )) &&
+						if ( newContext && ( elem = newContext.getElementById( m ) ) &&
 							contains( context, elem ) &&
 							elem.id === m ) {
 
@@ -790,12 +817,12 @@ function Sizzle( selector, context, results, seed ) {
 					}
 
 				// Type selector
-				} else if ( match[2] ) {
+				} else if ( match[ 2 ] ) {
 					push.apply( results, context.getElementsByTagName( selector ) );
 					return results;
 
 				// Class selector
-				} else if ( (m = match[3]) && support.getElementsByClassName &&
+				} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
 					context.getElementsByClassName ) {
 
 					push.apply( results, context.getElementsByClassName( m ) );
@@ -806,11 +833,11 @@ function Sizzle( selector, context, results, seed ) {
 			// Take advantage of querySelectorAll
 			if ( support.qsa &&
 				!nonnativeSelectorCache[ selector + " " ] &&
-				(!rbuggyQSA || !rbuggyQSA.test( selector )) &&
+				( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
 
 				// Support: IE 8 only
 				// Exclude object elements
-				(nodeType !== 1 || context.nodeName.toLowerCase() !== "object") ) {
+				( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
 
 				newSelector = selector;
 				newContext = context;
@@ -819,27 +846,36 @@ function Sizzle( selector, context, results, seed ) {
 				// descendant combinators, which is not what we want.
 				// In such cases, we work around the behavior by prefixing every selector in the
 				// list with an ID selector referencing the scope context.
+				// The technique has to be used as well when a leading combinator is used
+				// as such selectors are not recognized by querySelectorAll.
 				// Thanks to Andrew Dupont for this technique.
-				if ( nodeType === 1 && rdescend.test( selector ) ) {
+				if ( nodeType === 1 &&
+					( rdescend.test( selector ) || rcombinators.test( selector ) ) ) {
 
-					// Capture the context ID, setting it first if necessary
-					if ( (nid = context.getAttribute( "id" )) ) {
-						nid = nid.replace( rcssescape, fcssescape );
-					} else {
-						context.setAttribute( "id", (nid = expando) );
+					// Expand context for sibling selectors
+					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
+						context;
+
+					// We can use :scope instead of the ID hack if the browser
+					// supports it & if we're not changing the context.
+					if ( newContext !== context || !support.scope ) {
+
+						// Capture the context ID, setting it first if necessary
+						if ( ( nid = context.getAttribute( "id" ) ) ) {
+							nid = nid.replace( rcssescape, fcssescape );
+						} else {
+							context.setAttribute( "id", ( nid = expando ) );
+						}
 					}
 
 					// Prefix every selector in the list
 					groups = tokenize( selector );
 					i = groups.length;
 					while ( i-- ) {
-						groups[i] = "#" + nid + " " + toSelector( groups[i] );
+						groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " +
+							toSelector( groups[ i ] );
 					}
 					newSelector = groups.join( "," );
-
-					// Expand context for sibling selectors
-					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
-						context;
 				}
 
 				try {
@@ -872,12 +908,14 @@ function createCache() {
 	var keys = [];
 
 	function cache( key, value ) {
+
 		// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
 		if ( keys.push( key + " " ) > Expr.cacheLength ) {
+
 			// Only keep the most recent entries
 			delete cache[ keys.shift() ];
 		}
-		return (cache[ key + " " ] = value);
+		return ( cache[ key + " " ] = value );
 	}
 	return cache;
 }
@@ -896,17 +934,19 @@ function markFunction( fn ) {
  * @param {Function} fn Passed the created element and returns a boolean result
  */
 function assert( fn ) {
-	var el = document.createElement("fieldset");
+	var el = document.createElement( "fieldset" );
 
 	try {
 		return !!fn( el );
-	} catch (e) {
+	} catch ( e ) {
 		return false;
 	} finally {
+
 		// Remove from its parent by default
 		if ( el.parentNode ) {
 			el.parentNode.removeChild( el );
 		}
+
 		// release memory in IE
 		el = null;
 	}
@@ -918,11 +958,11 @@ function assert( fn ) {
  * @param {Function} handler The method that will be applied
  */
 function addHandle( attrs, handler ) {
-	var arr = attrs.split("|"),
+	var arr = attrs.split( "|" ),
 		i = arr.length;
 
 	while ( i-- ) {
-		Expr.attrHandle[ arr[i] ] = handler;
+		Expr.attrHandle[ arr[ i ] ] = handler;
 	}
 }
 
@@ -944,7 +984,7 @@ function siblingCheck( a, b ) {
 
 	// Check if b follows a
 	if ( cur ) {
-		while ( (cur = cur.nextSibling) ) {
+		while ( ( cur = cur.nextSibling ) ) {
 			if ( cur === b ) {
 				return -1;
 			}
@@ -972,7 +1012,7 @@ function createInputPseudo( type ) {
 function createButtonPseudo( type ) {
 	return function( elem ) {
 		var name = elem.nodeName.toLowerCase();
-		return (name === "input" || name === "button") && elem.type === type;
+		return ( name === "input" || name === "button" ) && elem.type === type;
 	};
 }
 
@@ -1015,7 +1055,7 @@ function createDisabledPseudo( disabled ) {
 					// Where there is no isDisabled, check manually
 					/* jshint -W018 */
 					elem.isDisabled !== !disabled &&
-						inDisabledFieldset( elem ) === disabled;
+					inDisabledFieldset( elem ) === disabled;
 			}
 
 			return elem.disabled === disabled;
@@ -1037,21 +1077,21 @@ function createDisabledPseudo( disabled ) {
  * @param {Function} fn
  */
 function createPositionalPseudo( fn ) {
-	return markFunction(function( argument ) {
+	return markFunction( function( argument ) {
 		argument = +argument;
-		return markFunction(function( seed, matches ) {
+		return markFunction( function( seed, matches ) {
 			var j,
 				matchIndexes = fn( [], seed.length, argument ),
 				i = matchIndexes.length;
 
 			// Match elements found at the specified indexes
 			while ( i-- ) {
-				if ( seed[ (j = matchIndexes[i]) ] ) {
-					seed[j] = !(matches[j] = seed[j]);
+				if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
+					seed[ j ] = !( matches[ j ] = seed[ j ] );
 				}
 			}
-		});
-	});
+		} );
+	} );
 }
 
 /**
@@ -1072,8 +1112,8 @@ support = Sizzle.support = {};
  * @returns {Boolean} True iff elem is a non-HTML XML node
  */
 isXML = Sizzle.isXML = function( elem ) {
-	var namespace = elem.namespaceURI,
-		docElem = (elem.ownerDocument || elem).documentElement;
+	var namespace = elem && elem.namespaceURI,
+		docElem = elem && ( elem.ownerDocument || elem ).documentElement;
 
 	// Support: IE <=8
 	// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
@@ -1091,7 +1131,11 @@ setDocument = Sizzle.setDocument = function( node ) {
 		doc = node ? node.ownerDocument || node : preferredDoc;
 
 	// Return early if doc is invalid or already selected
-	if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) {
 		return document;
 	}
 
@@ -1100,10 +1144,14 @@ setDocument = Sizzle.setDocument = function( node ) {
 	docElem = document.documentElement;
 	documentIsHTML = !isXML( document );
 
-	// Support: IE 9-11, Edge
+	// Support: IE 9 - 11+, Edge 12 - 18+
 	// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
-	if ( preferredDoc !== document &&
-		(subWindow = document.defaultView) && subWindow.top !== subWindow ) {
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( preferredDoc != document &&
+		( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
 
 		// Support: IE 11, Edge
 		if ( subWindow.addEventListener ) {
@@ -1115,25 +1163,36 @@ setDocument = Sizzle.setDocument = function( node ) {
 		}
 	}
 
+	// Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only,
+	// Safari 4 - 5 only, Opera <=11.6 - 12.x only
+	// IE/Edge & older browsers don't support the :scope pseudo-class.
+	// Support: Safari 6.0 only
+	// Safari 6.0 supports :scope but it's an alias of :root there.
+	support.scope = assert( function( el ) {
+		docElem.appendChild( el ).appendChild( document.createElement( "div" ) );
+		return typeof el.querySelectorAll !== "undefined" &&
+			!el.querySelectorAll( ":scope fieldset div" ).length;
+	} );
+
 	/* Attributes
 	---------------------------------------------------------------------- */
 
 	// Support: IE<8
 	// Verify that getAttribute really returns attributes and not properties
 	// (excepting IE8 booleans)
-	support.attributes = assert(function( el ) {
+	support.attributes = assert( function( el ) {
 		el.className = "i";
-		return !el.getAttribute("className");
-	});
+		return !el.getAttribute( "className" );
+	} );
 
 	/* getElement(s)By*
 	---------------------------------------------------------------------- */
 
 	// Check if getElementsByTagName("*") returns only elements
-	support.getElementsByTagName = assert(function( el ) {
-		el.appendChild( document.createComment("") );
-		return !el.getElementsByTagName("*").length;
-	});
+	support.getElementsByTagName = assert( function( el ) {
+		el.appendChild( document.createComment( "" ) );
+		return !el.getElementsByTagName( "*" ).length;
+	} );
 
 	// Support: IE<9
 	support.getElementsByClassName = rnative.test( document.getElementsByClassName );
@@ -1142,38 +1201,38 @@ setDocument = Sizzle.setDocument = function( node ) {
 	// Check if getElementById returns elements by name
 	// The broken getElementById methods don't pick up programmatically-set names,
 	// so use a roundabout getElementsByName test
-	support.getById = assert(function( el ) {
+	support.getById = assert( function( el ) {
 		docElem.appendChild( el ).id = expando;
 		return !document.getElementsByName || !document.getElementsByName( expando ).length;
-	});
+	} );
 
 	// ID filter and find
 	if ( support.getById ) {
-		Expr.filter["ID"] = function( id ) {
+		Expr.filter[ "ID" ] = function( id ) {
 			var attrId = id.replace( runescape, funescape );
 			return function( elem ) {
-				return elem.getAttribute("id") === attrId;
+				return elem.getAttribute( "id" ) === attrId;
 			};
 		};
-		Expr.find["ID"] = function( id, context ) {
+		Expr.find[ "ID" ] = function( id, context ) {
 			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
 				var elem = context.getElementById( id );
 				return elem ? [ elem ] : [];
 			}
 		};
 	} else {
-		Expr.filter["ID"] =  function( id ) {
+		Expr.filter[ "ID" ] =  function( id ) {
 			var attrId = id.replace( runescape, funescape );
 			return function( elem ) {
 				var node = typeof elem.getAttributeNode !== "undefined" &&
-					elem.getAttributeNode("id");
+					elem.getAttributeNode( "id" );
 				return node && node.value === attrId;
 			};
 		};
 
 		// Support: IE 6 - 7 only
 		// getElementById is not reliable as a find shortcut
-		Expr.find["ID"] = function( id, context ) {
+		Expr.find[ "ID" ] = function( id, context ) {
 			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
 				var node, i, elems,
 					elem = context.getElementById( id );
@@ -1181,7 +1240,7 @@ setDocument = Sizzle.setDocument = function( node ) {
 				if ( elem ) {
 
 					// Verify the id attribute
-					node = elem.getAttributeNode("id");
+					node = elem.getAttributeNode( "id" );
 					if ( node && node.value === id ) {
 						return [ elem ];
 					}
@@ -1189,8 +1248,8 @@ setDocument = Sizzle.setDocument = function( node ) {
 					// Fall back on getElementsByName
 					elems = context.getElementsByName( id );
 					i = 0;
-					while ( (elem = elems[i++]) ) {
-						node = elem.getAttributeNode("id");
+					while ( ( elem = elems[ i++ ] ) ) {
+						node = elem.getAttributeNode( "id" );
 						if ( node && node.value === id ) {
 							return [ elem ];
 						}
@@ -1203,7 +1262,7 @@ setDocument = Sizzle.setDocument = function( node ) {
 	}
 
 	// Tag
-	Expr.find["TAG"] = support.getElementsByTagName ?
+	Expr.find[ "TAG" ] = support.getElementsByTagName ?
 		function( tag, context ) {
 			if ( typeof context.getElementsByTagName !== "undefined" ) {
 				return context.getElementsByTagName( tag );
@@ -1218,12 +1277,13 @@ setDocument = Sizzle.setDocument = function( node ) {
 			var elem,
 				tmp = [],
 				i = 0,
+
 				// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
 				results = context.getElementsByTagName( tag );
 
 			// Filter out possible comments
 			if ( tag === "*" ) {
-				while ( (elem = results[i++]) ) {
+				while ( ( elem = results[ i++ ] ) ) {
 					if ( elem.nodeType === 1 ) {
 						tmp.push( elem );
 					}
@@ -1235,7 +1295,7 @@ setDocument = Sizzle.setDocument = function( node ) {
 		};
 
 	// Class
-	Expr.find["CLASS"] = support.getElementsByClassName && function( className, context ) {
+	Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
 		if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
 			return context.getElementsByClassName( className );
 		}
@@ -1256,10 +1316,14 @@ setDocument = Sizzle.setDocument = function( node ) {
 	// See https://bugs.jquery.com/ticket/13378
 	rbuggyQSA = [];
 
-	if ( (support.qsa = rnative.test( document.querySelectorAll )) ) {
+	if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
+
 		// Build QSA regex
 		// Regex strategy adopted from Diego Perini
-		assert(function( el ) {
+		assert( function( el ) {
+
+			var input;
+
 			// Select is set to empty string on purpose
 			// This is to test IE's treatment of not explicitly
 			// setting a boolean content attribute,
@@ -1273,78 +1337,98 @@ setDocument = Sizzle.setDocument = function( node ) {
 			// Nothing should be selected when empty strings follow ^= or $= or *=
 			// The test attribute must be unknown in Opera but "safe" for WinRT
 			// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
-			if ( el.querySelectorAll("[msallowcapture^='']").length ) {
+			if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
 				rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
 			}
 
 			// Support: IE8
 			// Boolean attributes and "value" are not treated correctly
-			if ( !el.querySelectorAll("[selected]").length ) {
+			if ( !el.querySelectorAll( "[selected]" ).length ) {
 				rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
 			}
 
 			// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
 			if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
-				rbuggyQSA.push("~=");
+				rbuggyQSA.push( "~=" );
+			}
+
+			// Support: IE 11+, Edge 15 - 18+
+			// IE 11/Edge don't find elements on a `[name='']` query in some cases.
+			// Adding a temporary attribute to the document before the selection works
+			// around the issue.
+			// Interestingly, IE 10 & older don't seem to have the issue.
+			input = document.createElement( "input" );
+			input.setAttribute( "name", "" );
+			el.appendChild( input );
+			if ( !el.querySelectorAll( "[name='']" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" +
+					whitespace + "*(?:''|\"\")" );
 			}
 
 			// Webkit/Opera - :checked should return selected option elements
 			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
 			// IE8 throws error here and will not see later tests
-			if ( !el.querySelectorAll(":checked").length ) {
-				rbuggyQSA.push(":checked");
+			if ( !el.querySelectorAll( ":checked" ).length ) {
+				rbuggyQSA.push( ":checked" );
 			}
 
 			// Support: Safari 8+, iOS 8+
 			// https://bugs.webkit.org/show_bug.cgi?id=136851
 			// In-page `selector#id sibling-combinator selector` fails
 			if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
-				rbuggyQSA.push(".#.+[+~]");
+				rbuggyQSA.push( ".#.+[+~]" );
 			}
-		});
 
-		assert(function( el ) {
+			// Support: Firefox <=3.6 - 5 only
+			// Old Firefox doesn't throw on a badly-escaped identifier.
+			el.querySelectorAll( "\\\f" );
+			rbuggyQSA.push( "[\\r\\n\\f]" );
+		} );
+
+		assert( function( el ) {
 			el.innerHTML = "<a href='' disabled='disabled'></a>" +
 				"<select disabled='disabled'><option/></select>";
 
 			// Support: Windows 8 Native Apps
 			// The type and name attributes are restricted during .innerHTML assignment
-			var input = document.createElement("input");
+			var input = document.createElement( "input" );
 			input.setAttribute( "type", "hidden" );
 			el.appendChild( input ).setAttribute( "name", "D" );
 
 			// Support: IE8
 			// Enforce case-sensitivity of name attribute
-			if ( el.querySelectorAll("[name=d]").length ) {
+			if ( el.querySelectorAll( "[name=d]" ).length ) {
 				rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
 			}
 
 			// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
 			// IE8 throws error here and will not see later tests
-			if ( el.querySelectorAll(":enabled").length !== 2 ) {
+			if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
 				rbuggyQSA.push( ":enabled", ":disabled" );
 			}
 
 			// Support: IE9-11+
 			// IE's :disabled selector does not pick up the children of disabled fieldsets
 			docElem.appendChild( el ).disabled = true;
-			if ( el.querySelectorAll(":disabled").length !== 2 ) {
+			if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
 				rbuggyQSA.push( ":enabled", ":disabled" );
 			}
 
+			// Support: Opera 10 - 11 only
 			// Opera 10-11 does not throw on post-comma invalid pseudos
-			el.querySelectorAll("*,:x");
-			rbuggyQSA.push(",.*:");
-		});
+			el.querySelectorAll( "*,:x" );
+			rbuggyQSA.push( ",.*:" );
+		} );
 	}
 
-	if ( (support.matchesSelector = rnative.test( (matches = docElem.matches ||
+	if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
 		docElem.webkitMatchesSelector ||
 		docElem.mozMatchesSelector ||
 		docElem.oMatchesSelector ||
-		docElem.msMatchesSelector) )) ) {
+		docElem.msMatchesSelector ) ) ) ) {
+
+		assert( function( el ) {
 
-		assert(function( el ) {
 			// Check to see if it's possible to do matchesSelector
 			// on a disconnected node (IE 9)
 			support.disconnectedMatch = matches.call( el, "*" );
@@ -1353,11 +1437,11 @@ setDocument = Sizzle.setDocument = function( node ) {
 			// Gecko does not error, returns false instead
 			matches.call( el, "[s!='']:x" );
 			rbuggyMatches.push( "!=", pseudos );
-		});
+		} );
 	}
 
-	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join("|") );
-	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join("|") );
+	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
+	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
 
 	/* Contains
 	---------------------------------------------------------------------- */
@@ -1374,11 +1458,11 @@ setDocument = Sizzle.setDocument = function( node ) {
 				adown.contains ?
 					adown.contains( bup ) :
 					a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
-			));
+			) );
 		} :
 		function( a, b ) {
 			if ( b ) {
-				while ( (b = b.parentNode) ) {
+				while ( ( b = b.parentNode ) ) {
 					if ( b === a ) {
 						return true;
 					}
@@ -1407,7 +1491,11 @@ setDocument = Sizzle.setDocument = function( node ) {
 		}
 
 		// Calculate position if both inputs belong to the same document
-		compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
+		// Support: IE 11+, Edge 17 - 18+
+		// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+		// two documents; shallow comparisons work.
+		// eslint-disable-next-line eqeqeq
+		compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ?
 			a.compareDocumentPosition( b ) :
 
 			// Otherwise we know they are disconnected
@@ -1415,13 +1503,24 @@ setDocument = Sizzle.setDocument = function( node ) {
 
 		// Disconnected nodes
 		if ( compare & 1 ||
-			(!support.sortDetached && b.compareDocumentPosition( a ) === compare) ) {
+			( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
 
 			// Choose the first element that is related to our preferred document
-			if ( a === document || a.ownerDocument === preferredDoc && contains(preferredDoc, a) ) {
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( a == document || a.ownerDocument == preferredDoc &&
+				contains( preferredDoc, a ) ) {
 				return -1;
 			}
-			if ( b === document || b.ownerDocument === preferredDoc && contains(preferredDoc, b) ) {
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( b == document || b.ownerDocument == preferredDoc &&
+				contains( preferredDoc, b ) ) {
 				return 1;
 			}
 
@@ -1434,6 +1533,7 @@ setDocument = Sizzle.setDocument = function( node ) {
 		return compare & 4 ? -1 : 1;
 	} :
 	function( a, b ) {
+
 		// Exit early if the nodes are identical
 		if ( a === b ) {
 			hasDuplicate = true;
@@ -1449,8 +1549,14 @@ setDocument = Sizzle.setDocument = function( node ) {
 
 		// Parentless nodes are either documents or disconnected
 		if ( !aup || !bup ) {
-			return a === document ? -1 :
-				b === document ? 1 :
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			return a == document ? -1 :
+				b == document ? 1 :
+				/* eslint-enable eqeqeq */
 				aup ? -1 :
 				bup ? 1 :
 				sortInput ?
@@ -1464,26 +1570,32 @@ setDocument = Sizzle.setDocument = function( node ) {
 
 		// Otherwise we need full lists of their ancestors for comparison
 		cur = a;
-		while ( (cur = cur.parentNode) ) {
+		while ( ( cur = cur.parentNode ) ) {
 			ap.unshift( cur );
 		}
 		cur = b;
-		while ( (cur = cur.parentNode) ) {
+		while ( ( cur = cur.parentNode ) ) {
 			bp.unshift( cur );
 		}
 
 		// Walk down the tree looking for a discrepancy
-		while ( ap[i] === bp[i] ) {
+		while ( ap[ i ] === bp[ i ] ) {
 			i++;
 		}
 
 		return i ?
+
 			// Do a sibling check if the nodes have a common ancestor
-			siblingCheck( ap[i], bp[i] ) :
+			siblingCheck( ap[ i ], bp[ i ] ) :
 
 			// Otherwise nodes in our document sort first
-			ap[i] === preferredDoc ? -1 :
-			bp[i] === preferredDoc ? 1 :
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			ap[ i ] == preferredDoc ? -1 :
+			bp[ i ] == preferredDoc ? 1 :
+			/* eslint-enable eqeqeq */
 			0;
 	};
 
@@ -1495,10 +1607,7 @@ Sizzle.matches = function( expr, elements ) {
 };
 
 Sizzle.matchesSelector = function( elem, expr ) {
-	// Set document vars if needed
-	if ( ( elem.ownerDocument || elem ) !== document ) {
-		setDocument( elem );
-	}
+	setDocument( elem );
 
 	if ( support.matchesSelector && documentIsHTML &&
 		!nonnativeSelectorCache[ expr + " " ] &&
@@ -1510,12 +1619,13 @@ Sizzle.matchesSelector = function( elem, expr ) {
 
 			// IE 9's matchesSelector returns false on disconnected nodes
 			if ( ret || support.disconnectedMatch ||
-					// As well, disconnected nodes are said to be in a document
-					// fragment in IE 9
-					elem.document && elem.document.nodeType !== 11 ) {
+
+				// As well, disconnected nodes are said to be in a document
+				// fragment in IE 9
+				elem.document && elem.document.nodeType !== 11 ) {
 				return ret;
 			}
-		} catch (e) {
+		} catch ( e ) {
 			nonnativeSelectorCache( expr, true );
 		}
 	}
@@ -1524,20 +1634,31 @@ Sizzle.matchesSelector = function( elem, expr ) {
 };
 
 Sizzle.contains = function( context, elem ) {
+
 	// Set document vars if needed
-	if ( ( context.ownerDocument || context ) !== document ) {
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( context.ownerDocument || context ) != document ) {
 		setDocument( context );
 	}
 	return contains( context, elem );
 };
 
 Sizzle.attr = function( elem, name ) {
+
 	// Set document vars if needed
-	if ( ( elem.ownerDocument || elem ) !== document ) {
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( elem.ownerDocument || elem ) != document ) {
 		setDocument( elem );
 	}
 
 	var fn = Expr.attrHandle[ name.toLowerCase() ],
+
 		// Don't get fooled by Object.prototype properties (jQuery #13807)
 		val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
 			fn( elem, name, !documentIsHTML ) :
@@ -1547,13 +1668,13 @@ Sizzle.attr = function( elem, name ) {
 		val :
 		support.attributes || !documentIsHTML ?
 			elem.getAttribute( name ) :
-			(val = elem.getAttributeNode(name)) && val.specified ?
+			( val = elem.getAttributeNode( name ) ) && val.specified ?
 				val.value :
 				null;
 };
 
 Sizzle.escape = function( sel ) {
-	return (sel + "").replace( rcssescape, fcssescape );
+	return ( sel + "" ).replace( rcssescape, fcssescape );
 };
 
 Sizzle.error = function( msg ) {
@@ -1576,7 +1697,7 @@ Sizzle.uniqueSort = function( results ) {
 	results.sort( sortOrder );
 
 	if ( hasDuplicate ) {
-		while ( (elem = results[i++]) ) {
+		while ( ( elem = results[ i++ ] ) ) {
 			if ( elem === results[ i ] ) {
 				j = duplicates.push( i );
 			}
@@ -1604,17 +1725,21 @@ getText = Sizzle.getText = function( elem ) {
 		nodeType = elem.nodeType;
 
 	if ( !nodeType ) {
+
 		// If no nodeType, this is expected to be an array
-		while ( (node = elem[i++]) ) {
+		while ( ( node = elem[ i++ ] ) ) {
+
 			// Do not traverse comment nodes
 			ret += getText( node );
 		}
 	} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
+
 		// Use textContent for elements
 		// innerText usage removed for consistency of new lines (jQuery #11153)
 		if ( typeof elem.textContent === "string" ) {
 			return elem.textContent;
 		} else {
+
 			// Traverse its children
 			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
 				ret += getText( elem );
@@ -1623,6 +1748,7 @@ getText = Sizzle.getText = function( elem ) {
 	} else if ( nodeType === 3 || nodeType === 4 ) {
 		return elem.nodeValue;
 	}
+
 	// Do not include comment or processing instruction nodes
 
 	return ret;
@@ -1650,19 +1776,21 @@ Expr = Sizzle.selectors = {
 
 	preFilter: {
 		"ATTR": function( match ) {
-			match[1] = match[1].replace( runescape, funescape );
+			match[ 1 ] = match[ 1 ].replace( runescape, funescape );
 
 			// Move the given value to match[3] whether quoted or unquoted
-			match[3] = ( match[3] || match[4] || match[5] || "" ).replace( runescape, funescape );
+			match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
+				match[ 5 ] || "" ).replace( runescape, funescape );
 
-			if ( match[2] === "~=" ) {
-				match[3] = " " + match[3] + " ";
+			if ( match[ 2 ] === "~=" ) {
+				match[ 3 ] = " " + match[ 3 ] + " ";
 			}
 
 			return match.slice( 0, 4 );
 		},
 
 		"CHILD": function( match ) {
+
 			/* matches from matchExpr["CHILD"]
 				1 type (only|nth|...)
 				2 what (child|of-type)
@@ -1673,22 +1801,25 @@ Expr = Sizzle.selectors = {
 				7 sign of y-component
 				8 y of y-component
 			*/
-			match[1] = match[1].toLowerCase();
+			match[ 1 ] = match[ 1 ].toLowerCase();
+
+			if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
 
-			if ( match[1].slice( 0, 3 ) === "nth" ) {
 				// nth-* requires argument
-				if ( !match[3] ) {
-					Sizzle.error( match[0] );
+				if ( !match[ 3 ] ) {
+					Sizzle.error( match[ 0 ] );
 				}
 
 				// numeric x and y parameters for Expr.filter.CHILD
 				// remember that false/true cast respectively to 0/1
-				match[4] = +( match[4] ? match[5] + (match[6] || 1) : 2 * ( match[3] === "even" || match[3] === "odd" ) );
-				match[5] = +( ( match[7] + match[8] ) || match[3] === "odd" );
+				match[ 4 ] = +( match[ 4 ] ?
+					match[ 5 ] + ( match[ 6 ] || 1 ) :
+					2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
+				match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
 
-			// other types prohibit arguments
-			} else if ( match[3] ) {
-				Sizzle.error( match[0] );
+				// other types prohibit arguments
+			} else if ( match[ 3 ] ) {
+				Sizzle.error( match[ 0 ] );
 			}
 
 			return match;
@@ -1696,26 +1827,28 @@ Expr = Sizzle.selectors = {
 
 		"PSEUDO": function( match ) {
 			var excess,
-				unquoted = !match[6] && match[2];
+				unquoted = !match[ 6 ] && match[ 2 ];
 
-			if ( matchExpr["CHILD"].test( match[0] ) ) {
+			if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
 				return null;
 			}
 
 			// Accept quoted arguments as-is
-			if ( match[3] ) {
-				match[2] = match[4] || match[5] || "";
+			if ( match[ 3 ] ) {
+				match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
 
 			// Strip excess characters from unquoted arguments
 			} else if ( unquoted && rpseudo.test( unquoted ) &&
+
 				// Get excess from tokenize (recursively)
-				(excess = tokenize( unquoted, true )) &&
+				( excess = tokenize( unquoted, true ) ) &&
+
 				// advance to the next closing parenthesis
-				(excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length) ) {
+				( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
 
 				// excess is a negative index
-				match[0] = match[0].slice( 0, excess );
-				match[2] = unquoted.slice( 0, excess );
+				match[ 0 ] = match[ 0 ].slice( 0, excess );
+				match[ 2 ] = unquoted.slice( 0, excess );
 			}
 
 			// Return only captures needed by the pseudo filter method (type and argument)
@@ -1728,7 +1861,9 @@ Expr = Sizzle.selectors = {
 		"TAG": function( nodeNameSelector ) {
 			var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
 			return nodeNameSelector === "*" ?
-				function() { return true; } :
+				function() {
+					return true;
+				} :
 				function( elem ) {
 					return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
 				};
@@ -1738,10 +1873,16 @@ Expr = Sizzle.selectors = {
 			var pattern = classCache[ className + " " ];
 
 			return pattern ||
-				(pattern = new RegExp( "(^|" + whitespace + ")" + className + "(" + whitespace + "|$)" )) &&
-				classCache( className, function( elem ) {
-					return pattern.test( typeof elem.className === "string" && elem.className || typeof elem.getAttribute !== "undefined" && elem.getAttribute("class") || "" );
-				});
+				( pattern = new RegExp( "(^|" + whitespace +
+					")" + className + "(" + whitespace + "|$)" ) ) && classCache(
+						className, function( elem ) {
+							return pattern.test(
+								typeof elem.className === "string" && elem.className ||
+								typeof elem.getAttribute !== "undefined" &&
+									elem.getAttribute( "class" ) ||
+								""
+							);
+				} );
 		},
 
 		"ATTR": function( name, operator, check ) {
@@ -1757,6 +1898,8 @@ Expr = Sizzle.selectors = {
 
 				result += "";
 
+				/* eslint-disable max-len */
+
 				return operator === "=" ? result === check :
 					operator === "!=" ? result !== check :
 					operator === "^=" ? check && result.indexOf( check ) === 0 :
@@ -1765,10 +1908,12 @@ Expr = Sizzle.selectors = {
 					operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
 					operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
 					false;
+				/* eslint-enable max-len */
+
 			};
 		},
 
-		"CHILD": function( type, what, argument, first, last ) {
+		"CHILD": function( type, what, _argument, first, last ) {
 			var simple = type.slice( 0, 3 ) !== "nth",
 				forward = type.slice( -4 ) !== "last",
 				ofType = what === "of-type";
@@ -1780,7 +1925,7 @@ Expr = Sizzle.selectors = {
 					return !!elem.parentNode;
 				} :
 
-				function( elem, context, xml ) {
+				function( elem, _context, xml ) {
 					var cache, uniqueCache, outerCache, node, nodeIndex, start,
 						dir = simple !== forward ? "nextSibling" : "previousSibling",
 						parent = elem.parentNode,
@@ -1794,7 +1939,7 @@ Expr = Sizzle.selectors = {
 						if ( simple ) {
 							while ( dir ) {
 								node = elem;
-								while ( (node = node[ dir ]) ) {
+								while ( ( node = node[ dir ] ) ) {
 									if ( ofType ?
 										node.nodeName.toLowerCase() === name :
 										node.nodeType === 1 ) {
@@ -1802,6 +1947,7 @@ Expr = Sizzle.selectors = {
 										return false;
 									}
 								}
+
 								// Reverse direction for :only-* (if we haven't yet done so)
 								start = dir = type === "only" && !start && "nextSibling";
 							}
@@ -1817,22 +1963,22 @@ Expr = Sizzle.selectors = {
 
 							// ...in a gzip-friendly way
 							node = parent;
-							outerCache = node[ expando ] || (node[ expando ] = {});
+							outerCache = node[ expando ] || ( node[ expando ] = {} );
 
 							// Support: IE <9 only
 							// Defend against cloned attroperties (jQuery gh-1709)
 							uniqueCache = outerCache[ node.uniqueID ] ||
-								(outerCache[ node.uniqueID ] = {});
+								( outerCache[ node.uniqueID ] = {} );
 
 							cache = uniqueCache[ type ] || [];
 							nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
 							diff = nodeIndex && cache[ 2 ];
 							node = nodeIndex && parent.childNodes[ nodeIndex ];
 
-							while ( (node = ++nodeIndex && node && node[ dir ] ||
+							while ( ( node = ++nodeIndex && node && node[ dir ] ||
 
 								// Fallback to seeking `elem` from the start
-								(diff = nodeIndex = 0) || start.pop()) ) {
+								( diff = nodeIndex = 0 ) || start.pop() ) ) {
 
 								// When found, cache indexes on `parent` and break
 								if ( node.nodeType === 1 && ++diff && node === elem ) {
@@ -1842,16 +1988,18 @@ Expr = Sizzle.selectors = {
 							}
 
 						} else {
+
 							// Use previously-cached element index if available
 							if ( useCache ) {
+
 								// ...in a gzip-friendly way
 								node = elem;
-								outerCache = node[ expando ] || (node[ expando ] = {});
+								outerCache = node[ expando ] || ( node[ expando ] = {} );
 
 								// Support: IE <9 only
 								// Defend against cloned attroperties (jQuery gh-1709)
 								uniqueCache = outerCache[ node.uniqueID ] ||
-									(outerCache[ node.uniqueID ] = {});
+									( outerCache[ node.uniqueID ] = {} );
 
 								cache = uniqueCache[ type ] || [];
 								nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
@@ -1861,9 +2009,10 @@ Expr = Sizzle.selectors = {
 							// xml :nth-child(...)
 							// or :nth-last-child(...) or :nth(-last)?-of-type(...)
 							if ( diff === false ) {
+
 								// Use the same loop as above to seek `elem` from the start
-								while ( (node = ++nodeIndex && node && node[ dir ] ||
-									(diff = nodeIndex = 0) || start.pop()) ) {
+								while ( ( node = ++nodeIndex && node && node[ dir ] ||
+									( diff = nodeIndex = 0 ) || start.pop() ) ) {
 
 									if ( ( ofType ?
 										node.nodeName.toLowerCase() === name :
@@ -1872,12 +2021,13 @@ Expr = Sizzle.selectors = {
 
 										// Cache the index of each encountered element
 										if ( useCache ) {
-											outerCache = node[ expando ] || (node[ expando ] = {});
+											outerCache = node[ expando ] ||
+												( node[ expando ] = {} );
 
 											// Support: IE <9 only
 											// Defend against cloned attroperties (jQuery gh-1709)
 											uniqueCache = outerCache[ node.uniqueID ] ||
-												(outerCache[ node.uniqueID ] = {});
+												( outerCache[ node.uniqueID ] = {} );
 
 											uniqueCache[ type ] = [ dirruns, diff ];
 										}
@@ -1898,6 +2048,7 @@ Expr = Sizzle.selectors = {
 		},
 
 		"PSEUDO": function( pseudo, argument ) {
+
 			// pseudo-class names are case-insensitive
 			// http://www.w3.org/TR/selectors/#pseudo-classes
 			// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
@@ -1917,15 +2068,15 @@ Expr = Sizzle.selectors = {
 			if ( fn.length > 1 ) {
 				args = [ pseudo, pseudo, "", argument ];
 				return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
-					markFunction(function( seed, matches ) {
+					markFunction( function( seed, matches ) {
 						var idx,
 							matched = fn( seed, argument ),
 							i = matched.length;
 						while ( i-- ) {
-							idx = indexOf( seed, matched[i] );
-							seed[ idx ] = !( matches[ idx ] = matched[i] );
+							idx = indexOf( seed, matched[ i ] );
+							seed[ idx ] = !( matches[ idx ] = matched[ i ] );
 						}
-					}) :
+					} ) :
 					function( elem ) {
 						return fn( elem, 0, args );
 					};
@@ -1936,8 +2087,10 @@ Expr = Sizzle.selectors = {
 	},
 
 	pseudos: {
+
 		// Potentially complex pseudos
-		"not": markFunction(function( selector ) {
+		"not": markFunction( function( selector ) {
+
 			// Trim the selector passed to compile
 			// to avoid treating leading and trailing
 			// spaces as combinators
@@ -1946,39 +2099,40 @@ Expr = Sizzle.selectors = {
 				matcher = compile( selector.replace( rtrim, "$1" ) );
 
 			return matcher[ expando ] ?
-				markFunction(function( seed, matches, context, xml ) {
+				markFunction( function( seed, matches, _context, xml ) {
 					var elem,
 						unmatched = matcher( seed, null, xml, [] ),
 						i = seed.length;
 
 					// Match elements unmatched by `matcher`
 					while ( i-- ) {
-						if ( (elem = unmatched[i]) ) {
-							seed[i] = !(matches[i] = elem);
+						if ( ( elem = unmatched[ i ] ) ) {
+							seed[ i ] = !( matches[ i ] = elem );
 						}
 					}
-				}) :
-				function( elem, context, xml ) {
-					input[0] = elem;
+				} ) :
+				function( elem, _context, xml ) {
+					input[ 0 ] = elem;
 					matcher( input, null, xml, results );
+
 					// Don't keep the element (issue #299)
-					input[0] = null;
+					input[ 0 ] = null;
 					return !results.pop();
 				};
-		}),
+		} ),
 
-		"has": markFunction(function( selector ) {
+		"has": markFunction( function( selector ) {
 			return function( elem ) {
 				return Sizzle( selector, elem ).length > 0;
 			};
-		}),
+		} ),
 
-		"contains": markFunction(function( text ) {
+		"contains": markFunction( function( text ) {
 			text = text.replace( runescape, funescape );
 			return function( elem ) {
 				return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
 			};
-		}),
+		} ),
 
 		// "Whether an element is represented by a :lang() selector
 		// is based solely on the element's language value
@@ -1988,25 +2142,26 @@ Expr = Sizzle.selectors = {
 		// The identifier C does not have to be a valid language name."
 		// http://www.w3.org/TR/selectors/#lang-pseudo
 		"lang": markFunction( function( lang ) {
+
 			// lang value must be a valid identifier
-			if ( !ridentifier.test(lang || "") ) {
+			if ( !ridentifier.test( lang || "" ) ) {
 				Sizzle.error( "unsupported lang: " + lang );
 			}
 			lang = lang.replace( runescape, funescape ).toLowerCase();
 			return function( elem ) {
 				var elemLang;
 				do {
-					if ( (elemLang = documentIsHTML ?
+					if ( ( elemLang = documentIsHTML ?
 						elem.lang :
-						elem.getAttribute("xml:lang") || elem.getAttribute("lang")) ) {
+						elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
 
 						elemLang = elemLang.toLowerCase();
 						return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
 					}
-				} while ( (elem = elem.parentNode) && elem.nodeType === 1 );
+				} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
 				return false;
 			};
-		}),
+		} ),
 
 		// Miscellaneous
 		"target": function( elem ) {
@@ -2019,7 +2174,9 @@ Expr = Sizzle.selectors = {
 		},
 
 		"focus": function( elem ) {
-			return elem === document.activeElement && (!document.hasFocus || document.hasFocus()) && !!(elem.type || elem.href || ~elem.tabIndex);
+			return elem === document.activeElement &&
+				( !document.hasFocus || document.hasFocus() ) &&
+				!!( elem.type || elem.href || ~elem.tabIndex );
 		},
 
 		// Boolean properties
@@ -2027,16 +2184,20 @@ Expr = Sizzle.selectors = {
 		"disabled": createDisabledPseudo( true ),
 
 		"checked": function( elem ) {
+
 			// In CSS3, :checked should return both checked and selected elements
 			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
 			var nodeName = elem.nodeName.toLowerCase();
-			return (nodeName === "input" && !!elem.checked) || (nodeName === "option" && !!elem.selected);
+			return ( nodeName === "input" && !!elem.checked ) ||
+				( nodeName === "option" && !!elem.selected );
 		},
 
 		"selected": function( elem ) {
+
 			// Accessing this property makes selected-by-default
 			// options in Safari work properly
 			if ( elem.parentNode ) {
+				// eslint-disable-next-line no-unused-expressions
 				elem.parentNode.selectedIndex;
 			}
 
@@ -2045,6 +2206,7 @@ Expr = Sizzle.selectors = {
 
 		// Contents
 		"empty": function( elem ) {
+
 			// http://www.w3.org/TR/selectors/#empty-pseudo
 			// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
 			//   but not by others (comment: 8; processing instruction: 7; etc.)
@@ -2058,7 +2220,7 @@ Expr = Sizzle.selectors = {
 		},
 
 		"parent": function( elem ) {
-			return !Expr.pseudos["empty"]( elem );
+			return !Expr.pseudos[ "empty" ]( elem );
 		},
 
 		// Element/input types
@@ -2082,39 +2244,40 @@ Expr = Sizzle.selectors = {
 
 				// Support: IE<8
 				// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
-				( (attr = elem.getAttribute("type")) == null || attr.toLowerCase() === "text" );
+				( ( attr = elem.getAttribute( "type" ) ) == null ||
+					attr.toLowerCase() === "text" );
 		},
 
 		// Position-in-collection
-		"first": createPositionalPseudo(function() {
+		"first": createPositionalPseudo( function() {
 			return [ 0 ];
-		}),
+		} ),
 
-		"last": createPositionalPseudo(function( matchIndexes, length ) {
+		"last": createPositionalPseudo( function( _matchIndexes, length ) {
 			return [ length - 1 ];
-		}),
+		} ),
 
-		"eq": createPositionalPseudo(function( matchIndexes, length, argument ) {
+		"eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
 			return [ argument < 0 ? argument + length : argument ];
-		}),
+		} ),
 
-		"even": createPositionalPseudo(function( matchIndexes, length ) {
+		"even": createPositionalPseudo( function( matchIndexes, length ) {
 			var i = 0;
 			for ( ; i < length; i += 2 ) {
 				matchIndexes.push( i );
 			}
 			return matchIndexes;
-		}),
+		} ),
 
-		"odd": createPositionalPseudo(function( matchIndexes, length ) {
+		"odd": createPositionalPseudo( function( matchIndexes, length ) {
 			var i = 1;
 			for ( ; i < length; i += 2 ) {
 				matchIndexes.push( i );
 			}
 			return matchIndexes;
-		}),
+		} ),
 
-		"lt": createPositionalPseudo(function( matchIndexes, length, argument ) {
+		"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
 			var i = argument < 0 ?
 				argument + length :
 				argument > length ?
@@ -2124,19 +2287,19 @@ Expr = Sizzle.selectors = {
 				matchIndexes.push( i );
 			}
 			return matchIndexes;
-		}),
+		} ),
 
-		"gt": createPositionalPseudo(function( matchIndexes, length, argument ) {
+		"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
 			var i = argument < 0 ? argument + length : argument;
 			for ( ; ++i < length; ) {
 				matchIndexes.push( i );
 			}
 			return matchIndexes;
-		})
+		} )
 	}
 };
 
-Expr.pseudos["nth"] = Expr.pseudos["eq"];
+Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
 
 // Add button/input type pseudos
 for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
@@ -2167,37 +2330,39 @@ tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
 	while ( soFar ) {
 
 		// Comma and first run
-		if ( !matched || (match = rcomma.exec( soFar )) ) {
+		if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
 			if ( match ) {
+
 				// Don't consume trailing commas as valid
-				soFar = soFar.slice( match[0].length ) || soFar;
+				soFar = soFar.slice( match[ 0 ].length ) || soFar;
 			}
-			groups.push( (tokens = []) );
+			groups.push( ( tokens = [] ) );
 		}
 
 		matched = false;
 
 		// Combinators
-		if ( (match = rcombinators.exec( soFar )) ) {
+		if ( ( match = rcombinators.exec( soFar ) ) ) {
 			matched = match.shift();
-			tokens.push({
+			tokens.push( {
 				value: matched,
+
 				// Cast descendant combinators to space
-				type: match[0].replace( rtrim, " " )
-			});
+				type: match[ 0 ].replace( rtrim, " " )
+			} );
 			soFar = soFar.slice( matched.length );
 		}
 
 		// Filters
 		for ( type in Expr.filter ) {
-			if ( (match = matchExpr[ type ].exec( soFar )) && (!preFilters[ type ] ||
-				(match = preFilters[ type ]( match ))) ) {
+			if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
+				( match = preFilters[ type ]( match ) ) ) ) {
 				matched = match.shift();
-				tokens.push({
+				tokens.push( {
 					value: matched,
 					type: type,
 					matches: match
-				});
+				} );
 				soFar = soFar.slice( matched.length );
 			}
 		}
@@ -2214,6 +2379,7 @@ tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
 		soFar.length :
 		soFar ?
 			Sizzle.error( selector ) :
+
 			// Cache the tokens
 			tokenCache( selector, groups ).slice( 0 );
 };
@@ -2223,7 +2389,7 @@ function toSelector( tokens ) {
 		len = tokens.length,
 		selector = "";
 	for ( ; i < len; i++ ) {
-		selector += tokens[i].value;
+		selector += tokens[ i ].value;
 	}
 	return selector;
 }
@@ -2236,9 +2402,10 @@ function addCombinator( matcher, combinator, base ) {
 		doneName = done++;
 
 	return combinator.first ?
+
 		// Check against closest ancestor/preceding element
 		function( elem, context, xml ) {
-			while ( (elem = elem[ dir ]) ) {
+			while ( ( elem = elem[ dir ] ) ) {
 				if ( elem.nodeType === 1 || checkNonElements ) {
 					return matcher( elem, context, xml );
 				}
@@ -2253,7 +2420,7 @@ function addCombinator( matcher, combinator, base ) {
 
 			// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
 			if ( xml ) {
-				while ( (elem = elem[ dir ]) ) {
+				while ( ( elem = elem[ dir ] ) ) {
 					if ( elem.nodeType === 1 || checkNonElements ) {
 						if ( matcher( elem, context, xml ) ) {
 							return true;
@@ -2261,27 +2428,29 @@ function addCombinator( matcher, combinator, base ) {
 					}
 				}
 			} else {
-				while ( (elem = elem[ dir ]) ) {
+				while ( ( elem = elem[ dir ] ) ) {
 					if ( elem.nodeType === 1 || checkNonElements ) {
-						outerCache = elem[ expando ] || (elem[ expando ] = {});
+						outerCache = elem[ expando ] || ( elem[ expando ] = {} );
 
 						// Support: IE <9 only
 						// Defend against cloned attroperties (jQuery gh-1709)
-						uniqueCache = outerCache[ elem.uniqueID ] || (outerCache[ elem.uniqueID ] = {});
+						uniqueCache = outerCache[ elem.uniqueID ] ||
+							( outerCache[ elem.uniqueID ] = {} );
 
 						if ( skip && skip === elem.nodeName.toLowerCase() ) {
 							elem = elem[ dir ] || elem;
-						} else if ( (oldCache = uniqueCache[ key ]) &&
+						} else if ( ( oldCache = uniqueCache[ key ] ) &&
 							oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
 
 							// Assign to newCache so results back-propagate to previous elements
-							return (newCache[ 2 ] = oldCache[ 2 ]);
+							return ( newCache[ 2 ] = oldCache[ 2 ] );
 						} else {
+
 							// Reuse newcache so results back-propagate to previous elements
 							uniqueCache[ key ] = newCache;
 
 							// A match means we're done; a fail means we have to keep checking
-							if ( (newCache[ 2 ] = matcher( elem, context, xml )) ) {
+							if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
 								return true;
 							}
 						}
@@ -2297,20 +2466,20 @@ function elementMatcher( matchers ) {
 		function( elem, context, xml ) {
 			var i = matchers.length;
 			while ( i-- ) {
-				if ( !matchers[i]( elem, context, xml ) ) {
+				if ( !matchers[ i ]( elem, context, xml ) ) {
 					return false;
 				}
 			}
 			return true;
 		} :
-		matchers[0];
+		matchers[ 0 ];
 }
 
 function multipleContexts( selector, contexts, results ) {
 	var i = 0,
 		len = contexts.length;
 	for ( ; i < len; i++ ) {
-		Sizzle( selector, contexts[i], results );
+		Sizzle( selector, contexts[ i ], results );
 	}
 	return results;
 }
@@ -2323,7 +2492,7 @@ function condense( unmatched, map, filter, context, xml ) {
 		mapped = map != null;
 
 	for ( ; i < len; i++ ) {
-		if ( (elem = unmatched[i]) ) {
+		if ( ( elem = unmatched[ i ] ) ) {
 			if ( !filter || filter( elem, context, xml ) ) {
 				newUnmatched.push( elem );
 				if ( mapped ) {
@@ -2343,14 +2512,18 @@ function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postS
 	if ( postFinder && !postFinder[ expando ] ) {
 		postFinder = setMatcher( postFinder, postSelector );
 	}
-	return markFunction(function( seed, results, context, xml ) {
+	return markFunction( function( seed, results, context, xml ) {
 		var temp, i, elem,
 			preMap = [],
 			postMap = [],
 			preexisting = results.length,
 
 			// Get initial elements from seed or context
-			elems = seed || multipleContexts( selector || "*", context.nodeType ? [ context ] : context, [] ),
+			elems = seed || multipleContexts(
+				selector || "*",
+				context.nodeType ? [ context ] : context,
+				[]
+			),
 
 			// Prefilter to get matcher input, preserving a map for seed-results synchronization
 			matcherIn = preFilter && ( seed || !selector ) ?
@@ -2358,6 +2531,7 @@ function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postS
 				elems,
 
 			matcherOut = matcher ?
+
 				// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
 				postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
 
@@ -2381,8 +2555,8 @@ function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postS
 			// Un-match failing elements by moving them back to matcherIn
 			i = temp.length;
 			while ( i-- ) {
-				if ( (elem = temp[i]) ) {
-					matcherOut[ postMap[i] ] = !(matcherIn[ postMap[i] ] = elem);
+				if ( ( elem = temp[ i ] ) ) {
+					matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
 				}
 			}
 		}
@@ -2390,25 +2564,27 @@ function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postS
 		if ( seed ) {
 			if ( postFinder || preFilter ) {
 				if ( postFinder ) {
+
 					// Get the final matcherOut by condensing this intermediate into postFinder contexts
 					temp = [];
 					i = matcherOut.length;
 					while ( i-- ) {
-						if ( (elem = matcherOut[i]) ) {
+						if ( ( elem = matcherOut[ i ] ) ) {
+
 							// Restore matcherIn since elem is not yet a final match
-							temp.push( (matcherIn[i] = elem) );
+							temp.push( ( matcherIn[ i ] = elem ) );
 						}
 					}
-					postFinder( null, (matcherOut = []), temp, xml );
+					postFinder( null, ( matcherOut = [] ), temp, xml );
 				}
 
 				// Move matched elements from seed to results to keep them synchronized
 				i = matcherOut.length;
 				while ( i-- ) {
-					if ( (elem = matcherOut[i]) &&
-						(temp = postFinder ? indexOf( seed, elem ) : preMap[i]) > -1 ) {
+					if ( ( elem = matcherOut[ i ] ) &&
+						( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
 
-						seed[temp] = !(results[temp] = elem);
+						seed[ temp ] = !( results[ temp ] = elem );
 					}
 				}
 			}
@@ -2426,14 +2602,14 @@ function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postS
 				push.apply( results, matcherOut );
 			}
 		}
-	});
+	} );
 }
 
 function matcherFromTokens( tokens ) {
 	var checkContext, matcher, j,
 		len = tokens.length,
-		leadingRelative = Expr.relative[ tokens[0].type ],
-		implicitRelative = leadingRelative || Expr.relative[" "],
+		leadingRelative = Expr.relative[ tokens[ 0 ].type ],
+		implicitRelative = leadingRelative || Expr.relative[ " " ],
 		i = leadingRelative ? 1 : 0,
 
 		// The foundational matcher ensures that elements are reachable from top-level context(s)
@@ -2445,38 +2621,43 @@ function matcherFromTokens( tokens ) {
 		}, implicitRelative, true ),
 		matchers = [ function( elem, context, xml ) {
 			var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
-				(checkContext = context).nodeType ?
+				( checkContext = context ).nodeType ?
 					matchContext( elem, context, xml ) :
 					matchAnyContext( elem, context, xml ) );
+
 			// Avoid hanging onto element (issue #299)
 			checkContext = null;
 			return ret;
 		} ];
 
 	for ( ; i < len; i++ ) {
-		if ( (matcher = Expr.relative[ tokens[i].type ]) ) {
-			matchers = [ addCombinator(elementMatcher( matchers ), matcher) ];
+		if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
+			matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
 		} else {
-			matcher = Expr.filter[ tokens[i].type ].apply( null, tokens[i].matches );
+			matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
 
 			// Return special upon seeing a positional matcher
 			if ( matcher[ expando ] ) {
+
 				// Find the next relative operator (if any) for proper handling
 				j = ++i;
 				for ( ; j < len; j++ ) {
-					if ( Expr.relative[ tokens[j].type ] ) {
+					if ( Expr.relative[ tokens[ j ].type ] ) {
 						break;
 					}
 				}
 				return setMatcher(
 					i > 1 && elementMatcher( matchers ),
 					i > 1 && toSelector(
-						// If the preceding token was a descendant combinator, insert an implicit any-element `*`
-						tokens.slice( 0, i - 1 ).concat({ value: tokens[ i - 2 ].type === " " ? "*" : "" })
+
+					// If the preceding token was a descendant combinator, insert an implicit any-element `*`
+					tokens
+						.slice( 0, i - 1 )
+						.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
 					).replace( rtrim, "$1" ),
 					matcher,
 					i < j && matcherFromTokens( tokens.slice( i, j ) ),
-					j < len && matcherFromTokens( (tokens = tokens.slice( j )) ),
+					j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
 					j < len && toSelector( tokens )
 				);
 			}
@@ -2497,28 +2678,40 @@ function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
 				unmatched = seed && [],
 				setMatched = [],
 				contextBackup = outermostContext,
+
 				// We must always have either seed elements or outermost context
-				elems = seed || byElement && Expr.find["TAG"]( "*", outermost ),
+				elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
+
 				// Use integer dirruns iff this is the outermost matcher
-				dirrunsUnique = (dirruns += contextBackup == null ? 1 : Math.random() || 0.1),
+				dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
 				len = elems.length;
 
 			if ( outermost ) {
-				outermostContext = context === document || context || outermost;
+
+				// Support: IE 11+, Edge 17 - 18+
+				// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+				// two documents; shallow comparisons work.
+				// eslint-disable-next-line eqeqeq
+				outermostContext = context == document || context || outermost;
 			}
 
 			// Add elements passing elementMatchers directly to results
 			// Support: IE<9, Safari
 			// Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
-			for ( ; i !== len && (elem = elems[i]) != null; i++ ) {
+			for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
 				if ( byElement && elem ) {
 					j = 0;
-					if ( !context && elem.ownerDocument !== document ) {
+
+					// Support: IE 11+, Edge 17 - 18+
+					// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+					// two documents; shallow comparisons work.
+					// eslint-disable-next-line eqeqeq
+					if ( !context && elem.ownerDocument != document ) {
 						setDocument( elem );
 						xml = !documentIsHTML;
 					}
-					while ( (matcher = elementMatchers[j++]) ) {
-						if ( matcher( elem, context || document, xml) ) {
+					while ( ( matcher = elementMatchers[ j++ ] ) ) {
+						if ( matcher( elem, context || document, xml ) ) {
 							results.push( elem );
 							break;
 						}
@@ -2530,8 +2723,9 @@ function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
 
 				// Track unmatched elements for set filters
 				if ( bySet ) {
+
 					// They will have gone through all possible matchers
-					if ( (elem = !matcher && elem) ) {
+					if ( ( elem = !matcher && elem ) ) {
 						matchedCount--;
 					}
 
@@ -2555,16 +2749,17 @@ function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
 			// numerically zero.
 			if ( bySet && i !== matchedCount ) {
 				j = 0;
-				while ( (matcher = setMatchers[j++]) ) {
+				while ( ( matcher = setMatchers[ j++ ] ) ) {
 					matcher( unmatched, setMatched, context, xml );
 				}
 
 				if ( seed ) {
+
 					// Reintegrate element matches to eliminate the need for sorting
 					if ( matchedCount > 0 ) {
 						while ( i-- ) {
-							if ( !(unmatched[i] || setMatched[i]) ) {
-								setMatched[i] = pop.call( results );
+							if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
+								setMatched[ i ] = pop.call( results );
 							}
 						}
 					}
@@ -2605,13 +2800,14 @@ compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
 		cached = compilerCache[ selector + " " ];
 
 	if ( !cached ) {
+
 		// Generate a function of recursive functions that can be used to check each element
 		if ( !match ) {
 			match = tokenize( selector );
 		}
 		i = match.length;
 		while ( i-- ) {
-			cached = matcherFromTokens( match[i] );
+			cached = matcherFromTokens( match[ i ] );
 			if ( cached[ expando ] ) {
 				setMatchers.push( cached );
 			} else {
@@ -2620,7 +2816,10 @@ compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
 		}
 
 		// Cache the compiled function
-		cached = compilerCache( selector, matcherFromGroupMatchers( elementMatchers, setMatchers ) );
+		cached = compilerCache(
+			selector,
+			matcherFromGroupMatchers( elementMatchers, setMatchers )
+		);
 
 		// Save selector and tokenization
 		cached.selector = selector;
@@ -2640,7 +2839,7 @@ compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
 select = Sizzle.select = function( selector, context, results, seed ) {
 	var i, tokens, token, type, find,
 		compiled = typeof selector === "function" && selector,
-		match = !seed && tokenize( (selector = compiled.selector || selector) );
+		match = !seed && tokenize( ( selector = compiled.selector || selector ) );
 
 	results = results || [];
 
@@ -2649,11 +2848,12 @@ select = Sizzle.select = function( selector, context, results, seed ) {
 	if ( match.length === 1 ) {
 
 		// Reduce context if the leading compound selector is an ID
-		tokens = match[0] = match[0].slice( 0 );
-		if ( tokens.length > 2 && (token = tokens[0]).type === "ID" &&
-				context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[1].type ] ) {
+		tokens = match[ 0 ] = match[ 0 ].slice( 0 );
+		if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
+			context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
 
-			context = ( Expr.find["ID"]( token.matches[0].replace(runescape, funescape), context ) || [] )[0];
+			context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
+				.replace( runescape, funescape ), context ) || [] )[ 0 ];
 			if ( !context ) {
 				return results;
 
@@ -2666,20 +2866,22 @@ select = Sizzle.select = function( selector, context, results, seed ) {
 		}
 
 		// Fetch a seed set for right-to-left matching
-		i = matchExpr["needsContext"].test( selector ) ? 0 : tokens.length;
+		i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
 		while ( i-- ) {
-			token = tokens[i];
+			token = tokens[ i ];
 
 			// Abort if we hit a combinator
-			if ( Expr.relative[ (type = token.type) ] ) {
+			if ( Expr.relative[ ( type = token.type ) ] ) {
 				break;
 			}
-			if ( (find = Expr.find[ type ]) ) {
+			if ( ( find = Expr.find[ type ] ) ) {
+
 				// Search, expanding context for leading sibling combinators
-				if ( (seed = find(
-					token.matches[0].replace( runescape, funescape ),
-					rsibling.test( tokens[0].type ) && testContext( context.parentNode ) || context
-				)) ) {
+				if ( ( seed = find(
+					token.matches[ 0 ].replace( runescape, funescape ),
+					rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
+						context
+				) ) ) {
 
 					// If seed is empty or no tokens remain, we can return early
 					tokens.splice( i, 1 );
@@ -2710,7 +2912,7 @@ select = Sizzle.select = function( selector, context, results, seed ) {
 // One-time assignments
 
 // Sort stability
-support.sortStable = expando.split("").sort( sortOrder ).join("") === expando;
+support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
 
 // Support: Chrome 14-35+
 // Always assume duplicates if they aren't passed to the comparison function
@@ -2721,58 +2923,59 @@ setDocument();
 
 // Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
 // Detached nodes confoundingly follow *each other*
-support.sortDetached = assert(function( el ) {
+support.sortDetached = assert( function( el ) {
+
 	// Should return 1, but returns 4 (following)
-	return el.compareDocumentPosition( document.createElement("fieldset") ) & 1;
-});
+	return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
+} );
 
 // Support: IE<8
 // Prevent attribute/property "interpolation"
 // https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
-if ( !assert(function( el ) {
+if ( !assert( function( el ) {
 	el.innerHTML = "<a href='#'></a>";
-	return el.firstChild.getAttribute("href") === "#" ;
-}) ) {
+	return el.firstChild.getAttribute( "href" ) === "#";
+} ) ) {
 	addHandle( "type|href|height|width", function( elem, name, isXML ) {
 		if ( !isXML ) {
 			return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
 		}
-	});
+	} );
 }
 
 // Support: IE<9
 // Use defaultValue in place of getAttribute("value")
-if ( !support.attributes || !assert(function( el ) {
+if ( !support.attributes || !assert( function( el ) {
 	el.innerHTML = "<input/>";
 	el.firstChild.setAttribute( "value", "" );
 	return el.firstChild.getAttribute( "value" ) === "";
-}) ) {
-	addHandle( "value", function( elem, name, isXML ) {
+} ) ) {
+	addHandle( "value", function( elem, _name, isXML ) {
 		if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
 			return elem.defaultValue;
 		}
-	});
+	} );
 }
 
 // Support: IE<9
 // Use getAttributeNode to fetch booleans when getAttribute lies
-if ( !assert(function( el ) {
-	return el.getAttribute("disabled") == null;
-}) ) {
+if ( !assert( function( el ) {
+	return el.getAttribute( "disabled" ) == null;
+} ) ) {
 	addHandle( booleans, function( elem, name, isXML ) {
 		var val;
 		if ( !isXML ) {
 			return elem[ name ] === true ? name.toLowerCase() :
-					(val = elem.getAttributeNode( name )) && val.specified ?
+				( val = elem.getAttributeNode( name ) ) && val.specified ?
 					val.value :
-				null;
+					null;
 		}
-	});
+	} );
 }
 
 return Sizzle;
 
-})( window );
+} )( window );
 
 
 
@@ -2825,9 +3028,9 @@ var rneedsContext = jQuery.expr.match.needsContext;
 
 function nodeName( elem, name ) {
 
-  return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
+	return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
 
-};
+}
 var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
 
 
@@ -3141,7 +3344,7 @@ jQuery.each( {
 	parents: function( elem ) {
 		return dir( elem, "parentNode" );
 	},
-	parentsUntil: function( elem, i, until ) {
+	parentsUntil: function( elem, _i, until ) {
 		return dir( elem, "parentNode", until );
 	},
 	next: function( elem ) {
@@ -3156,10 +3359,10 @@ jQuery.each( {
 	prevAll: function( elem ) {
 		return dir( elem, "previousSibling" );
 	},
-	nextUntil: function( elem, i, until ) {
+	nextUntil: function( elem, _i, until ) {
 		return dir( elem, "nextSibling", until );
 	},
-	prevUntil: function( elem, i, until ) {
+	prevUntil: function( elem, _i, until ) {
 		return dir( elem, "previousSibling", until );
 	},
 	siblings: function( elem ) {
@@ -3169,7 +3372,13 @@ jQuery.each( {
 		return siblings( elem.firstChild );
 	},
 	contents: function( elem ) {
-		if ( typeof elem.contentDocument !== "undefined" ) {
+		if ( elem.contentDocument != null &&
+
+			// Support: IE 11+
+			// <object> elements with no `data` attribute has an object
+			// `contentDocument` with a `null` prototype.
+			getProto( elem.contentDocument ) ) {
+
 			return elem.contentDocument;
 		}
 
@@ -3512,7 +3721,7 @@ jQuery.extend( {
 					var fns = arguments;
 
 					return jQuery.Deferred( function( newDefer ) {
-						jQuery.each( tuples, function( i, tuple ) {
+						jQuery.each( tuples, function( _i, tuple ) {
 
 							// Map tuples (progress, done, fail) to arguments (done, fail, progress)
 							var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
@@ -3792,8 +4001,8 @@ jQuery.extend( {
 			resolveContexts = Array( i ),
 			resolveValues = slice.call( arguments ),
 
-			// the master Deferred
-			master = jQuery.Deferred(),
+			// the primary Deferred
+			primary = jQuery.Deferred(),
 
 			// subordinate callback factory
 			updateFunc = function( i ) {
@@ -3801,30 +4010,30 @@ jQuery.extend( {
 					resolveContexts[ i ] = this;
 					resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
 					if ( !( --remaining ) ) {
-						master.resolveWith( resolveContexts, resolveValues );
+						primary.resolveWith( resolveContexts, resolveValues );
 					}
 				};
 			};
 
 		// Single- and empty arguments are adopted like Promise.resolve
 		if ( remaining <= 1 ) {
-			adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject,
+			adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject,
 				!remaining );
 
 			// Use .then() to unwrap secondary thenables (cf. gh-3000)
-			if ( master.state() === "pending" ||
+			if ( primary.state() === "pending" ||
 				isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
 
-				return master.then();
+				return primary.then();
 			}
 		}
 
 		// Multiple arguments are aggregated like Promise.all array elements
 		while ( i-- ) {
-			adoptValue( resolveValues[ i ], updateFunc( i ), master.reject );
+			adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject );
 		}
 
-		return master.promise();
+		return primary.promise();
 	}
 } );
 
@@ -3965,7 +4174,7 @@ var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
 			// ...except when executing function values
 			} else {
 				bulk = fn;
-				fn = function( elem, key, value ) {
+				fn = function( elem, _key, value ) {
 					return bulk.call( jQuery( elem ), value );
 				};
 			}
@@ -3975,8 +4184,8 @@ var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
 			for ( ; i < len; i++ ) {
 				fn(
 					elems[ i ], key, raw ?
-					value :
-					value.call( elems[ i ], i, fn( elems[ i ], key ) )
+						value :
+						value.call( elems[ i ], i, fn( elems[ i ], key ) )
 				);
 			}
 		}
@@ -4000,7 +4209,7 @@ var rmsPrefix = /^-ms-/,
 	rdashAlpha = /-([a-z])/g;
 
 // Used by camelCase as callback to replace()
-function fcamelCase( all, letter ) {
+function fcamelCase( _all, letter ) {
 	return letter.toUpperCase();
 }
 
@@ -4528,27 +4737,6 @@ var isHiddenWithinTree = function( elem, el ) {
 			jQuery.css( elem, "display" ) === "none";
 	};
 
-var swap = function( elem, options, callback, args ) {
-	var ret, name,
-		old = {};
-
-	// Remember the old values, and insert the new ones
-	for ( name in options ) {
-		old[ name ] = elem.style[ name ];
-		elem.style[ name ] = options[ name ];
-	}
-
-	ret = callback.apply( elem, args || [] );
-
-	// Revert the old values
-	for ( name in options ) {
-		elem.style[ name ] = old[ name ];
-	}
-
-	return ret;
-};
-
-
 
 
 function adjustCSS( elem, prop, valueParts, tween ) {
@@ -4719,11 +4907,40 @@ var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
 
 
 
-// We have to close these tags to support XHTML (#13200)
-var wrapMap = {
+( function() {
+	var fragment = document.createDocumentFragment(),
+		div = fragment.appendChild( document.createElement( "div" ) ),
+		input = document.createElement( "input" );
+
+	// Support: Android 4.0 - 4.3 only
+	// Check state lost if the name is set (#11217)
+	// Support: Windows Web Apps (WWA)
+	// `name` and `type` must use .setAttribute for WWA (#14901)
+	input.setAttribute( "type", "radio" );
+	input.setAttribute( "checked", "checked" );
+	input.setAttribute( "name", "t" );
+
+	div.appendChild( input );
+
+	// Support: Android <=4.1 only
+	// Older WebKit doesn't clone checked state correctly in fragments
+	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
+
+	// Support: IE <=11 only
+	// Make sure textarea (and checkbox) defaultValue is properly cloned
+	div.innerHTML = "<textarea>x</textarea>";
+	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
 
 	// Support: IE <=9 only
-	option: [ 1, "<select multiple='multiple'>", "</select>" ],
+	// IE <=9 replaces <option> tags with their contents when inserted outside of
+	// the select element.
+	div.innerHTML = "<option></option>";
+	support.option = !!div.lastChild;
+} )();
+
+
+// We have to close these tags to support XHTML (#13200)
+var wrapMap = {
 
 	// XHTML parsers do not magically insert elements in the
 	// same way that tag soup parsers do. So we cannot shorten
@@ -4736,12 +4953,14 @@ var wrapMap = {
 	_default: [ 0, "", "" ]
 };
 
-// Support: IE <=9 only
-wrapMap.optgroup = wrapMap.option;
-
 wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
 wrapMap.th = wrapMap.td;
 
+// Support: IE <=9 only
+if ( !support.option ) {
+	wrapMap.optgroup = wrapMap.option = [ 1, "<select multiple='multiple'>", "</select>" ];
+}
+
 
 function getAll( context, tag ) {
 
@@ -4874,36 +5093,7 @@ function buildFragment( elems, context, scripts, selection, ignored ) {
 }
 
 
-( function() {
-	var fragment = document.createDocumentFragment(),
-		div = fragment.appendChild( document.createElement( "div" ) ),
-		input = document.createElement( "input" );
-
-	// Support: Android 4.0 - 4.3 only
-	// Check state lost if the name is set (#11217)
-	// Support: Windows Web Apps (WWA)
-	// `name` and `type` must use .setAttribute for WWA (#14901)
-	input.setAttribute( "type", "radio" );
-	input.setAttribute( "checked", "checked" );
-	input.setAttribute( "name", "t" );
-
-	div.appendChild( input );
-
-	// Support: Android <=4.1 only
-	// Older WebKit doesn't clone checked state correctly in fragments
-	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
-
-	// Support: IE <=11 only
-	// Make sure textarea (and checkbox) defaultValue is properly cloned
-	div.innerHTML = "<textarea>x</textarea>";
-	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
-} )();
-
-
-var
-	rkeyEvent = /^key/,
-	rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/,
-	rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
+var rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
 
 function returnTrue() {
 	return true;
@@ -5008,8 +5198,8 @@ jQuery.event = {
 			special, handlers, type, namespaces, origType,
 			elemData = dataPriv.get( elem );
 
-		// Don't attach events to noData or text/comment nodes (but allow plain objects)
-		if ( !elemData ) {
+		// Only attach events to objects that accept data
+		if ( !acceptData( elem ) ) {
 			return;
 		}
 
@@ -5033,7 +5223,7 @@ jQuery.event = {
 
 		// Init the element's event structure and main handler, if this is the first
 		if ( !( events = elemData.events ) ) {
-			events = elemData.events = {};
+			events = elemData.events = Object.create( null );
 		}
 		if ( !( eventHandle = elemData.handle ) ) {
 			eventHandle = elemData.handle = function( e ) {
@@ -5191,12 +5381,15 @@ jQuery.event = {
 
 	dispatch: function( nativeEvent ) {
 
-		// Make a writable jQuery.Event from the native event object
-		var event = jQuery.event.fix( nativeEvent );
-
 		var i, j, ret, matched, handleObj, handlerQueue,
 			args = new Array( arguments.length ),
-			handlers = ( dataPriv.get( this, "events" ) || {} )[ event.type ] || [],
+
+			// Make a writable jQuery.Event from the native event object
+			event = jQuery.event.fix( nativeEvent ),
+
+			handlers = (
+				dataPriv.get( this, "events" ) || Object.create( null )
+			)[ event.type ] || [],
 			special = jQuery.event.special[ event.type ] || {};
 
 		// Use the fix-ed jQuery.Event rather than the (read-only) native event
@@ -5320,12 +5513,12 @@ jQuery.event = {
 			get: isFunction( hook ) ?
 				function() {
 					if ( this.originalEvent ) {
-							return hook( this.originalEvent );
+						return hook( this.originalEvent );
 					}
 				} :
 				function() {
 					if ( this.originalEvent ) {
-							return this.originalEvent[ name ];
+						return this.originalEvent[ name ];
 					}
 				},
 
@@ -5464,7 +5657,13 @@ function leverageNative( el, type, expectSync ) {
 						// Cancel the outer synthetic event
 						event.stopImmediatePropagation();
 						event.preventDefault();
-						return result.value;
+
+						// Support: Chrome 86+
+						// In Chrome, if an element having a focusout handler is blurred by
+						// clicking outside of it, it invokes the handler synchronously. If
+						// that handler calls `.remove()` on the element, the data is cleared,
+						// leaving `result` undefined. We need to guard against this.
+						return result && result.value;
 					}
 
 				// If this is an inner synthetic event for an event with a bubbling surrogate
@@ -5629,34 +5828,7 @@ jQuery.each( {
 	targetTouches: true,
 	toElement: true,
 	touches: true,
-
-	which: function( event ) {
-		var button = event.button;
-
-		// Add which for key events
-		if ( event.which == null && rkeyEvent.test( event.type ) ) {
-			return event.charCode != null ? event.charCode : event.keyCode;
-		}
-
-		// Add which for click: 1 === left; 2 === middle; 3 === right
-		if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) {
-			if ( button & 1 ) {
-				return 1;
-			}
-
-			if ( button & 2 ) {
-				return 3;
-			}
-
-			if ( button & 4 ) {
-				return 2;
-			}
-
-			return 0;
-		}
-
-		return event.which;
-	}
+	which: true
 }, jQuery.event.addProp );
 
 jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) {
@@ -5682,6 +5854,12 @@ jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateTyp
 			return true;
 		},
 
+		// Suppress native focus or blur as it's already being fired
+		// in leverageNative.
+		_default: function() {
+			return true;
+		},
+
 		delegateType: delegateType
 	};
 } );
@@ -5771,13 +5949,6 @@ jQuery.fn.extend( {
 
 var
 
-	/* eslint-disable max-len */
-
-	// See https://github.com/eslint/eslint/issues/3229
-	rxhtmlTag = /<(?!area|br|col|embed|hr|img|input|link|meta|param)(([a-z][^\/\0>\x20\t\r\n\f]*)[^>]*)\/>/gi,
-
-	/* eslint-enable */
-
 	// Support: IE <=10 - 11, Edge 12 - 13 only
 	// In IE/Edge using regex groups here causes severe slowdowns.
 	// See https://connect.microsoft.com/IE/feedback/details/1736512/
@@ -5814,7 +5985,7 @@ function restoreScript( elem ) {
 }
 
 function cloneCopyEvent( src, dest ) {
-	var i, l, type, pdataOld, pdataCur, udataOld, udataCur, events;
+	var i, l, type, pdataOld, udataOld, udataCur, events;
 
 	if ( dest.nodeType !== 1 ) {
 		return;
@@ -5822,13 +5993,11 @@ function cloneCopyEvent( src, dest ) {
 
 	// 1. Copy private data: events, handlers, etc.
 	if ( dataPriv.hasData( src ) ) {
-		pdataOld = dataPriv.access( src );
-		pdataCur = dataPriv.set( dest, pdataOld );
+		pdataOld = dataPriv.get( src );
 		events = pdataOld.events;
 
 		if ( events ) {
-			delete pdataCur.handle;
-			pdataCur.events = {};
+			dataPriv.remove( dest, "handle events" );
 
 			for ( type in events ) {
 				for ( i = 0, l = events[ type ].length; i < l; i++ ) {
@@ -5864,7 +6033,7 @@ function fixInput( src, dest ) {
 function domManip( collection, args, callback, ignored ) {
 
 	// Flatten any nested arrays
-	args = concat.apply( [], args );
+	args = flat( args );
 
 	var fragment, first, scripts, hasScripts, node, doc,
 		i = 0,
@@ -5939,7 +6108,7 @@ function domManip( collection, args, callback, ignored ) {
 							if ( jQuery._evalUrl && !node.noModule ) {
 								jQuery._evalUrl( node.src, {
 									nonce: node.nonce || node.getAttribute( "nonce" )
-								} );
+								}, doc );
 							}
 						} else {
 							DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc );
@@ -5976,7 +6145,7 @@ function remove( elem, selector, keepData ) {
 
 jQuery.extend( {
 	htmlPrefilter: function( html ) {
-		return html.replace( rxhtmlTag, "<$1></$2>" );
+		return html;
 	},
 
 	clone: function( elem, dataAndEvents, deepDataAndEvents ) {
@@ -6238,6 +6407,27 @@ var getStyles = function( elem ) {
 		return view.getComputedStyle( elem );
 	};
 
+var swap = function( elem, options, callback ) {
+	var ret, name,
+		old = {};
+
+	// Remember the old values, and insert the new ones
+	for ( name in options ) {
+		old[ name ] = elem.style[ name ];
+		elem.style[ name ] = options[ name ];
+	}
+
+	ret = callback.call( elem );
+
+	// Revert the old values
+	for ( name in options ) {
+		elem.style[ name ] = old[ name ];
+	}
+
+	return ret;
+};
+
+
 var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
 
 
@@ -6295,7 +6485,7 @@ var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
 	}
 
 	var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
-		reliableMarginLeftVal,
+		reliableTrDimensionsVal, reliableMarginLeftVal,
 		container = document.createElement( "div" ),
 		div = document.createElement( "div" );
 
@@ -6330,6 +6520,54 @@ var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
 		scrollboxSize: function() {
 			computeStyleTests();
 			return scrollboxSizeVal;
+		},
+
+		// Support: IE 9 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Behavior in IE 9 is more subtle than in newer versions & it passes
+		// some versions of this test; make sure not to make it pass there!
+		//
+		// Support: Firefox 70+
+		// Only Firefox includes border widths
+		// in computed dimensions. (gh-4529)
+		reliableTrDimensions: function() {
+			var table, tr, trChild, trStyle;
+			if ( reliableTrDimensionsVal == null ) {
+				table = document.createElement( "table" );
+				tr = document.createElement( "tr" );
+				trChild = document.createElement( "div" );
+
+				table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate";
+				tr.style.cssText = "border:1px solid";
+
+				// Support: Chrome 86+
+				// Height set through cssText does not get applied.
+				// Computed height then comes back as 0.
+				tr.style.height = "1px";
+				trChild.style.height = "9px";
+
+				// Support: Android 8 Chrome 86+
+				// In our bodyBackground.html iframe,
+				// display for all div elements is set to "inline",
+				// which causes a problem only in Android 8 Chrome 86.
+				// Ensuring the div is display: block
+				// gets around this issue.
+				trChild.style.display = "block";
+
+				documentElement
+					.appendChild( table )
+					.appendChild( tr )
+					.appendChild( trChild );
+
+				trStyle = window.getComputedStyle( tr );
+				reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) +
+					parseInt( trStyle.borderTopWidth, 10 ) +
+					parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight;
+
+				documentElement.removeChild( table );
+			}
+			return reliableTrDimensionsVal;
 		}
 	} );
 } )();
@@ -6454,7 +6692,7 @@ var
 		fontWeight: "400"
 	};
 
-function setPositiveNumber( elem, value, subtract ) {
+function setPositiveNumber( _elem, value, subtract ) {
 
 	// Any relative (+/-) values have already been
 	// normalized at this point
@@ -6559,17 +6797,26 @@ function getWidthOrHeight( elem, dimension, extra ) {
 	}
 
 
-	// Fall back to offsetWidth/offsetHeight when value is "auto"
-	// This happens for inline elements with no explicit setting (gh-3571)
-	// Support: Android <=4.1 - 4.3 only
-	// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
-	// Support: IE 9-11 only
-	// Also use offsetWidth/offsetHeight for when box sizing is unreliable
-	// We use getClientRects() to check for hidden/disconnected.
-	// In those cases, the computed value can be trusted to be border-box
+	// Support: IE 9 - 11 only
+	// Use offsetWidth/offsetHeight for when box sizing is unreliable.
+	// In those cases, the computed value can be trusted to be border-box.
 	if ( ( !support.boxSizingReliable() && isBorderBox ||
+
+		// Support: IE 10 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Interestingly, in some cases IE 9 doesn't suffer from this issue.
+		!support.reliableTrDimensions() && nodeName( elem, "tr" ) ||
+
+		// Fall back to offsetWidth/offsetHeight when value is "auto"
+		// This happens for inline elements with no explicit setting (gh-3571)
 		val === "auto" ||
+
+		// Support: Android <=4.1 - 4.3 only
+		// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
 		!parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) &&
+
+		// Make sure the element is visible & connected
 		elem.getClientRects().length ) {
 
 		isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box";
@@ -6764,7 +7011,7 @@ jQuery.extend( {
 	}
 } );
 
-jQuery.each( [ "height", "width" ], function( i, dimension ) {
+jQuery.each( [ "height", "width" ], function( _i, dimension ) {
 	jQuery.cssHooks[ dimension ] = {
 		get: function( elem, computed, extra ) {
 			if ( computed ) {
@@ -6780,10 +7027,10 @@ jQuery.each( [ "height", "width" ], function( i, dimension ) {
 					// Running getBoundingClientRect on a disconnected node
 					// in IE throws an error.
 					( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
-						swap( elem, cssShow, function() {
-							return getWidthOrHeight( elem, dimension, extra );
-						} ) :
-						getWidthOrHeight( elem, dimension, extra );
+					swap( elem, cssShow, function() {
+						return getWidthOrHeight( elem, dimension, extra );
+					} ) :
+					getWidthOrHeight( elem, dimension, extra );
 			}
 		},
 
@@ -6842,7 +7089,7 @@ jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
 					swap( elem, { marginLeft: 0 }, function() {
 						return elem.getBoundingClientRect().left;
 					} )
-				) + "px";
+			) + "px";
 		}
 	}
 );
@@ -6981,7 +7228,7 @@ Tween.propHooks = {
 			if ( jQuery.fx.step[ tween.prop ] ) {
 				jQuery.fx.step[ tween.prop ]( tween );
 			} else if ( tween.elem.nodeType === 1 && (
-					jQuery.cssHooks[ tween.prop ] ||
+				jQuery.cssHooks[ tween.prop ] ||
 					tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) {
 				jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
 			} else {
@@ -7226,7 +7473,7 @@ function defaultPrefilter( elem, props, opts ) {
 
 			anim.done( function() {
 
-			/* eslint-enable no-loop-func */
+				/* eslint-enable no-loop-func */
 
 				// The final step of a "hide" animation is actually hiding the element
 				if ( !hidden ) {
@@ -7346,7 +7593,7 @@ function Animation( elem, properties, options ) {
 			tweens: [],
 			createTween: function( prop, end ) {
 				var tween = jQuery.Tween( elem, animation.opts, prop, end,
-						animation.opts.specialEasing[ prop ] || animation.opts.easing );
+					animation.opts.specialEasing[ prop ] || animation.opts.easing );
 				animation.tweens.push( tween );
 				return tween;
 			},
@@ -7519,7 +7766,8 @@ jQuery.fn.extend( {
 					anim.stop( true );
 				}
 			};
-			doAnimation.finish = doAnimation;
+
+		doAnimation.finish = doAnimation;
 
 		return empty || optall.queue === false ?
 			this.each( doAnimation ) :
@@ -7537,7 +7785,7 @@ jQuery.fn.extend( {
 			clearQueue = type;
 			type = undefined;
 		}
-		if ( clearQueue && type !== false ) {
+		if ( clearQueue ) {
 			this.queue( type || "fx", [] );
 		}
 
@@ -7620,7 +7868,7 @@ jQuery.fn.extend( {
 	}
 } );
 
-jQuery.each( [ "toggle", "show", "hide" ], function( i, name ) {
+jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) {
 	var cssFn = jQuery.fn[ name ];
 	jQuery.fn[ name ] = function( speed, easing, callback ) {
 		return speed == null || typeof speed === "boolean" ?
@@ -7841,7 +8089,7 @@ boolHook = {
 	}
 };
 
-jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( i, name ) {
+jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) {
 	var getter = attrHandle[ name ] || jQuery.find.attr;
 
 	attrHandle[ name ] = function( elem, name, isXML ) {
@@ -8159,8 +8407,8 @@ jQuery.fn.extend( {
 				if ( this.setAttribute ) {
 					this.setAttribute( "class",
 						className || value === false ?
-						"" :
-						dataPriv.get( this, "__className__" ) || ""
+							"" :
+							dataPriv.get( this, "__className__" ) || ""
 					);
 				}
 			}
@@ -8175,7 +8423,7 @@ jQuery.fn.extend( {
 		while ( ( elem = this[ i++ ] ) ) {
 			if ( elem.nodeType === 1 &&
 				( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
-					return true;
+				return true;
 			}
 		}
 
@@ -8465,7 +8713,7 @@ jQuery.extend( jQuery.event, {
 				special.bindType || type;
 
 			// jQuery handler
-			handle = ( dataPriv.get( cur, "events" ) || {} )[ event.type ] &&
+			handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] &&
 				dataPriv.get( cur, "handle" );
 			if ( handle ) {
 				handle.apply( cur, data );
@@ -8576,7 +8824,10 @@ if ( !support.focusin ) {
 
 		jQuery.event.special[ fix ] = {
 			setup: function() {
-				var doc = this.ownerDocument || this,
+
+				// Handle: regular nodes (via `this.ownerDocument`), window
+				// (via `this.document`) & document (via `this`).
+				var doc = this.ownerDocument || this.document || this,
 					attaches = dataPriv.access( doc, fix );
 
 				if ( !attaches ) {
@@ -8585,7 +8836,7 @@ if ( !support.focusin ) {
 				dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
 			},
 			teardown: function() {
-				var doc = this.ownerDocument || this,
+				var doc = this.ownerDocument || this.document || this,
 					attaches = dataPriv.access( doc, fix ) - 1;
 
 				if ( !attaches ) {
@@ -8601,7 +8852,7 @@ if ( !support.focusin ) {
 }
 var location = window.location;
 
-var nonce = Date.now();
+var nonce = { guid: Date.now() };
 
 var rquery = ( /\?/ );
 
@@ -8609,7 +8860,7 @@ var rquery = ( /\?/ );
 
 // Cross-browser xml parsing
 jQuery.parseXML = function( data ) {
-	var xml;
+	var xml, parserErrorElem;
 	if ( !data || typeof data !== "string" ) {
 		return null;
 	}
@@ -8618,12 +8869,17 @@ jQuery.parseXML = function( data ) {
 	// IE throws on parseFromString with invalid input.
 	try {
 		xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
-	} catch ( e ) {
-		xml = undefined;
-	}
+	} catch ( e ) {}
 
-	if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) {
-		jQuery.error( "Invalid XML: " + data );
+	parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ];
+	if ( !xml || parserErrorElem ) {
+		jQuery.error( "Invalid XML: " + (
+			parserErrorElem ?
+				jQuery.map( parserErrorElem.childNodes, function( el ) {
+					return el.textContent;
+				} ).join( "\n" ) :
+				data
+		) );
 	}
 	return xml;
 };
@@ -8724,16 +8980,14 @@ jQuery.fn.extend( {
 			// Can add propHook for "elements" to filter or add form elements
 			var elements = jQuery.prop( this, "elements" );
 			return elements ? jQuery.makeArray( elements ) : this;
-		} )
-		.filter( function() {
+		} ).filter( function() {
 			var type = this.type;
 
 			// Use .is( ":disabled" ) so that fieldset[disabled] works
 			return this.name && !jQuery( this ).is( ":disabled" ) &&
 				rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
 				( this.checked || !rcheckableType.test( type ) );
-		} )
-		.map( function( i, elem ) {
+		} ).map( function( _i, elem ) {
 			var val = jQuery( this ).val();
 
 			if ( val == null ) {
@@ -8786,7 +9040,8 @@ var
 
 	// Anchor tag for parsing the document origin
 	originAnchor = document.createElement( "a" );
-	originAnchor.href = location.href;
+
+originAnchor.href = location.href;
 
 // Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
 function addToPrefiltersOrTransports( structure ) {
@@ -9167,8 +9422,8 @@ jQuery.extend( {
 			// Context for global events is callbackContext if it is a DOM node or jQuery collection
 			globalEventContext = s.context &&
 				( callbackContext.nodeType || callbackContext.jquery ) ?
-					jQuery( callbackContext ) :
-					jQuery.event,
+				jQuery( callbackContext ) :
+				jQuery.event,
 
 			// Deferreds
 			deferred = jQuery.Deferred(),
@@ -9346,7 +9601,8 @@ jQuery.extend( {
 			// Add or update anti-cache param if needed
 			if ( s.cache === false ) {
 				cacheURL = cacheURL.replace( rantiCache, "$1" );
-				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce++ ) + uncached;
+				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) +
+					uncached;
 			}
 
 			// Put hash and anti-cache on the URL that will be requested (gh-1732)
@@ -9479,6 +9735,13 @@ jQuery.extend( {
 				response = ajaxHandleResponses( s, jqXHR, responses );
 			}
 
+			// Use a noop converter for missing script but not if jsonp
+			if ( !isSuccess &&
+				jQuery.inArray( "script", s.dataTypes ) > -1 &&
+				jQuery.inArray( "json", s.dataTypes ) < 0 ) {
+				s.converters[ "text script" ] = function() {};
+			}
+
 			// Convert no matter what (that way responseXXX fields are always set)
 			response = ajaxConvert( s, response, jqXHR, isSuccess );
 
@@ -9569,7 +9832,7 @@ jQuery.extend( {
 	}
 } );
 
-jQuery.each( [ "get", "post" ], function( i, method ) {
+jQuery.each( [ "get", "post" ], function( _i, method ) {
 	jQuery[ method ] = function( url, data, callback, type ) {
 
 		// Shift arguments if data argument was omitted
@@ -9590,8 +9853,17 @@ jQuery.each( [ "get", "post" ], function( i, method ) {
 	};
 } );
 
+jQuery.ajaxPrefilter( function( s ) {
+	var i;
+	for ( i in s.headers ) {
+		if ( i.toLowerCase() === "content-type" ) {
+			s.contentType = s.headers[ i ] || "";
+		}
+	}
+} );
+
 
-jQuery._evalUrl = function( url, options ) {
+jQuery._evalUrl = function( url, options, doc ) {
 	return jQuery.ajax( {
 		url: url,
 
@@ -9609,7 +9881,7 @@ jQuery._evalUrl = function( url, options ) {
 			"text script": function() {}
 		},
 		dataFilter: function( response ) {
-			jQuery.globalEval( response, options );
+			jQuery.globalEval( response, options, doc );
 		}
 	} );
 };
@@ -9931,7 +10203,7 @@ var oldCallbacks = [],
 jQuery.ajaxSetup( {
 	jsonp: "callback",
 	jsonpCallback: function() {
-		var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce++ ) );
+		var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce.guid++ ) );
 		this[ callback ] = true;
 		return callback;
 	}
@@ -10148,23 +10420,6 @@ jQuery.fn.load = function( url, params, callback ) {
 
 
 
-// Attach a bunch of functions for handling common AJAX events
-jQuery.each( [
-	"ajaxStart",
-	"ajaxStop",
-	"ajaxComplete",
-	"ajaxError",
-	"ajaxSuccess",
-	"ajaxSend"
-], function( i, type ) {
-	jQuery.fn[ type ] = function( fn ) {
-		return this.on( type, fn );
-	};
-} );
-
-
-
-
 jQuery.expr.pseudos.animated = function( elem ) {
 	return jQuery.grep( jQuery.timers, function( fn ) {
 		return elem === fn.elem;
@@ -10371,7 +10626,7 @@ jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function(
 // Blink bug: https://bugs.chromium.org/p/chromium/issues/detail?id=589347
 // getComputedStyle returns percent when specified for top/left/bottom/right;
 // rather than make the css module depend on the offset module, just check for it here
-jQuery.each( [ "top", "left" ], function( i, prop ) {
+jQuery.each( [ "top", "left" ], function( _i, prop ) {
 	jQuery.cssHooks[ prop ] = addGetHookIf( support.pixelPosition,
 		function( elem, computed ) {
 			if ( computed ) {
@@ -10389,8 +10644,11 @@ jQuery.each( [ "top", "left" ], function( i, prop ) {
 
 // Create innerHeight, innerWidth, height, width, outerHeight and outerWidth methods
 jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
-	jQuery.each( { padding: "inner" + name, content: type, "": "outer" + name },
-		function( defaultExtra, funcName ) {
+	jQuery.each( {
+		padding: "inner" + name,
+		content: type,
+		"": "outer" + name
+	}, function( defaultExtra, funcName ) {
 
 		// Margin is only for outerHeight, outerWidth
 		jQuery.fn[ funcName ] = function( margin, value ) {
@@ -10434,25 +10692,19 @@ jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
 } );
 
 
-jQuery.each( ( "blur focus focusin focusout resize scroll click dblclick " +
-	"mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " +
-	"change select submit keydown keypress keyup contextmenu" ).split( " " ),
-	function( i, name ) {
-
-	// Handle event binding
-	jQuery.fn[ name ] = function( data, fn ) {
-		return arguments.length > 0 ?
-			this.on( name, null, data, fn ) :
-			this.trigger( name );
+jQuery.each( [
+	"ajaxStart",
+	"ajaxStop",
+	"ajaxComplete",
+	"ajaxError",
+	"ajaxSuccess",
+	"ajaxSend"
+], function( _i, type ) {
+	jQuery.fn[ type ] = function( fn ) {
+		return this.on( type, fn );
 	};
 } );
 
-jQuery.fn.extend( {
-	hover: function( fnOver, fnOut ) {
-		return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver );
-	}
-} );
-
 
 
 
@@ -10474,9 +10726,35 @@ jQuery.fn.extend( {
 		return arguments.length === 1 ?
 			this.off( selector, "**" ) :
 			this.off( types, selector || "**", fn );
+	},
+
+	hover: function( fnOver, fnOut ) {
+		return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver );
 	}
 } );
 
+jQuery.each(
+	( "blur focus focusin focusout resize scroll click dblclick " +
+	"mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " +
+	"change select submit keydown keypress keyup contextmenu" ).split( " " ),
+	function( _i, name ) {
+
+		// Handle event binding
+		jQuery.fn[ name ] = function( data, fn ) {
+			return arguments.length > 0 ?
+				this.on( name, null, data, fn ) :
+				this.trigger( name );
+		};
+	}
+);
+
+
+
+
+// Support: Android <=4.0 only
+// Make sure we trim BOM and NBSP
+var rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
+
 // Bind a function to a context, optionally partially applying any
 // arguments.
 // jQuery.proxy is deprecated to promote standards (specifically Function#bind)
@@ -10539,6 +10817,11 @@ jQuery.isNumeric = function( obj ) {
 		!isNaN( obj - parseFloat( obj ) );
 };
 
+jQuery.trim = function( text ) {
+	return text == null ?
+		"" :
+		( text + "" ).replace( rtrim, "" );
+};
 
 
 
@@ -10587,7 +10870,7 @@ jQuery.noConflict = function( deep ) {
 // Expose jQuery and $ identifiers, even in AMD
 // (#7102#comment:10, https://github.com/jquery/jquery/pull/557)
 // and CommonJS for browser emulators (#13566)
-if ( !noGlobal ) {
+if ( typeof noGlobal === "undefined" ) {
 	window.jQuery = window.$ = jQuery;
 }
 
diff --git a/docs/build/html/_static/jquery.js b/docs/build/html/_static/jquery.js
index a1c07fd..c4c6022 100644
--- a/docs/build/html/_static/jquery.js
+++ b/docs/build/html/_static/jquery.js
@@ -1,2 +1,2 @@
-/*! jQuery v3.4.1 | (c) JS Foundation and other contributors | jquery.org/license */
-!function(e,t){"use strict";"object"==typeof module&&"object"==typeof module.exports?module.exports=e.document?t(e,!0):function(e){if(!e.document)throw new Error("jQuery requires a window with a document");return t(e)}:t(e)}("undefined"!=typeof window?window:this,function(C,e){"use strict";var t=[],E=C.document,r=Object.getPrototypeOf,s=t.slice,g=t.concat,u=t.push,i=t.indexOf,n={},o=n.toString,v=n.hasOwnProperty,a=v.toString,l=a.call(Object),y={},m=function(e){return"function"==typeof e&&"number"!=typeof e.nodeType},x=function(e){return null!=e&&e===e.window},c={type:!0,src:!0,nonce:!0,noModule:!0};function b(e,t,n){var r,i,o=(n=n||E).createElement("script");if(o.text=e,t)for(r in c)(i=t[r]||t.getAttribute&&t.getAttribute(r))&&o.setAttribute(r,i);n.head.appendChild(o).parentNode.removeChild(o)}function w(e){return null==e?e+"":"object"==typeof e||"function"==typeof e?n[o.call(e)]||"object":typeof e}var f="3.4.1",k=function(e,t){return new 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new file mode 100644
index 0000000..db09cd0
--- /dev/null
+++ b/docs/build/html/_static/js/basicstrap.js
@@ -0,0 +1,26 @@
+$(document).ready(function(){
+
+  // Inline code styles to Bootstrap style.
+  $('tt.docutils.literal').not(".xref").each(function (i, e) {
+    // ignore references
+    if (!$(e).parent().hasClass("reference")) {
+      $(e).replaceWith(function () {
+        return $("<code />").html($(this).html());
+      });
+  }});
+
+  /*
+   * Scroll the window to avoid the topnav bar
+   * https://github.com/twitter/bootstrap/issues/1768
+   */
+  if ($(".navbar.navbar-fixed-top").length > 0) {
+    // var navHeight = $(".navbar").height(),
+    var navHeight = 40,
+      shiftWindow = function() { scrollBy(0, -navHeight - 10); };
+    if (location.hash) {
+      setTimeout(shiftWindow, 1);
+    }
+    window.addEventListener("hashchange", shiftWindow);
+  }
+
+});
\ No newline at end of file
diff --git a/docs/build/html/_static/js/bootstrap2.min.js b/docs/build/html/_static/js/bootstrap2.min.js
new file mode 100644
index 0000000..f9cbdae
--- /dev/null
+++ b/docs/build/html/_static/js/bootstrap2.min.js
@@ -0,0 +1,6 @@
+/*!
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+*/
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diff --git a/docs/build/html/_static/js/bootstrap3.min.js b/docs/build/html/_static/js/bootstrap3.min.js
new file mode 100644
index 0000000..c8f82e5
--- /dev/null
+++ b/docs/build/html/_static/js/bootstrap3.min.js
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new file mode 100644
index 0000000..c0f19d8
--- /dev/null
+++ b/docs/build/html/_static/js/jquery.cookie-1.4.1.min.js
@@ -0,0 +1,2 @@
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new file mode 100644
index 0000000..c0f19d8
--- /dev/null
+++ b/docs/build/html/_static/js/jquery.cookie.min.js
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diff --git a/docs/build/html/_static/language_data.js b/docs/build/html/_static/language_data.js
index d2b4ee9..2e22b06 100644
--- a/docs/build/html/_static/language_data.js
+++ b/docs/build/html/_static/language_data.js
@@ -5,15 +5,16 @@
  * This script contains the language-specific data used by searchtools.js,
  * namely the list of stopwords, stemmer, scorer and splitter.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
 
-var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
+var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
 
 
-/* Non-minified version JS is _stemmer.js if file is provided */ 
+/* Non-minified version is copied as a separate JS file, is available */
+
 /**
  * Porter Stemmer
  */
@@ -196,102 +197,3 @@ var Stemmer = function() {
   }
 }
 
-
-
-
-
-var splitChars = (function() {
-    var result = {};
-    var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
-         1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
-         2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
-         2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
-         3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
-         3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
-         4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
-         8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
-         11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
-         43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
-    var i, j, start, end;
-    for (i = 0; i < singles.length; i++) {
-        result[singles[i]] = true;
-    }
-    var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
-         [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
-         [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
-         [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
-         [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
-         [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
-         [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
-         [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
-         [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
-         [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
-         [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
-         [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
-         [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
-         [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
-         [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
-         [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
-         [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
-         [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
-         [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
-         [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
-         [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
-         [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
-         [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
-         [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
-         [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
-         [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
-         [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
-         [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
-         [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
-         [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
-         [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
-         [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
-         [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
-         [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
-         [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
-         [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
-         [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
-         [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
-         [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
-         [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
-         [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
-         [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
-         [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
-         [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
-         [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
-         [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
-         [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
-         [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
-         [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
-    for (i = 0; i < ranges.length; i++) {
-        start = ranges[i][0];
-        end = ranges[i][1];
-        for (j = start; j <= end; j++) {
-            result[j] = true;
-        }
-    }
-    return result;
-})();
-
-function splitQuery(query) {
-    var result = [];
-    var start = -1;
-    for (var i = 0; i < query.length; i++) {
-        if (splitChars[query.charCodeAt(i)]) {
-            if (start !== -1) {
-                result.push(query.slice(start, i));
-                start = -1;
-            }
-        } else if (start === -1) {
-            start = i;
-        }
-    }
-    if (start !== -1) {
-        result.push(query.slice(start));
-    }
-    return result;
-}
-
-
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index 20c4814..7a18115 100644
--- a/docs/build/html/_static/pygments.css
+++ b/docs/build/html/_static/pygments.css
@@ -1,21 +1,26 @@
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+span.linenos { color: #666666; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
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-.highlight  { background: #eeffcc; }
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@@ -26,7 +31,7 @@
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-.highlight .mo { color: #208050 } /* Literal.Number.Oct */
+.highlight .mb { color: #40a070 } /* Literal.Number.Bin */
+.highlight .mf { color: #40a070 } /* Literal.Number.Float */
+.highlight .mh { color: #40a070 } /* Literal.Number.Hex */
+.highlight .mi { color: #40a070 } /* Literal.Number.Integer */
+.highlight .mo { color: #40a070 } /* Literal.Number.Oct */
 .highlight .sa { color: #4070a0 } /* Literal.String.Affix */
 .highlight .sb { color: #4070a0 } /* Literal.String.Backtick */
 .highlight .sc { color: #4070a0 } /* Literal.String.Char */
@@ -66,4 +71,4 @@
 .highlight .vg { color: #bb60d5 } /* Name.Variable.Global */
 .highlight .vi { color: #bb60d5 } /* Name.Variable.Instance */
 .highlight .vm { color: #bb60d5 } /* Name.Variable.Magic */
-.highlight .il { color: #208050 } /* Literal.Number.Integer.Long */
\ No newline at end of file
+.highlight .il { color: #40a070 } /* Literal.Number.Integer.Long */
\ No newline at end of file
diff --git a/docs/build/html/_static/searchtools.js b/docs/build/html/_static/searchtools.js
index d11b33a..e89e34d 100644
--- a/docs/build/html/_static/searchtools.js
+++ b/docs/build/html/_static/searchtools.js
@@ -4,22 +4,24 @@
  *
  * Sphinx JavaScript utilities for the full-text search.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
+"use strict";
 
-if (!Scorer) {
-  /**
-   * Simple result scoring code.
-   */
+/**
+ * Simple result scoring code.
+ */
+if (typeof Scorer === "undefined") {
   var Scorer = {
     // Implement the following function to further tweak the score for each result
-    // The function takes a result array [filename, title, anchor, descr, score]
+    // The function takes a result array [docname, title, anchor, descr, score, filename]
     // and returns the new score.
     /*
-    score: function(result) {
-      return result[4];
+    score: result => {
+      const [docname, title, anchor, descr, score, filename] = result
+      return score
     },
     */
 
@@ -28,9 +30,11 @@ if (!Scorer) {
     // or matches in the last dotted part of the object name
     objPartialMatch: 6,
     // Additive scores depending on the priority of the object
-    objPrio: {0:  15,   // used to be importantResults
-              1:  5,   // used to be objectResults
-              2: -5},  // used to be unimportantResults
+    objPrio: {
+      0: 15, // used to be importantResults
+      1: 5, // used to be objectResults
+      2: -5, // used to be unimportantResults
+    },
     //  Used when the priority is not in the mapping.
     objPrioDefault: 0,
 
@@ -39,442 +43,495 @@ if (!Scorer) {
     partialTitle: 7,
     // query found in terms
     term: 5,
-    partialTerm: 2
+    partialTerm: 2,
   };
 }
 
-if (!splitQuery) {
-  function splitQuery(query) {
-    return query.split(/\s+/);
+const _removeChildren = (element) => {
+  while (element && element.lastChild) element.removeChild(element.lastChild);
+};
+
+/**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+const _escapeRegExp = (string) =>
+  string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+
+const _displayItem = (item, searchTerms) => {
+  const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
+  const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT;
+  const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+  const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+  const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
+
+  const [docName, title, anchor, descr, score, _filename] = item;
+
+  let listItem = document.createElement("li");
+  let requestUrl;
+  let linkUrl;
+  if (docBuilder === "dirhtml") {
+    // dirhtml builder
+    let dirname = docName + "/";
+    if (dirname.match(/\/index\/$/))
+      dirname = dirname.substring(0, dirname.length - 6);
+    else if (dirname === "index/") dirname = "";
+    requestUrl = docUrlRoot + dirname;
+    linkUrl = requestUrl;
+  } else {
+    // normal html builders
+    requestUrl = docUrlRoot + docName + docFileSuffix;
+    linkUrl = docName + docLinkSuffix;
+  }
+  let linkEl = listItem.appendChild(document.createElement("a"));
+  linkEl.href = linkUrl + anchor;
+  linkEl.dataset.score = score;
+  linkEl.innerHTML = title;
+  if (descr)
+    listItem.appendChild(document.createElement("span")).innerHTML =
+      " (" + descr + ")";
+  else if (showSearchSummary)
+    fetch(requestUrl)
+      .then((responseData) => responseData.text())
+      .then((data) => {
+        if (data)
+          listItem.appendChild(
+            Search.makeSearchSummary(data, searchTerms)
+          );
+      });
+  Search.output.appendChild(listItem);
+};
+const _finishSearch = (resultCount) => {
+  Search.stopPulse();
+  Search.title.innerText = _("Search Results");
+  if (!resultCount)
+    Search.status.innerText = Documentation.gettext(
+      "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
+    );
+  else
+    Search.status.innerText = _(
+      `Search finished, found ${resultCount} page(s) matching the search query.`
+    );
+};
+const _displayNextItem = (
+  results,
+  resultCount,
+  searchTerms
+) => {
+  // results left, load the summary and display it
+  // this is intended to be dynamic (don't sub resultsCount)
+  if (results.length) {
+    _displayItem(results.pop(), searchTerms);
+    setTimeout(
+      () => _displayNextItem(results, resultCount, searchTerms),
+      5
+    );
   }
+  // search finished, update title and status message
+  else _finishSearch(resultCount);
+};
+
+/**
+ * Default splitQuery function. Can be overridden in ``sphinx.search`` with a
+ * custom function per language.
+ *
+ * The regular expression works by splitting the string on consecutive characters
+ * that are not Unicode letters, numbers, underscores, or emoji characters.
+ * This is the same as ``\W+`` in Python, preserving the surrogate pair area.
+ */
+if (typeof splitQuery === "undefined") {
+  var splitQuery = (query) => query
+      .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
+      .filter(term => term)  // remove remaining empty strings
 }
 
 /**
  * Search Module
  */
-var Search = {
-
-  _index : null,
-  _queued_query : null,
-  _pulse_status : -1,
-
-  htmlToText : function(htmlString) {
-      var htmlElement = document.createElement('span');
-      htmlElement.innerHTML = htmlString;
-      $(htmlElement).find('.headerlink').remove();
-      docContent = $(htmlElement).find('[role=main]')[0];
-      if(docContent === undefined) {
-          console.warn("Content block not found. Sphinx search tries to obtain it " +
-                       "via '[role=main]'. Could you check your theme or template.");
-          return "";
-      }
-      return docContent.textContent || docContent.innerText;
+const Search = {
+  _index: null,
+  _queued_query: null,
+  _pulse_status: -1,
+
+  htmlToText: (htmlString) => {
+    const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html');
+    htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() });
+    const docContent = htmlElement.querySelector('[role="main"]');
+    if (docContent !== undefined) return docContent.textContent;
+    console.warn(
+      "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template."
+    );
+    return "";
   },
 
-  init : function() {
-      var params = $.getQueryParameters();
-      if (params.q) {
-          var query = params.q[0];
-          $('input[name="q"]')[0].value = query;
-          this.performSearch(query);
-      }
+  init: () => {
+    const query = new URLSearchParams(window.location.search).get("q");
+    document
+      .querySelectorAll('input[name="q"]')
+      .forEach((el) => (el.value = query));
+    if (query) Search.performSearch(query);
   },
 
-  loadIndex : function(url) {
-    $.ajax({type: "GET", url: url, data: null,
-            dataType: "script", cache: true,
-            complete: function(jqxhr, textstatus) {
-              if (textstatus != "success") {
-                document.getElementById("searchindexloader").src = url;
-              }
-            }});
-  },
+  loadIndex: (url) =>
+    (document.body.appendChild(document.createElement("script")).src = url),
 
-  setIndex : function(index) {
-    var q;
-    this._index = index;
-    if ((q = this._queued_query) !== null) {
-      this._queued_query = null;
-      Search.query(q);
+  setIndex: (index) => {
+    Search._index = index;
+    if (Search._queued_query !== null) {
+      const query = Search._queued_query;
+      Search._queued_query = null;
+      Search.query(query);
     }
   },
 
-  hasIndex : function() {
-      return this._index !== null;
-  },
+  hasIndex: () => Search._index !== null,
 
-  deferQuery : function(query) {
-      this._queued_query = query;
-  },
+  deferQuery: (query) => (Search._queued_query = query),
 
-  stopPulse : function() {
-      this._pulse_status = 0;
-  },
+  stopPulse: () => (Search._pulse_status = -1),
 
-  startPulse : function() {
-    if (this._pulse_status >= 0)
-        return;
-    function pulse() {
-      var i;
+  startPulse: () => {
+    if (Search._pulse_status >= 0) return;
+
+    const pulse = () => {
       Search._pulse_status = (Search._pulse_status + 1) % 4;
-      var dotString = '';
-      for (i = 0; i < Search._pulse_status; i++)
-        dotString += '.';
-      Search.dots.text(dotString);
-      if (Search._pulse_status > -1)
-        window.setTimeout(pulse, 500);
-    }
+      Search.dots.innerText = ".".repeat(Search._pulse_status);
+      if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
+    };
     pulse();
   },
 
   /**
    * perform a search for something (or wait until index is loaded)
    */
-  performSearch : function(query) {
+  performSearch: (query) => {
     // create the required interface elements
-    this.out = $('#search-results');
-    this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
-    this.dots = $('<span></span>').appendTo(this.title);
-    this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
-    this.output = $('<ul class="search"/>').appendTo(this.out);
-
-    $('#search-progress').text(_('Preparing search...'));
-    this.startPulse();
+    const searchText = document.createElement("h2");
+    searchText.textContent = _("Searching");
+    const searchSummary = document.createElement("p");
+    searchSummary.classList.add("search-summary");
+    searchSummary.innerText = "";
+    const searchList = document.createElement("ul");
+    searchList.classList.add("search");
+
+    const out = document.getElementById("search-results");
+    Search.title = out.appendChild(searchText);
+    Search.dots = Search.title.appendChild(document.createElement("span"));
+    Search.status = out.appendChild(searchSummary);
+    Search.output = out.appendChild(searchList);
+
+    const searchProgress = document.getElementById("search-progress");
+    // Some themes don't use the search progress node
+    if (searchProgress) {
+      searchProgress.innerText = _("Preparing search...");
+    }
+    Search.startPulse();
 
     // index already loaded, the browser was quick!
-    if (this.hasIndex())
-      this.query(query);
-    else
-      this.deferQuery(query);
+    if (Search.hasIndex()) Search.query(query);
+    else Search.deferQuery(query);
   },
 
   /**
    * execute search (requires search index to be loaded)
    */
-  query : function(query) {
-    var i;
-
-    // stem the searchterms and add them to the correct list
-    var stemmer = new Stemmer();
-    var searchterms = [];
-    var excluded = [];
-    var hlterms = [];
-    var tmp = splitQuery(query);
-    var objectterms = [];
-    for (i = 0; i < tmp.length; i++) {
-      if (tmp[i] !== "") {
-          objectterms.push(tmp[i].toLowerCase());
-      }
+  query: (query) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
+    const allTitles = Search._index.alltitles;
+    const indexEntries = Search._index.indexentries;
+
+    // stem the search terms and add them to the correct list
+    const stemmer = new Stemmer();
+    const searchTerms = new Set();
+    const excludedTerms = new Set();
+    const highlightTerms = new Set();
+    const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
+    splitQuery(query.trim()).forEach((queryTerm) => {
+      const queryTermLower = queryTerm.toLowerCase();
+
+      // maybe skip this "word"
+      // stopwords array is from language_data.js
+      if (
+        stopwords.indexOf(queryTermLower) !== -1 ||
+        queryTerm.match(/^\d+$/)
+      )
+        return;
 
-      if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i].match(/^\d+$/) ||
-          tmp[i] === "") {
-        // skip this "word"
-        continue;
-      }
       // stem the word
-      var word = stemmer.stemWord(tmp[i].toLowerCase());
-      // prevent stemmer from cutting word smaller than two chars
-      if(word.length < 3 && tmp[i].length >= 3) {
-        word = tmp[i];
-      }
-      var toAppend;
+      let word = stemmer.stemWord(queryTermLower);
       // select the correct list
-      if (word[0] == '-') {
-        toAppend = excluded;
-        word = word.substr(1);
-      }
+      if (word[0] === "-") excludedTerms.add(word.substr(1));
       else {
-        toAppend = searchterms;
-        hlterms.push(tmp[i].toLowerCase());
+        searchTerms.add(word);
+        highlightTerms.add(queryTermLower);
       }
-      // only add if not already in the list
-      if (!$u.contains(toAppend, word))
-        toAppend.push(word);
-    }
-    var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
+    });
 
-    // console.debug('SEARCH: searching for:');
-    // console.info('required: ', searchterms);
-    // console.info('excluded: ', excluded);
+    if (SPHINX_HIGHLIGHT_ENABLED) {  // set in sphinx_highlight.js
+      localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
+    }
 
-    // prepare search
-    var terms = this._index.terms;
-    var titleterms = this._index.titleterms;
+    // console.debug("SEARCH: searching for:");
+    // console.info("required: ", [...searchTerms]);
+    // console.info("excluded: ", [...excludedTerms]);
+
+    // array of [docname, title, anchor, descr, score, filename]
+    let results = [];
+    _removeChildren(document.getElementById("search-progress"));
+
+    const queryLower = query.toLowerCase();
+    for (const [title, foundTitles] of Object.entries(allTitles)) {
+      if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) {
+        for (const [file, id] of foundTitles) {
+          let score = Math.round(100 * queryLower.length / title.length)
+          results.push([
+            docNames[file],
+            titles[file] !== title ? `${titles[file]} > ${title}` : title,
+            id !== null ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
 
-    // array of [filename, title, anchor, descr, score]
-    var results = [];
-    $('#search-progress').empty();
+    // search for explicit entries in index directives
+    for (const [entry, foundEntries] of Object.entries(indexEntries)) {
+      if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
+        for (const [file, id] of foundEntries) {
+          let score = Math.round(100 * queryLower.length / entry.length)
+          results.push([
+            docNames[file],
+            titles[file],
+            id ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
 
     // lookup as object
-    for (i = 0; i < objectterms.length; i++) {
-      var others = [].concat(objectterms.slice(0, i),
-                             objectterms.slice(i+1, objectterms.length));
-      results = results.concat(this.performObjectSearch(objectterms[i], others));
-    }
+    objectTerms.forEach((term) =>
+      results.push(...Search.performObjectSearch(term, objectTerms))
+    );
 
     // lookup as search terms in fulltext
-    results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
+    results.push(...Search.performTermsSearch(searchTerms, excludedTerms));
 
     // let the scorer override scores with a custom scoring function
-    if (Scorer.score) {
-      for (i = 0; i < results.length; i++)
-        results[i][4] = Scorer.score(results[i]);
-    }
+    if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item)));
 
     // now sort the results by score (in opposite order of appearance, since the
     // display function below uses pop() to retrieve items) and then
     // alphabetically
-    results.sort(function(a, b) {
-      var left = a[4];
-      var right = b[4];
-      if (left > right) {
-        return 1;
-      } else if (left < right) {
-        return -1;
-      } else {
+    results.sort((a, b) => {
+      const leftScore = a[4];
+      const rightScore = b[4];
+      if (leftScore === rightScore) {
         // same score: sort alphabetically
-        left = a[1].toLowerCase();
-        right = b[1].toLowerCase();
-        return (left > right) ? -1 : ((left < right) ? 1 : 0);
+        const leftTitle = a[1].toLowerCase();
+        const rightTitle = b[1].toLowerCase();
+        if (leftTitle === rightTitle) return 0;
+        return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
       }
+      return leftScore > rightScore ? 1 : -1;
     });
 
+    // remove duplicate search results
+    // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
+    let seen = new Set();
+    results = results.reverse().reduce((acc, result) => {
+      let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
+      if (!seen.has(resultStr)) {
+        acc.push(result);
+        seen.add(resultStr);
+      }
+      return acc;
+    }, []);
+
+    results = results.reverse();
+
     // for debugging
     //Search.lastresults = results.slice();  // a copy
-    //console.info('search results:', Search.lastresults);
+    // console.info("search results:", Search.lastresults);
 
     // print the results
-    var resultCount = results.length;
-    function displayNextItem() {
-      // results left, load the summary and display it
-      if (results.length) {
-        var item = results.pop();
-        var listItem = $('<li style="display:none"></li>');
-        var requestUrl = "";
-        if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
-          // dirhtml builder
-          var dirname = item[0] + '/';
-          if (dirname.match(/\/index\/$/)) {
-            dirname = dirname.substring(0, dirname.length-6);
-          } else if (dirname == 'index/') {
-            dirname = '';
-          }
-          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
-
-        } else {
-          // normal html builders
-          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
-        }
-        listItem.append($('<a/>').attr('href',
-            requestUrl +
-            highlightstring + item[2]).html(item[1]));
-        if (item[3]) {
-          listItem.append($('<span> (' + item[3] + ')</span>'));
-          Search.output.append(listItem);
-          listItem.slideDown(5, function() {
-            displayNextItem();
-          });
-        } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
-          $.ajax({url: requestUrl,
-                  dataType: "text",
-                  complete: function(jqxhr, textstatus) {
-                    var data = jqxhr.responseText;
-                    if (data !== '' && data !== undefined) {
-                      listItem.append(Search.makeSearchSummary(data, searchterms, hlterms));
-                    }
-                    Search.output.append(listItem);
-                    listItem.slideDown(5, function() {
-                      displayNextItem();
-                    });
-                  }});
-        } else {
-          // no source available, just display title
-          Search.output.append(listItem);
-          listItem.slideDown(5, function() {
-            displayNextItem();
-          });
-        }
-      }
-      // search finished, update title and status message
-      else {
-        Search.stopPulse();
-        Search.title.text(_('Search Results'));
-        if (!resultCount)
-          Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
-        else
-            Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
-        Search.status.fadeIn(500);
-      }
-    }
-    displayNextItem();
+    _displayNextItem(results, results.length, searchTerms);
   },
 
   /**
    * search for object names
    */
-  performObjectSearch : function(object, otherterms) {
-    var filenames = this._index.filenames;
-    var docnames = this._index.docnames;
-    var objects = this._index.objects;
-    var objnames = this._index.objnames;
-    var titles = this._index.titles;
-
-    var i;
-    var results = [];
-
-    for (var prefix in objects) {
-      for (var name in objects[prefix]) {
-        var fullname = (prefix ? prefix + '.' : '') + name;
-        var fullnameLower = fullname.toLowerCase()
-        if (fullnameLower.indexOf(object) > -1) {
-          var score = 0;
-          var parts = fullnameLower.split('.');
-          // check for different match types: exact matches of full name or
-          // "last name" (i.e. last dotted part)
-          if (fullnameLower == object || parts[parts.length - 1] == object) {
-            score += Scorer.objNameMatch;
-          // matches in last name
-          } else if (parts[parts.length - 1].indexOf(object) > -1) {
-            score += Scorer.objPartialMatch;
-          }
-          var match = objects[prefix][name];
-          var objname = objnames[match[1]][2];
-          var title = titles[match[0]];
-          // If more than one term searched for, we require other words to be
-          // found in the name/title/description
-          if (otherterms.length > 0) {
-            var haystack = (prefix + ' ' + name + ' ' +
-                            objname + ' ' + title).toLowerCase();
-            var allfound = true;
-            for (i = 0; i < otherterms.length; i++) {
-              if (haystack.indexOf(otherterms[i]) == -1) {
-                allfound = false;
-                break;
-              }
-            }
-            if (!allfound) {
-              continue;
-            }
-          }
-          var descr = objname + _(', in ') + title;
-
-          var anchor = match[3];
-          if (anchor === '')
-            anchor = fullname;
-          else if (anchor == '-')
-            anchor = objnames[match[1]][1] + '-' + fullname;
-          // add custom score for some objects according to scorer
-          if (Scorer.objPrio.hasOwnProperty(match[2])) {
-            score += Scorer.objPrio[match[2]];
-          } else {
-            score += Scorer.objPrioDefault;
-          }
-          results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
-        }
+  performObjectSearch: (object, objectTerms) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const objects = Search._index.objects;
+    const objNames = Search._index.objnames;
+    const titles = Search._index.titles;
+
+    const results = [];
+
+    const objectSearchCallback = (prefix, match) => {
+      const name = match[4]
+      const fullname = (prefix ? prefix + "." : "") + name;
+      const fullnameLower = fullname.toLowerCase();
+      if (fullnameLower.indexOf(object) < 0) return;
+
+      let score = 0;
+      const parts = fullnameLower.split(".");
+
+      // check for different match types: exact matches of full name or
+      // "last name" (i.e. last dotted part)
+      if (fullnameLower === object || parts.slice(-1)[0] === object)
+        score += Scorer.objNameMatch;
+      else if (parts.slice(-1)[0].indexOf(object) > -1)
+        score += Scorer.objPartialMatch; // matches in last name
+
+      const objName = objNames[match[1]][2];
+      const title = titles[match[0]];
+
+      // If more than one term searched for, we require other words to be
+      // found in the name/title/description
+      const otherTerms = new Set(objectTerms);
+      otherTerms.delete(object);
+      if (otherTerms.size > 0) {
+        const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
+        if (
+          [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
+        )
+          return;
       }
-    }
 
+      let anchor = match[3];
+      if (anchor === "") anchor = fullname;
+      else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
+
+      const descr = objName + _(", in ") + title;
+
+      // add custom score for some objects according to scorer
+      if (Scorer.objPrio.hasOwnProperty(match[2]))
+        score += Scorer.objPrio[match[2]];
+      else score += Scorer.objPrioDefault;
+
+      results.push([
+        docNames[match[0]],
+        fullname,
+        "#" + anchor,
+        descr,
+        score,
+        filenames[match[0]],
+      ]);
+    };
+    Object.keys(objects).forEach((prefix) =>
+      objects[prefix].forEach((array) =>
+        objectSearchCallback(prefix, array)
+      )
+    );
     return results;
   },
 
   /**
    * search for full-text terms in the index
    */
-  performTermsSearch : function(searchterms, excluded, terms, titleterms) {
-    var docnames = this._index.docnames;
-    var filenames = this._index.filenames;
-    var titles = this._index.titles;
+  performTermsSearch: (searchTerms, excludedTerms) => {
+    // prepare search
+    const terms = Search._index.terms;
+    const titleTerms = Search._index.titleterms;
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
 
-    var i, j, file;
-    var fileMap = {};
-    var scoreMap = {};
-    var results = [];
+    const scoreMap = new Map();
+    const fileMap = new Map();
 
     // perform the search on the required terms
-    for (i = 0; i < searchterms.length; i++) {
-      var word = searchterms[i];
-      var files = [];
-      var _o = [
-        {files: terms[word], score: Scorer.term},
-        {files: titleterms[word], score: Scorer.title}
+    searchTerms.forEach((word) => {
+      const files = [];
+      const arr = [
+        { files: terms[word], score: Scorer.term },
+        { files: titleTerms[word], score: Scorer.title },
       ];
       // add support for partial matches
       if (word.length > 2) {
-        for (var w in terms) {
-          if (w.match(word) && !terms[word]) {
-            _o.push({files: terms[w], score: Scorer.partialTerm})
-          }
-        }
-        for (var w in titleterms) {
-          if (w.match(word) && !titleterms[word]) {
-              _o.push({files: titleterms[w], score: Scorer.partialTitle})
-          }
-        }
+        const escapedWord = _escapeRegExp(word);
+        Object.keys(terms).forEach((term) => {
+          if (term.match(escapedWord) && !terms[word])
+            arr.push({ files: terms[term], score: Scorer.partialTerm });
+        });
+        Object.keys(titleTerms).forEach((term) => {
+          if (term.match(escapedWord) && !titleTerms[word])
+            arr.push({ files: titleTerms[word], score: Scorer.partialTitle });
+        });
       }
 
       // no match but word was a required one
-      if ($u.every(_o, function(o){return o.files === undefined;})) {
-        break;
-      }
+      if (arr.every((record) => record.files === undefined)) return;
+
       // found search word in contents
-      $u.each(_o, function(o) {
-        var _files = o.files;
-        if (_files === undefined)
-          return
-
-        if (_files.length === undefined)
-          _files = [_files];
-        files = files.concat(_files);
-
-        // set score for the word in each file to Scorer.term
-        for (j = 0; j < _files.length; j++) {
-          file = _files[j];
-          if (!(file in scoreMap))
-            scoreMap[file] = {};
-          scoreMap[file][word] = o.score;
-        }
+      arr.forEach((record) => {
+        if (record.files === undefined) return;
+
+        let recordFiles = record.files;
+        if (recordFiles.length === undefined) recordFiles = [recordFiles];
+        files.push(...recordFiles);
+
+        // set score for the word in each file
+        recordFiles.forEach((file) => {
+          if (!scoreMap.has(file)) scoreMap.set(file, {});
+          scoreMap.get(file)[word] = record.score;
+        });
       });
 
       // create the mapping
-      for (j = 0; j < files.length; j++) {
-        file = files[j];
-        if (file in fileMap && fileMap[file].indexOf(word) === -1)
-          fileMap[file].push(word);
-        else
-          fileMap[file] = [word];
-      }
-    }
+      files.forEach((file) => {
+        if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1)
+          fileMap.get(file).push(word);
+        else fileMap.set(file, [word]);
+      });
+    });
 
     // now check if the files don't contain excluded terms
-    for (file in fileMap) {
-      var valid = true;
-
+    const results = [];
+    for (const [file, wordList] of fileMap) {
       // check if all requirements are matched
-      var filteredTermCount = // as search terms with length < 3 are discarded: ignore
-        searchterms.filter(function(term){return term.length > 2}).length
+
+      // as search terms with length < 3 are discarded
+      const filteredTermCount = [...searchTerms].filter(
+        (term) => term.length > 2
+      ).length;
       if (
-        fileMap[file].length != searchterms.length &&
-        fileMap[file].length != filteredTermCount
-      ) continue;
+        wordList.length !== searchTerms.size &&
+        wordList.length !== filteredTermCount
+      )
+        continue;
 
       // ensure that none of the excluded terms is in the search result
-      for (i = 0; i < excluded.length; i++) {
-        if (terms[excluded[i]] == file ||
-            titleterms[excluded[i]] == file ||
-            $u.contains(terms[excluded[i]] || [], file) ||
-            $u.contains(titleterms[excluded[i]] || [], file)) {
-          valid = false;
-          break;
-        }
-      }
+      if (
+        [...excludedTerms].some(
+          (term) =>
+            terms[term] === file ||
+            titleTerms[term] === file ||
+            (terms[term] || []).includes(file) ||
+            (titleTerms[term] || []).includes(file)
+        )
+      )
+        break;
 
-      // if we have still a valid result we can add it to the result list
-      if (valid) {
-        // select one (max) score for the file.
-        // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
-        var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
-        results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
-      }
+      // select one (max) score for the file.
+      const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w]));
+      // add result to the result list
+      results.push([
+        docNames[file],
+        titles[file],
+        "",
+        null,
+        score,
+        filenames[file],
+      ]);
     }
     return results;
   },
@@ -482,31 +539,28 @@ var Search = {
   /**
    * helper function to return a node containing the
    * search summary for a given text. keywords is a list
-   * of stemmed words, hlwords is the list of normal, unstemmed
-   * words. the first one is used to find the occurrence, the
-   * latter for highlighting it.
+   * of stemmed words.
    */
-  makeSearchSummary : function(htmlText, keywords, hlwords) {
-    var text = Search.htmlToText(htmlText);
-    var textLower = text.toLowerCase();
-    var start = 0;
-    $.each(keywords, function() {
-      var i = textLower.indexOf(this.toLowerCase());
-      if (i > -1)
-        start = i;
-    });
-    start = Math.max(start - 120, 0);
-    var excerpt = ((start > 0) ? '...' : '') +
-      $.trim(text.substr(start, 240)) +
-      ((start + 240 - text.length) ? '...' : '');
-    var rv = $('<div class="context"></div>').text(excerpt);
-    $.each(hlwords, function() {
-      rv = rv.highlightText(this, 'highlighted');
-    });
-    return rv;
-  }
+  makeSearchSummary: (htmlText, keywords) => {
+    const text = Search.htmlToText(htmlText);
+    if (text === "") return null;
+
+    const textLower = text.toLowerCase();
+    const actualStartPosition = [...keywords]
+      .map((k) => textLower.indexOf(k.toLowerCase()))
+      .filter((i) => i > -1)
+      .slice(-1)[0];
+    const startWithContext = Math.max(actualStartPosition - 120, 0);
+
+    const top = startWithContext === 0 ? "" : "...";
+    const tail = startWithContext + 240 < text.length ? "..." : "";
+
+    let summary = document.createElement("p");
+    summary.classList.add("context");
+    summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
+
+    return summary;
+  },
 };
 
-$(document).ready(function() {
-  Search.init();
-});
+_ready(Search.init);
diff --git a/docs/build/html/_static/sidebar.js b/docs/build/html/_static/sidebar.js
deleted file mode 100644
index 657f8be..0000000
--- a/docs/build/html/_static/sidebar.js
+++ /dev/null
@@ -1,159 +0,0 @@
-/*
- * sidebar.js
- * ~~~~~~~~~~
- *
- * This script makes the Sphinx sidebar collapsible.
- *
- * .sphinxsidebar contains .sphinxsidebarwrapper.  This script adds
- * in .sphixsidebar, after .sphinxsidebarwrapper, the #sidebarbutton
- * used to collapse and expand the sidebar.
- *
- * When the sidebar is collapsed the .sphinxsidebarwrapper is hidden
- * and the width of the sidebar and the margin-left of the document
- * are decreased. When the sidebar is expanded the opposite happens.
- * This script saves a per-browser/per-session cookie used to
- * remember the position of the sidebar among the pages.
- * Once the browser is closed the cookie is deleted and the position
- * reset to the default (expanded).
- *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
- * :license: BSD, see LICENSE for details.
- *
- */
-
-$(function() {
-  
-  
-  
-  
-  
-  
-  
-
-  // global elements used by the functions.
-  // the 'sidebarbutton' element is defined as global after its
-  // creation, in the add_sidebar_button function
-  var bodywrapper = $('.bodywrapper');
-  var sidebar = $('.sphinxsidebar');
-  var sidebarwrapper = $('.sphinxsidebarwrapper');
-
-  // for some reason, the document has no sidebar; do not run into errors
-  if (!sidebar.length) return;
-
-  // original margin-left of the bodywrapper and width of the sidebar
-  // with the sidebar expanded
-  var bw_margin_expanded = bodywrapper.css('margin-left');
-  var ssb_width_expanded = sidebar.width();
-
-  // margin-left of the bodywrapper and width of the sidebar
-  // with the sidebar collapsed
-  var bw_margin_collapsed = '.8em';
-  var ssb_width_collapsed = '.8em';
-
-  // colors used by the current theme
-  var dark_color = $('.related').css('background-color');
-  var light_color = $('.document').css('background-color');
-
-  function sidebar_is_collapsed() {
-    return sidebarwrapper.is(':not(:visible)');
-  }
-
-  function toggle_sidebar() {
-    if (sidebar_is_collapsed())
-      expand_sidebar();
-    else
-      collapse_sidebar();
-  }
-
-  function collapse_sidebar() {
-    sidebarwrapper.hide();
-    sidebar.css('width', ssb_width_collapsed);
-    bodywrapper.css('margin-left', bw_margin_collapsed);
-    sidebarbutton.css({
-        'margin-left': '0',
-        'height': bodywrapper.height()
-    });
-    sidebarbutton.find('span').text('»');
-    sidebarbutton.attr('title', _('Expand sidebar'));
-    document.cookie = 'sidebar=collapsed';
-  }
-
-  function expand_sidebar() {
-    bodywrapper.css('margin-left', bw_margin_expanded);
-    sidebar.css('width', ssb_width_expanded);
-    sidebarwrapper.show();
-    sidebarbutton.css({
-        'margin-left': ssb_width_expanded-12,
-        'height': bodywrapper.height()
-    });
-    sidebarbutton.find('span').text('«');
-    sidebarbutton.attr('title', _('Collapse sidebar'));
-    document.cookie = 'sidebar=expanded';
-  }
-
-  function add_sidebar_button() {
-    sidebarwrapper.css({
-        'float': 'left',
-        'margin-right': '0',
-        'width': ssb_width_expanded - 28
-    });
-    // create the button
-    sidebar.append(
-        '<div id="sidebarbutton"><span>&laquo;</span></div>'
-    );
-    var sidebarbutton = $('#sidebarbutton');
-    light_color = sidebarbutton.css('background-color');
-    // find the height of the viewport to center the '<<' in the page
-    var viewport_height;
-    if (window.innerHeight)
- 	  viewport_height = window.innerHeight;
-    else
-	  viewport_height = $(window).height();
-    sidebarbutton.find('span').css({
-        'display': 'block',
-        'margin-top': (viewport_height - sidebar.position().top - 20) / 2
-    });
-
-    sidebarbutton.click(toggle_sidebar);
-    sidebarbutton.attr('title', _('Collapse sidebar'));
-    sidebarbutton.css({
-        'color': '#FFFFFF',
-        'border-left': '1px solid ' + dark_color,
-        'font-size': '1.2em',
-        'cursor': 'pointer',
-        'height': bodywrapper.height(),
-        'padding-top': '1px',
-        'margin-left': ssb_width_expanded - 12
-    });
-
-    sidebarbutton.hover(
-      function () {
-          $(this).css('background-color', dark_color);
-      },
-      function () {
-          $(this).css('background-color', light_color);
-      }
-    );
-  }
-
-  function set_position_from_cookie() {
-    if (!document.cookie)
-      return;
-    var items = document.cookie.split(';');
-    for(var k=0; k<items.length; k++) {
-      var key_val = items[k].split('=');
-      var key = key_val[0].replace(/ /, "");  // strip leading spaces
-      if (key == 'sidebar') {
-        var value = key_val[1];
-        if ((value == 'collapsed') && (!sidebar_is_collapsed()))
-          collapse_sidebar();
-        else if ((value == 'expanded') && (sidebar_is_collapsed()))
-          expand_sidebar();
-      }
-    }
-  }
-
-  add_sidebar_button();
-  var sidebarbutton = $('#sidebarbutton');
-  set_position_from_cookie();
-});
\ No newline at end of file
diff --git a/docs/build/html/_static/sphinx_highlight.js b/docs/build/html/_static/sphinx_highlight.js
new file mode 100644
index 0000000..aae669d
--- /dev/null
+++ b/docs/build/html/_static/sphinx_highlight.js
@@ -0,0 +1,144 @@
+/* Highlighting utilities for Sphinx HTML documentation. */
+"use strict";
+
+const SPHINX_HIGHLIGHT_ENABLED = true
+
+/**
+ * highlight a given string on a node by wrapping it in
+ * span elements with the given class name.
+ */
+const _highlight = (node, addItems, text, className) => {
+  if (node.nodeType === Node.TEXT_NODE) {
+    const val = node.nodeValue;
+    const parent = node.parentNode;
+    const pos = val.toLowerCase().indexOf(text);
+    if (
+      pos >= 0 &&
+      !parent.classList.contains(className) &&
+      !parent.classList.contains("nohighlight")
+    ) {
+      let span;
+
+      const closestNode = parent.closest("body, svg, foreignObject");
+      const isInSVG = closestNode && closestNode.matches("svg");
+      if (isInSVG) {
+        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+      } else {
+        span = document.createElement("span");
+        span.classList.add(className);
+      }
+
+      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+      parent.insertBefore(
+        span,
+        parent.insertBefore(
+          document.createTextNode(val.substr(pos + text.length)),
+          node.nextSibling
+        )
+      );
+      node.nodeValue = val.substr(0, pos);
+
+      if (isInSVG) {
+        const rect = document.createElementNS(
+          "http://www.w3.org/2000/svg",
+          "rect"
+        );
+        const bbox = parent.getBBox();
+        rect.x.baseVal.value = bbox.x;
+        rect.y.baseVal.value = bbox.y;
+        rect.width.baseVal.value = bbox.width;
+        rect.height.baseVal.value = bbox.height;
+        rect.setAttribute("class", className);
+        addItems.push({ parent: parent, target: rect });
+      }
+    }
+  } else if (node.matches && !node.matches("button, select, textarea")) {
+    node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
+  }
+};
+const _highlightText = (thisNode, text, className) => {
+  let addItems = [];
+  _highlight(thisNode, addItems, text, className);
+  addItems.forEach((obj) =>
+    obj.parent.insertAdjacentElement("beforebegin", obj.target)
+  );
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const SphinxHighlight = {
+
+  /**
+   * highlight the search words provided in localstorage in the text
+   */
+  highlightSearchWords: () => {
+    if (!SPHINX_HIGHLIGHT_ENABLED) return;  // bail if no highlight
+
+    // get and clear terms from localstorage
+    const url = new URL(window.location);
+    const highlight =
+        localStorage.getItem("sphinx_highlight_terms")
+        || url.searchParams.get("highlight")
+        || "";
+    localStorage.removeItem("sphinx_highlight_terms")
+    url.searchParams.delete("highlight");
+    window.history.replaceState({}, "", url);
+
+    // get individual terms from highlight string
+    const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
+    if (terms.length === 0) return; // nothing to do
+
+    // There should never be more than one element matching "div.body"
+    const divBody = document.querySelectorAll("div.body");
+    const body = divBody.length ? divBody[0] : document.querySelector("body");
+    window.setTimeout(() => {
+      terms.forEach((term) => _highlightText(body, term, "highlighted"));
+    }, 10);
+
+    const searchBox = document.getElementById("searchbox");
+    if (searchBox === null) return;
+    searchBox.appendChild(
+      document
+        .createRange()
+        .createContextualFragment(
+          '<p class="highlight-link">' +
+            '<a href="javascript:SphinxHighlight.hideSearchWords()">' +
+            _("Hide Search Matches") +
+            "</a></p>"
+        )
+    );
+  },
+
+  /**
+   * helper function to hide the search marks again
+   */
+  hideSearchWords: () => {
+    document
+      .querySelectorAll("#searchbox .highlight-link")
+      .forEach((el) => el.remove());
+    document
+      .querySelectorAll("span.highlighted")
+      .forEach((el) => el.classList.remove("highlighted"));
+    localStorage.removeItem("sphinx_highlight_terms")
+  },
+
+  initEscapeListener: () => {
+    // only install a listener if it is really needed
+    if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return;
+      if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) {
+        SphinxHighlight.hideSearchWords();
+        event.preventDefault();
+      }
+    });
+  },
+};
+
+_ready(SphinxHighlight.highlightSearchWords);
+_ready(SphinxHighlight.initEscapeListener);
diff --git a/docs/build/html/_static/underscore-1.13.1.js b/docs/build/html/_static/underscore-1.13.1.js
new file mode 100644
index 0000000..ffd77af
--- /dev/null
+++ b/docs/build/html/_static/underscore-1.13.1.js
@@ -0,0 +1,2042 @@
+(function (global, factory) {
+  typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
+  typeof define === 'function' && define.amd ? define('underscore', factory) :
+  (global = typeof globalThis !== 'undefined' ? globalThis : global || self, (function () {
+    var current = global._;
+    var exports = global._ = factory();
+    exports.noConflict = function () { global._ = current; return exports; };
+  }()));
+}(this, (function () {
+  //     Underscore.js 1.13.1
+  //     https://underscorejs.org
+  //     (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+  //     Underscore may be freely distributed under the MIT license.
+
+  // Current version.
+  var VERSION = '1.13.1';
+
+  // Establish the root object, `window` (`self`) in the browser, `global`
+  // on the server, or `this` in some virtual machines. We use `self`
+  // instead of `window` for `WebWorker` support.
+  var root = typeof self == 'object' && self.self === self && self ||
+            typeof global == 'object' && global.global === global && global ||
+            Function('return this')() ||
+            {};
+
+  // Save bytes in the minified (but not gzipped) version:
+  var ArrayProto = Array.prototype, ObjProto = Object.prototype;
+  var SymbolProto = typeof Symbol !== 'undefined' ? Symbol.prototype : null;
+
+  // Create quick reference variables for speed access to core prototypes.
+  var push = ArrayProto.push,
+      slice = ArrayProto.slice,
+      toString = ObjProto.toString,
+      hasOwnProperty = ObjProto.hasOwnProperty;
+
+  // Modern feature detection.
+  var supportsArrayBuffer = typeof ArrayBuffer !== 'undefined',
+      supportsDataView = typeof DataView !== 'undefined';
+
+  // All **ECMAScript 5+** native function implementations that we hope to use
+  // are declared here.
+  var nativeIsArray = Array.isArray,
+      nativeKeys = Object.keys,
+      nativeCreate = Object.create,
+      nativeIsView = supportsArrayBuffer && ArrayBuffer.isView;
+
+  // Create references to these builtin functions because we override them.
+  var _isNaN = isNaN,
+      _isFinite = isFinite;
+
+  // Keys in IE < 9 that won't be iterated by `for key in ...` and thus missed.
+  var hasEnumBug = !{toString: null}.propertyIsEnumerable('toString');
+  var nonEnumerableProps = ['valueOf', 'isPrototypeOf', 'toString',
+    'propertyIsEnumerable', 'hasOwnProperty', 'toLocaleString'];
+
+  // The largest integer that can be represented exactly.
+  var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1;
+
+  // Some functions take a variable number of arguments, or a few expected
+  // arguments at the beginning and then a variable number of values to operate
+  // on. This helper accumulates all remaining arguments past the function’s
+  // argument length (or an explicit `startIndex`), into an array that becomes
+  // the last argument. Similar to ES6’s "rest parameter".
+  function restArguments(func, startIndex) {
+    startIndex = startIndex == null ? func.length - 1 : +startIndex;
+    return function() {
+      var length = Math.max(arguments.length - startIndex, 0),
+          rest = Array(length),
+          index = 0;
+      for (; index < length; index++) {
+        rest[index] = arguments[index + startIndex];
+      }
+      switch (startIndex) {
+        case 0: return func.call(this, rest);
+        case 1: return func.call(this, arguments[0], rest);
+        case 2: return func.call(this, arguments[0], arguments[1], rest);
+      }
+      var args = Array(startIndex + 1);
+      for (index = 0; index < startIndex; index++) {
+        args[index] = arguments[index];
+      }
+      args[startIndex] = rest;
+      return func.apply(this, args);
+    };
+  }
+
+  // Is a given variable an object?
+  function isObject(obj) {
+    var type = typeof obj;
+    return type === 'function' || type === 'object' && !!obj;
+  }
+
+  // Is a given value equal to null?
+  function isNull(obj) {
+    return obj === null;
+  }
+
+  // Is a given variable undefined?
+  function isUndefined(obj) {
+    return obj === void 0;
+  }
+
+  // Is a given value a boolean?
+  function isBoolean(obj) {
+    return obj === true || obj === false || toString.call(obj) === '[object Boolean]';
+  }
+
+  // Is a given value a DOM element?
+  function isElement(obj) {
+    return !!(obj && obj.nodeType === 1);
+  }
+
+  // Internal function for creating a `toString`-based type tester.
+  function tagTester(name) {
+    var tag = '[object ' + name + ']';
+    return function(obj) {
+      return toString.call(obj) === tag;
+    };
+  }
+
+  var isString = tagTester('String');
+
+  var isNumber = tagTester('Number');
+
+  var isDate = tagTester('Date');
+
+  var isRegExp = tagTester('RegExp');
+
+  var isError = tagTester('Error');
+
+  var isSymbol = tagTester('Symbol');
+
+  var isArrayBuffer = tagTester('ArrayBuffer');
+
+  var isFunction = tagTester('Function');
+
+  // Optimize `isFunction` if appropriate. Work around some `typeof` bugs in old
+  // v8, IE 11 (#1621), Safari 8 (#1929), and PhantomJS (#2236).
+  var nodelist = root.document && root.document.childNodes;
+  if (typeof /./ != 'function' && typeof Int8Array != 'object' && typeof nodelist != 'function') {
+    isFunction = function(obj) {
+      return typeof obj == 'function' || false;
+    };
+  }
+
+  var isFunction$1 = isFunction;
+
+  var hasObjectTag = tagTester('Object');
+
+  // In IE 10 - Edge 13, `DataView` has string tag `'[object Object]'`.
+  // In IE 11, the most common among them, this problem also applies to
+  // `Map`, `WeakMap` and `Set`.
+  var hasStringTagBug = (
+        supportsDataView && hasObjectTag(new DataView(new ArrayBuffer(8)))
+      ),
+      isIE11 = (typeof Map !== 'undefined' && hasObjectTag(new Map));
+
+  var isDataView = tagTester('DataView');
+
+  // In IE 10 - Edge 13, we need a different heuristic
+  // to determine whether an object is a `DataView`.
+  function ie10IsDataView(obj) {
+    return obj != null && isFunction$1(obj.getInt8) && isArrayBuffer(obj.buffer);
+  }
+
+  var isDataView$1 = (hasStringTagBug ? ie10IsDataView : isDataView);
+
+  // Is a given value an array?
+  // Delegates to ECMA5's native `Array.isArray`.
+  var isArray = nativeIsArray || tagTester('Array');
+
+  // Internal function to check whether `key` is an own property name of `obj`.
+  function has$1(obj, key) {
+    return obj != null && hasOwnProperty.call(obj, key);
+  }
+
+  var isArguments = tagTester('Arguments');
+
+  // Define a fallback version of the method in browsers (ahem, IE < 9), where
+  // there isn't any inspectable "Arguments" type.
+  (function() {
+    if (!isArguments(arguments)) {
+      isArguments = function(obj) {
+        return has$1(obj, 'callee');
+      };
+    }
+  }());
+
+  var isArguments$1 = isArguments;
+
+  // Is a given object a finite number?
+  function isFinite$1(obj) {
+    return !isSymbol(obj) && _isFinite(obj) && !isNaN(parseFloat(obj));
+  }
+
+  // Is the given value `NaN`?
+  function isNaN$1(obj) {
+    return isNumber(obj) && _isNaN(obj);
+  }
+
+  // Predicate-generating function. Often useful outside of Underscore.
+  function constant(value) {
+    return function() {
+      return value;
+    };
+  }
+
+  // Common internal logic for `isArrayLike` and `isBufferLike`.
+  function createSizePropertyCheck(getSizeProperty) {
+    return function(collection) {
+      var sizeProperty = getSizeProperty(collection);
+      return typeof sizeProperty == 'number' && sizeProperty >= 0 && sizeProperty <= MAX_ARRAY_INDEX;
+    }
+  }
+
+  // Internal helper to generate a function to obtain property `key` from `obj`.
+  function shallowProperty(key) {
+    return function(obj) {
+      return obj == null ? void 0 : obj[key];
+    };
+  }
+
+  // Internal helper to obtain the `byteLength` property of an object.
+  var getByteLength = shallowProperty('byteLength');
+
+  // Internal helper to determine whether we should spend extensive checks against
+  // `ArrayBuffer` et al.
+  var isBufferLike = createSizePropertyCheck(getByteLength);
+
+  // Is a given value a typed array?
+  var typedArrayPattern = /\[object ((I|Ui)nt(8|16|32)|Float(32|64)|Uint8Clamped|Big(I|Ui)nt64)Array\]/;
+  function isTypedArray(obj) {
+    // `ArrayBuffer.isView` is the most future-proof, so use it when available.
+    // Otherwise, fall back on the above regular expression.
+    return nativeIsView ? (nativeIsView(obj) && !isDataView$1(obj)) :
+                  isBufferLike(obj) && typedArrayPattern.test(toString.call(obj));
+  }
+
+  var isTypedArray$1 = supportsArrayBuffer ? isTypedArray : constant(false);
+
+  // Internal helper to obtain the `length` property of an object.
+  var getLength = shallowProperty('length');
+
+  // Internal helper to create a simple lookup structure.
+  // `collectNonEnumProps` used to depend on `_.contains`, but this led to
+  // circular imports. `emulatedSet` is a one-off solution that only works for
+  // arrays of strings.
+  function emulatedSet(keys) {
+    var hash = {};
+    for (var l = keys.length, i = 0; i < l; ++i) hash[keys[i]] = true;
+    return {
+      contains: function(key) { return hash[key]; },
+      push: function(key) {
+        hash[key] = true;
+        return keys.push(key);
+      }
+    };
+  }
+
+  // Internal helper. Checks `keys` for the presence of keys in IE < 9 that won't
+  // be iterated by `for key in ...` and thus missed. Extends `keys` in place if
+  // needed.
+  function collectNonEnumProps(obj, keys) {
+    keys = emulatedSet(keys);
+    var nonEnumIdx = nonEnumerableProps.length;
+    var constructor = obj.constructor;
+    var proto = isFunction$1(constructor) && constructor.prototype || ObjProto;
+
+    // Constructor is a special case.
+    var prop = 'constructor';
+    if (has$1(obj, prop) && !keys.contains(prop)) keys.push(prop);
+
+    while (nonEnumIdx--) {
+      prop = nonEnumerableProps[nonEnumIdx];
+      if (prop in obj && obj[prop] !== proto[prop] && !keys.contains(prop)) {
+        keys.push(prop);
+      }
+    }
+  }
+
+  // Retrieve the names of an object's own properties.
+  // Delegates to **ECMAScript 5**'s native `Object.keys`.
+  function keys(obj) {
+    if (!isObject(obj)) return [];
+    if (nativeKeys) return nativeKeys(obj);
+    var keys = [];
+    for (var key in obj) if (has$1(obj, key)) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  }
+
+  // Is a given array, string, or object empty?
+  // An "empty" object has no enumerable own-properties.
+  function isEmpty(obj) {
+    if (obj == null) return true;
+    // Skip the more expensive `toString`-based type checks if `obj` has no
+    // `.length`.
+    var length = getLength(obj);
+    if (typeof length == 'number' && (
+      isArray(obj) || isString(obj) || isArguments$1(obj)
+    )) return length === 0;
+    return getLength(keys(obj)) === 0;
+  }
+
+  // Returns whether an object has a given set of `key:value` pairs.
+  function isMatch(object, attrs) {
+    var _keys = keys(attrs), length = _keys.length;
+    if (object == null) return !length;
+    var obj = Object(object);
+    for (var i = 0; i < length; i++) {
+      var key = _keys[i];
+      if (attrs[key] !== obj[key] || !(key in obj)) return false;
+    }
+    return true;
+  }
+
+  // If Underscore is called as a function, it returns a wrapped object that can
+  // be used OO-style. This wrapper holds altered versions of all functions added
+  // through `_.mixin`. Wrapped objects may be chained.
+  function _$1(obj) {
+    if (obj instanceof _$1) return obj;
+    if (!(this instanceof _$1)) return new _$1(obj);
+    this._wrapped = obj;
+  }
+
+  _$1.VERSION = VERSION;
+
+  // Extracts the result from a wrapped and chained object.
+  _$1.prototype.value = function() {
+    return this._wrapped;
+  };
+
+  // Provide unwrapping proxies for some methods used in engine operations
+  // such as arithmetic and JSON stringification.
+  _$1.prototype.valueOf = _$1.prototype.toJSON = _$1.prototype.value;
+
+  _$1.prototype.toString = function() {
+    return String(this._wrapped);
+  };
+
+  // Internal function to wrap or shallow-copy an ArrayBuffer,
+  // typed array or DataView to a new view, reusing the buffer.
+  function toBufferView(bufferSource) {
+    return new Uint8Array(
+      bufferSource.buffer || bufferSource,
+      bufferSource.byteOffset || 0,
+      getByteLength(bufferSource)
+    );
+  }
+
+  // We use this string twice, so give it a name for minification.
+  var tagDataView = '[object DataView]';
+
+  // Internal recursive comparison function for `_.isEqual`.
+  function eq(a, b, aStack, bStack) {
+    // Identical objects are equal. `0 === -0`, but they aren't identical.
+    // See the [Harmony `egal` proposal](https://wiki.ecmascript.org/doku.php?id=harmony:egal).
+    if (a === b) return a !== 0 || 1 / a === 1 / b;
+    // `null` or `undefined` only equal to itself (strict comparison).
+    if (a == null || b == null) return false;
+    // `NaN`s are equivalent, but non-reflexive.
+    if (a !== a) return b !== b;
+    // Exhaust primitive checks
+    var type = typeof a;
+    if (type !== 'function' && type !== 'object' && typeof b != 'object') return false;
+    return deepEq(a, b, aStack, bStack);
+  }
+
+  // Internal recursive comparison function for `_.isEqual`.
+  function deepEq(a, b, aStack, bStack) {
+    // Unwrap any wrapped objects.
+    if (a instanceof _$1) a = a._wrapped;
+    if (b instanceof _$1) b = b._wrapped;
+    // Compare `[[Class]]` names.
+    var className = toString.call(a);
+    if (className !== toString.call(b)) return false;
+    // Work around a bug in IE 10 - Edge 13.
+    if (hasStringTagBug && className == '[object Object]' && isDataView$1(a)) {
+      if (!isDataView$1(b)) return false;
+      className = tagDataView;
+    }
+    switch (className) {
+      // These types are compared by value.
+      case '[object RegExp]':
+        // RegExps are coerced to strings for comparison (Note: '' + /a/i === '/a/i')
+      case '[object String]':
+        // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
+        // equivalent to `new String("5")`.
+        return '' + a === '' + b;
+      case '[object Number]':
+        // `NaN`s are equivalent, but non-reflexive.
+        // Object(NaN) is equivalent to NaN.
+        if (+a !== +a) return +b !== +b;
+        // An `egal` comparison is performed for other numeric values.
+        return +a === 0 ? 1 / +a === 1 / b : +a === +b;
+      case '[object Date]':
+      case '[object Boolean]':
+        // Coerce dates and booleans to numeric primitive values. Dates are compared by their
+        // millisecond representations. Note that invalid dates with millisecond representations
+        // of `NaN` are not equivalent.
+        return +a === +b;
+      case '[object Symbol]':
+        return SymbolProto.valueOf.call(a) === SymbolProto.valueOf.call(b);
+      case '[object ArrayBuffer]':
+      case tagDataView:
+        // Coerce to typed array so we can fall through.
+        return deepEq(toBufferView(a), toBufferView(b), aStack, bStack);
+    }
+
+    var areArrays = className === '[object Array]';
+    if (!areArrays && isTypedArray$1(a)) {
+        var byteLength = getByteLength(a);
+        if (byteLength !== getByteLength(b)) return false;
+        if (a.buffer === b.buffer && a.byteOffset === b.byteOffset) return true;
+        areArrays = true;
+    }
+    if (!areArrays) {
+      if (typeof a != 'object' || typeof b != 'object') return false;
+
+      // Objects with different constructors are not equivalent, but `Object`s or `Array`s
+      // from different frames are.
+      var aCtor = a.constructor, bCtor = b.constructor;
+      if (aCtor !== bCtor && !(isFunction$1(aCtor) && aCtor instanceof aCtor &&
+                               isFunction$1(bCtor) && bCtor instanceof bCtor)
+                          && ('constructor' in a && 'constructor' in b)) {
+        return false;
+      }
+    }
+    // Assume equality for cyclic structures. The algorithm for detecting cyclic
+    // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`.
+
+    // Initializing stack of traversed objects.
+    // It's done here since we only need them for objects and arrays comparison.
+    aStack = aStack || [];
+    bStack = bStack || [];
+    var length = aStack.length;
+    while (length--) {
+      // Linear search. Performance is inversely proportional to the number of
+      // unique nested structures.
+      if (aStack[length] === a) return bStack[length] === b;
+    }
+
+    // Add the first object to the stack of traversed objects.
+    aStack.push(a);
+    bStack.push(b);
+
+    // Recursively compare objects and arrays.
+    if (areArrays) {
+      // Compare array lengths to determine if a deep comparison is necessary.
+      length = a.length;
+      if (length !== b.length) return false;
+      // Deep compare the contents, ignoring non-numeric properties.
+      while (length--) {
+        if (!eq(a[length], b[length], aStack, bStack)) return false;
+      }
+    } else {
+      // Deep compare objects.
+      var _keys = keys(a), key;
+      length = _keys.length;
+      // Ensure that both objects contain the same number of properties before comparing deep equality.
+      if (keys(b).length !== length) return false;
+      while (length--) {
+        // Deep compare each member
+        key = _keys[length];
+        if (!(has$1(b, key) && eq(a[key], b[key], aStack, bStack))) return false;
+      }
+    }
+    // Remove the first object from the stack of traversed objects.
+    aStack.pop();
+    bStack.pop();
+    return true;
+  }
+
+  // Perform a deep comparison to check if two objects are equal.
+  function isEqual(a, b) {
+    return eq(a, b);
+  }
+
+  // Retrieve all the enumerable property names of an object.
+  function allKeys(obj) {
+    if (!isObject(obj)) return [];
+    var keys = [];
+    for (var key in obj) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  }
+
+  // Since the regular `Object.prototype.toString` type tests don't work for
+  // some types in IE 11, we use a fingerprinting heuristic instead, based
+  // on the methods. It's not great, but it's the best we got.
+  // The fingerprint method lists are defined below.
+  function ie11fingerprint(methods) {
+    var length = getLength(methods);
+    return function(obj) {
+      if (obj == null) return false;
+      // `Map`, `WeakMap` and `Set` have no enumerable keys.
+      var keys = allKeys(obj);
+      if (getLength(keys)) return false;
+      for (var i = 0; i < length; i++) {
+        if (!isFunction$1(obj[methods[i]])) return false;
+      }
+      // If we are testing against `WeakMap`, we need to ensure that
+      // `obj` doesn't have a `forEach` method in order to distinguish
+      // it from a regular `Map`.
+      return methods !== weakMapMethods || !isFunction$1(obj[forEachName]);
+    };
+  }
+
+  // In the interest of compact minification, we write
+  // each string in the fingerprints only once.
+  var forEachName = 'forEach',
+      hasName = 'has',
+      commonInit = ['clear', 'delete'],
+      mapTail = ['get', hasName, 'set'];
+
+  // `Map`, `WeakMap` and `Set` each have slightly different
+  // combinations of the above sublists.
+  var mapMethods = commonInit.concat(forEachName, mapTail),
+      weakMapMethods = commonInit.concat(mapTail),
+      setMethods = ['add'].concat(commonInit, forEachName, hasName);
+
+  var isMap = isIE11 ? ie11fingerprint(mapMethods) : tagTester('Map');
+
+  var isWeakMap = isIE11 ? ie11fingerprint(weakMapMethods) : tagTester('WeakMap');
+
+  var isSet = isIE11 ? ie11fingerprint(setMethods) : tagTester('Set');
+
+  var isWeakSet = tagTester('WeakSet');
+
+  // Retrieve the values of an object's properties.
+  function values(obj) {
+    var _keys = keys(obj);
+    var length = _keys.length;
+    var values = Array(length);
+    for (var i = 0; i < length; i++) {
+      values[i] = obj[_keys[i]];
+    }
+    return values;
+  }
+
+  // Convert an object into a list of `[key, value]` pairs.
+  // The opposite of `_.object` with one argument.
+  function pairs(obj) {
+    var _keys = keys(obj);
+    var length = _keys.length;
+    var pairs = Array(length);
+    for (var i = 0; i < length; i++) {
+      pairs[i] = [_keys[i], obj[_keys[i]]];
+    }
+    return pairs;
+  }
+
+  // Invert the keys and values of an object. The values must be serializable.
+  function invert(obj) {
+    var result = {};
+    var _keys = keys(obj);
+    for (var i = 0, length = _keys.length; i < length; i++) {
+      result[obj[_keys[i]]] = _keys[i];
+    }
+    return result;
+  }
+
+  // Return a sorted list of the function names available on the object.
+  function functions(obj) {
+    var names = [];
+    for (var key in obj) {
+      if (isFunction$1(obj[key])) names.push(key);
+    }
+    return names.sort();
+  }
+
+  // An internal function for creating assigner functions.
+  function createAssigner(keysFunc, defaults) {
+    return function(obj) {
+      var length = arguments.length;
+      if (defaults) obj = Object(obj);
+      if (length < 2 || obj == null) return obj;
+      for (var index = 1; index < length; index++) {
+        var source = arguments[index],
+            keys = keysFunc(source),
+            l = keys.length;
+        for (var i = 0; i < l; i++) {
+          var key = keys[i];
+          if (!defaults || obj[key] === void 0) obj[key] = source[key];
+        }
+      }
+      return obj;
+    };
+  }
+
+  // Extend a given object with all the properties in passed-in object(s).
+  var extend = createAssigner(allKeys);
+
+  // Assigns a given object with all the own properties in the passed-in
+  // object(s).
+  // (https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Object/assign)
+  var extendOwn = createAssigner(keys);
+
+  // Fill in a given object with default properties.
+  var defaults = createAssigner(allKeys, true);
+
+  // Create a naked function reference for surrogate-prototype-swapping.
+  function ctor() {
+    return function(){};
+  }
+
+  // An internal function for creating a new object that inherits from another.
+  function baseCreate(prototype) {
+    if (!isObject(prototype)) return {};
+    if (nativeCreate) return nativeCreate(prototype);
+    var Ctor = ctor();
+    Ctor.prototype = prototype;
+    var result = new Ctor;
+    Ctor.prototype = null;
+    return result;
+  }
+
+  // Creates an object that inherits from the given prototype object.
+  // If additional properties are provided then they will be added to the
+  // created object.
+  function create(prototype, props) {
+    var result = baseCreate(prototype);
+    if (props) extendOwn(result, props);
+    return result;
+  }
+
+  // Create a (shallow-cloned) duplicate of an object.
+  function clone(obj) {
+    if (!isObject(obj)) return obj;
+    return isArray(obj) ? obj.slice() : extend({}, obj);
+  }
+
+  // Invokes `interceptor` with the `obj` and then returns `obj`.
+  // The primary purpose of this method is to "tap into" a method chain, in
+  // order to perform operations on intermediate results within the chain.
+  function tap(obj, interceptor) {
+    interceptor(obj);
+    return obj;
+  }
+
+  // Normalize a (deep) property `path` to array.
+  // Like `_.iteratee`, this function can be customized.
+  function toPath$1(path) {
+    return isArray(path) ? path : [path];
+  }
+  _$1.toPath = toPath$1;
+
+  // Internal wrapper for `_.toPath` to enable minification.
+  // Similar to `cb` for `_.iteratee`.
+  function toPath(path) {
+    return _$1.toPath(path);
+  }
+
+  // Internal function to obtain a nested property in `obj` along `path`.
+  function deepGet(obj, path) {
+    var length = path.length;
+    for (var i = 0; i < length; i++) {
+      if (obj == null) return void 0;
+      obj = obj[path[i]];
+    }
+    return length ? obj : void 0;
+  }
+
+  // Get the value of the (deep) property on `path` from `object`.
+  // If any property in `path` does not exist or if the value is
+  // `undefined`, return `defaultValue` instead.
+  // The `path` is normalized through `_.toPath`.
+  function get(object, path, defaultValue) {
+    var value = deepGet(object, toPath(path));
+    return isUndefined(value) ? defaultValue : value;
+  }
+
+  // Shortcut function for checking if an object has a given property directly on
+  // itself (in other words, not on a prototype). Unlike the internal `has`
+  // function, this public version can also traverse nested properties.
+  function has(obj, path) {
+    path = toPath(path);
+    var length = path.length;
+    for (var i = 0; i < length; i++) {
+      var key = path[i];
+      if (!has$1(obj, key)) return false;
+      obj = obj[key];
+    }
+    return !!length;
+  }
+
+  // Keep the identity function around for default iteratees.
+  function identity(value) {
+    return value;
+  }
+
+  // Returns a predicate for checking whether an object has a given set of
+  // `key:value` pairs.
+  function matcher(attrs) {
+    attrs = extendOwn({}, attrs);
+    return function(obj) {
+      return isMatch(obj, attrs);
+    };
+  }
+
+  // Creates a function that, when passed an object, will traverse that object’s
+  // properties down the given `path`, specified as an array of keys or indices.
+  function property(path) {
+    path = toPath(path);
+    return function(obj) {
+      return deepGet(obj, path);
+    };
+  }
+
+  // Internal function that returns an efficient (for current engines) version
+  // of the passed-in callback, to be repeatedly applied in other Underscore
+  // functions.
+  function optimizeCb(func, context, argCount) {
+    if (context === void 0) return func;
+    switch (argCount == null ? 3 : argCount) {
+      case 1: return function(value) {
+        return func.call(context, value);
+      };
+      // The 2-argument case is omitted because we’re not using it.
+      case 3: return function(value, index, collection) {
+        return func.call(context, value, index, collection);
+      };
+      case 4: return function(accumulator, value, index, collection) {
+        return func.call(context, accumulator, value, index, collection);
+      };
+    }
+    return function() {
+      return func.apply(context, arguments);
+    };
+  }
+
+  // An internal function to generate callbacks that can be applied to each
+  // element in a collection, returning the desired result — either `_.identity`,
+  // an arbitrary callback, a property matcher, or a property accessor.
+  function baseIteratee(value, context, argCount) {
+    if (value == null) return identity;
+    if (isFunction$1(value)) return optimizeCb(value, context, argCount);
+    if (isObject(value) && !isArray(value)) return matcher(value);
+    return property(value);
+  }
+
+  // External wrapper for our callback generator. Users may customize
+  // `_.iteratee` if they want additional predicate/iteratee shorthand styles.
+  // This abstraction hides the internal-only `argCount` argument.
+  function iteratee(value, context) {
+    return baseIteratee(value, context, Infinity);
+  }
+  _$1.iteratee = iteratee;
+
+  // The function we call internally to generate a callback. It invokes
+  // `_.iteratee` if overridden, otherwise `baseIteratee`.
+  function cb(value, context, argCount) {
+    if (_$1.iteratee !== iteratee) return _$1.iteratee(value, context);
+    return baseIteratee(value, context, argCount);
+  }
+
+  // Returns the results of applying the `iteratee` to each element of `obj`.
+  // In contrast to `_.map` it returns an object.
+  function mapObject(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var _keys = keys(obj),
+        length = _keys.length,
+        results = {};
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys[index];
+      results[currentKey] = iteratee(obj[currentKey], currentKey, obj);
+    }
+    return results;
+  }
+
+  // Predicate-generating function. Often useful outside of Underscore.
+  function noop(){}
+
+  // Generates a function for a given object that returns a given property.
+  function propertyOf(obj) {
+    if (obj == null) return noop;
+    return function(path) {
+      return get(obj, path);
+    };
+  }
+
+  // Run a function **n** times.
+  function times(n, iteratee, context) {
+    var accum = Array(Math.max(0, n));
+    iteratee = optimizeCb(iteratee, context, 1);
+    for (var i = 0; i < n; i++) accum[i] = iteratee(i);
+    return accum;
+  }
+
+  // Return a random integer between `min` and `max` (inclusive).
+  function random(min, max) {
+    if (max == null) {
+      max = min;
+      min = 0;
+    }
+    return min + Math.floor(Math.random() * (max - min + 1));
+  }
+
+  // A (possibly faster) way to get the current timestamp as an integer.
+  var now = Date.now || function() {
+    return new Date().getTime();
+  };
+
+  // Internal helper to generate functions for escaping and unescaping strings
+  // to/from HTML interpolation.
+  function createEscaper(map) {
+    var escaper = function(match) {
+      return map[match];
+    };
+    // Regexes for identifying a key that needs to be escaped.
+    var source = '(?:' + keys(map).join('|') + ')';
+    var testRegexp = RegExp(source);
+    var replaceRegexp = RegExp(source, 'g');
+    return function(string) {
+      string = string == null ? '' : '' + string;
+      return testRegexp.test(string) ? string.replace(replaceRegexp, escaper) : string;
+    };
+  }
+
+  // Internal list of HTML entities for escaping.
+  var escapeMap = {
+    '&': '&amp;',
+    '<': '&lt;',
+    '>': '&gt;',
+    '"': '&quot;',
+    "'": '&#x27;',
+    '`': '&#x60;'
+  };
+
+  // Function for escaping strings to HTML interpolation.
+  var _escape = createEscaper(escapeMap);
+
+  // Internal list of HTML entities for unescaping.
+  var unescapeMap = invert(escapeMap);
+
+  // Function for unescaping strings from HTML interpolation.
+  var _unescape = createEscaper(unescapeMap);
+
+  // By default, Underscore uses ERB-style template delimiters. Change the
+  // following template settings to use alternative delimiters.
+  var templateSettings = _$1.templateSettings = {
+    evaluate: /<%([\s\S]+?)%>/g,
+    interpolate: /<%=([\s\S]+?)%>/g,
+    escape: /<%-([\s\S]+?)%>/g
+  };
+
+  // When customizing `_.templateSettings`, if you don't want to define an
+  // interpolation, evaluation or escaping regex, we need one that is
+  // guaranteed not to match.
+  var noMatch = /(.)^/;
+
+  // Certain characters need to be escaped so that they can be put into a
+  // string literal.
+  var escapes = {
+    "'": "'",
+    '\\': '\\',
+    '\r': 'r',
+    '\n': 'n',
+    '\u2028': 'u2028',
+    '\u2029': 'u2029'
+  };
+
+  var escapeRegExp = /\\|'|\r|\n|\u2028|\u2029/g;
+
+  function escapeChar(match) {
+    return '\\' + escapes[match];
+  }
+
+  // In order to prevent third-party code injection through
+  // `_.templateSettings.variable`, we test it against the following regular
+  // expression. It is intentionally a bit more liberal than just matching valid
+  // identifiers, but still prevents possible loopholes through defaults or
+  // destructuring assignment.
+  var bareIdentifier = /^\s*(\w|\$)+\s*$/;
+
+  // JavaScript micro-templating, similar to John Resig's implementation.
+  // Underscore templating handles arbitrary delimiters, preserves whitespace,
+  // and correctly escapes quotes within interpolated code.
+  // NB: `oldSettings` only exists for backwards compatibility.
+  function template(text, settings, oldSettings) {
+    if (!settings && oldSettings) settings = oldSettings;
+    settings = defaults({}, settings, _$1.templateSettings);
+
+    // Combine delimiters into one regular expression via alternation.
+    var matcher = RegExp([
+      (settings.escape || noMatch).source,
+      (settings.interpolate || noMatch).source,
+      (settings.evaluate || noMatch).source
+    ].join('|') + '|$', 'g');
+
+    // Compile the template source, escaping string literals appropriately.
+    var index = 0;
+    var source = "__p+='";
+    text.replace(matcher, function(match, escape, interpolate, evaluate, offset) {
+      source += text.slice(index, offset).replace(escapeRegExp, escapeChar);
+      index = offset + match.length;
+
+      if (escape) {
+        source += "'+\n((__t=(" + escape + "))==null?'':_.escape(__t))+\n'";
+      } else if (interpolate) {
+        source += "'+\n((__t=(" + interpolate + "))==null?'':__t)+\n'";
+      } else if (evaluate) {
+        source += "';\n" + evaluate + "\n__p+='";
+      }
+
+      // Adobe VMs need the match returned to produce the correct offset.
+      return match;
+    });
+    source += "';\n";
+
+    var argument = settings.variable;
+    if (argument) {
+      // Insure against third-party code injection. (CVE-2021-23358)
+      if (!bareIdentifier.test(argument)) throw new Error(
+        'variable is not a bare identifier: ' + argument
+      );
+    } else {
+      // If a variable is not specified, place data values in local scope.
+      source = 'with(obj||{}){\n' + source + '}\n';
+      argument = 'obj';
+    }
+
+    source = "var __t,__p='',__j=Array.prototype.join," +
+      "print=function(){__p+=__j.call(arguments,'');};\n" +
+      source + 'return __p;\n';
+
+    var render;
+    try {
+      render = new Function(argument, '_', source);
+    } catch (e) {
+      e.source = source;
+      throw e;
+    }
+
+    var template = function(data) {
+      return render.call(this, data, _$1);
+    };
+
+    // Provide the compiled source as a convenience for precompilation.
+    template.source = 'function(' + argument + '){\n' + source + '}';
+
+    return template;
+  }
+
+  // Traverses the children of `obj` along `path`. If a child is a function, it
+  // is invoked with its parent as context. Returns the value of the final
+  // child, or `fallback` if any child is undefined.
+  function result(obj, path, fallback) {
+    path = toPath(path);
+    var length = path.length;
+    if (!length) {
+      return isFunction$1(fallback) ? fallback.call(obj) : fallback;
+    }
+    for (var i = 0; i < length; i++) {
+      var prop = obj == null ? void 0 : obj[path[i]];
+      if (prop === void 0) {
+        prop = fallback;
+        i = length; // Ensure we don't continue iterating.
+      }
+      obj = isFunction$1(prop) ? prop.call(obj) : prop;
+    }
+    return obj;
+  }
+
+  // Generate a unique integer id (unique within the entire client session).
+  // Useful for temporary DOM ids.
+  var idCounter = 0;
+  function uniqueId(prefix) {
+    var id = ++idCounter + '';
+    return prefix ? prefix + id : id;
+  }
+
+  // Start chaining a wrapped Underscore object.
+  function chain(obj) {
+    var instance = _$1(obj);
+    instance._chain = true;
+    return instance;
+  }
+
+  // Internal function to execute `sourceFunc` bound to `context` with optional
+  // `args`. Determines whether to execute a function as a constructor or as a
+  // normal function.
+  function executeBound(sourceFunc, boundFunc, context, callingContext, args) {
+    if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args);
+    var self = baseCreate(sourceFunc.prototype);
+    var result = sourceFunc.apply(self, args);
+    if (isObject(result)) return result;
+    return self;
+  }
+
+  // Partially apply a function by creating a version that has had some of its
+  // arguments pre-filled, without changing its dynamic `this` context. `_` acts
+  // as a placeholder by default, allowing any combination of arguments to be
+  // pre-filled. Set `_.partial.placeholder` for a custom placeholder argument.
+  var partial = restArguments(function(func, boundArgs) {
+    var placeholder = partial.placeholder;
+    var bound = function() {
+      var position = 0, length = boundArgs.length;
+      var args = Array(length);
+      for (var i = 0; i < length; i++) {
+        args[i] = boundArgs[i] === placeholder ? arguments[position++] : boundArgs[i];
+      }
+      while (position < arguments.length) args.push(arguments[position++]);
+      return executeBound(func, bound, this, this, args);
+    };
+    return bound;
+  });
+
+  partial.placeholder = _$1;
+
+  // Create a function bound to a given object (assigning `this`, and arguments,
+  // optionally).
+  var bind = restArguments(function(func, context, args) {
+    if (!isFunction$1(func)) throw new TypeError('Bind must be called on a function');
+    var bound = restArguments(function(callArgs) {
+      return executeBound(func, bound, context, this, args.concat(callArgs));
+    });
+    return bound;
+  });
+
+  // Internal helper for collection methods to determine whether a collection
+  // should be iterated as an array or as an object.
+  // Related: https://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength
+  // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094
+  var isArrayLike = createSizePropertyCheck(getLength);
+
+  // Internal implementation of a recursive `flatten` function.
+  function flatten$1(input, depth, strict, output) {
+    output = output || [];
+    if (!depth && depth !== 0) {
+      depth = Infinity;
+    } else if (depth <= 0) {
+      return output.concat(input);
+    }
+    var idx = output.length;
+    for (var i = 0, length = getLength(input); i < length; i++) {
+      var value = input[i];
+      if (isArrayLike(value) && (isArray(value) || isArguments$1(value))) {
+        // Flatten current level of array or arguments object.
+        if (depth > 1) {
+          flatten$1(value, depth - 1, strict, output);
+          idx = output.length;
+        } else {
+          var j = 0, len = value.length;
+          while (j < len) output[idx++] = value[j++];
+        }
+      } else if (!strict) {
+        output[idx++] = value;
+      }
+    }
+    return output;
+  }
+
+  // Bind a number of an object's methods to that object. Remaining arguments
+  // are the method names to be bound. Useful for ensuring that all callbacks
+  // defined on an object belong to it.
+  var bindAll = restArguments(function(obj, keys) {
+    keys = flatten$1(keys, false, false);
+    var index = keys.length;
+    if (index < 1) throw new Error('bindAll must be passed function names');
+    while (index--) {
+      var key = keys[index];
+      obj[key] = bind(obj[key], obj);
+    }
+    return obj;
+  });
+
+  // Memoize an expensive function by storing its results.
+  function memoize(func, hasher) {
+    var memoize = function(key) {
+      var cache = memoize.cache;
+      var address = '' + (hasher ? hasher.apply(this, arguments) : key);
+      if (!has$1(cache, address)) cache[address] = func.apply(this, arguments);
+      return cache[address];
+    };
+    memoize.cache = {};
+    return memoize;
+  }
+
+  // Delays a function for the given number of milliseconds, and then calls
+  // it with the arguments supplied.
+  var delay = restArguments(function(func, wait, args) {
+    return setTimeout(function() {
+      return func.apply(null, args);
+    }, wait);
+  });
+
+  // Defers a function, scheduling it to run after the current call stack has
+  // cleared.
+  var defer = partial(delay, _$1, 1);
+
+  // Returns a function, that, when invoked, will only be triggered at most once
+  // during a given window of time. Normally, the throttled function will run
+  // as much as it can, without ever going more than once per `wait` duration;
+  // but if you'd like to disable the execution on the leading edge, pass
+  // `{leading: false}`. To disable execution on the trailing edge, ditto.
+  function throttle(func, wait, options) {
+    var timeout, context, args, result;
+    var previous = 0;
+    if (!options) options = {};
+
+    var later = function() {
+      previous = options.leading === false ? 0 : now();
+      timeout = null;
+      result = func.apply(context, args);
+      if (!timeout) context = args = null;
+    };
+
+    var throttled = function() {
+      var _now = now();
+      if (!previous && options.leading === false) previous = _now;
+      var remaining = wait - (_now - previous);
+      context = this;
+      args = arguments;
+      if (remaining <= 0 || remaining > wait) {
+        if (timeout) {
+          clearTimeout(timeout);
+          timeout = null;
+        }
+        previous = _now;
+        result = func.apply(context, args);
+        if (!timeout) context = args = null;
+      } else if (!timeout && options.trailing !== false) {
+        timeout = setTimeout(later, remaining);
+      }
+      return result;
+    };
+
+    throttled.cancel = function() {
+      clearTimeout(timeout);
+      previous = 0;
+      timeout = context = args = null;
+    };
+
+    return throttled;
+  }
+
+  // When a sequence of calls of the returned function ends, the argument
+  // function is triggered. The end of a sequence is defined by the `wait`
+  // parameter. If `immediate` is passed, the argument function will be
+  // triggered at the beginning of the sequence instead of at the end.
+  function debounce(func, wait, immediate) {
+    var timeout, previous, args, result, context;
+
+    var later = function() {
+      var passed = now() - previous;
+      if (wait > passed) {
+        timeout = setTimeout(later, wait - passed);
+      } else {
+        timeout = null;
+        if (!immediate) result = func.apply(context, args);
+        // This check is needed because `func` can recursively invoke `debounced`.
+        if (!timeout) args = context = null;
+      }
+    };
+
+    var debounced = restArguments(function(_args) {
+      context = this;
+      args = _args;
+      previous = now();
+      if (!timeout) {
+        timeout = setTimeout(later, wait);
+        if (immediate) result = func.apply(context, args);
+      }
+      return result;
+    });
+
+    debounced.cancel = function() {
+      clearTimeout(timeout);
+      timeout = args = context = null;
+    };
+
+    return debounced;
+  }
+
+  // Returns the first function passed as an argument to the second,
+  // allowing you to adjust arguments, run code before and after, and
+  // conditionally execute the original function.
+  function wrap(func, wrapper) {
+    return partial(wrapper, func);
+  }
+
+  // Returns a negated version of the passed-in predicate.
+  function negate(predicate) {
+    return function() {
+      return !predicate.apply(this, arguments);
+    };
+  }
+
+  // Returns a function that is the composition of a list of functions, each
+  // consuming the return value of the function that follows.
+  function compose() {
+    var args = arguments;
+    var start = args.length - 1;
+    return function() {
+      var i = start;
+      var result = args[start].apply(this, arguments);
+      while (i--) result = args[i].call(this, result);
+      return result;
+    };
+  }
+
+  // Returns a function that will only be executed on and after the Nth call.
+  function after(times, func) {
+    return function() {
+      if (--times < 1) {
+        return func.apply(this, arguments);
+      }
+    };
+  }
+
+  // Returns a function that will only be executed up to (but not including) the
+  // Nth call.
+  function before(times, func) {
+    var memo;
+    return function() {
+      if (--times > 0) {
+        memo = func.apply(this, arguments);
+      }
+      if (times <= 1) func = null;
+      return memo;
+    };
+  }
+
+  // Returns a function that will be executed at most one time, no matter how
+  // often you call it. Useful for lazy initialization.
+  var once = partial(before, 2);
+
+  // Returns the first key on an object that passes a truth test.
+  function findKey(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = keys(obj), key;
+    for (var i = 0, length = _keys.length; i < length; i++) {
+      key = _keys[i];
+      if (predicate(obj[key], key, obj)) return key;
+    }
+  }
+
+  // Internal function to generate `_.findIndex` and `_.findLastIndex`.
+  function createPredicateIndexFinder(dir) {
+    return function(array, predicate, context) {
+      predicate = cb(predicate, context);
+      var length = getLength(array);
+      var index = dir > 0 ? 0 : length - 1;
+      for (; index >= 0 && index < length; index += dir) {
+        if (predicate(array[index], index, array)) return index;
+      }
+      return -1;
+    };
+  }
+
+  // Returns the first index on an array-like that passes a truth test.
+  var findIndex = createPredicateIndexFinder(1);
+
+  // Returns the last index on an array-like that passes a truth test.
+  var findLastIndex = createPredicateIndexFinder(-1);
+
+  // Use a comparator function to figure out the smallest index at which
+  // an object should be inserted so as to maintain order. Uses binary search.
+  function sortedIndex(array, obj, iteratee, context) {
+    iteratee = cb(iteratee, context, 1);
+    var value = iteratee(obj);
+    var low = 0, high = getLength(array);
+    while (low < high) {
+      var mid = Math.floor((low + high) / 2);
+      if (iteratee(array[mid]) < value) low = mid + 1; else high = mid;
+    }
+    return low;
+  }
+
+  // Internal function to generate the `_.indexOf` and `_.lastIndexOf` functions.
+  function createIndexFinder(dir, predicateFind, sortedIndex) {
+    return function(array, item, idx) {
+      var i = 0, length = getLength(array);
+      if (typeof idx == 'number') {
+        if (dir > 0) {
+          i = idx >= 0 ? idx : Math.max(idx + length, i);
+        } else {
+          length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1;
+        }
+      } else if (sortedIndex && idx && length) {
+        idx = sortedIndex(array, item);
+        return array[idx] === item ? idx : -1;
+      }
+      if (item !== item) {
+        idx = predicateFind(slice.call(array, i, length), isNaN$1);
+        return idx >= 0 ? idx + i : -1;
+      }
+      for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) {
+        if (array[idx] === item) return idx;
+      }
+      return -1;
+    };
+  }
+
+  // Return the position of the first occurrence of an item in an array,
+  // or -1 if the item is not included in the array.
+  // If the array is large and already in sort order, pass `true`
+  // for **isSorted** to use binary search.
+  var indexOf = createIndexFinder(1, findIndex, sortedIndex);
+
+  // Return the position of the last occurrence of an item in an array,
+  // or -1 if the item is not included in the array.
+  var lastIndexOf = createIndexFinder(-1, findLastIndex);
+
+  // Return the first value which passes a truth test.
+  function find(obj, predicate, context) {
+    var keyFinder = isArrayLike(obj) ? findIndex : findKey;
+    var key = keyFinder(obj, predicate, context);
+    if (key !== void 0 && key !== -1) return obj[key];
+  }
+
+  // Convenience version of a common use case of `_.find`: getting the first
+  // object containing specific `key:value` pairs.
+  function findWhere(obj, attrs) {
+    return find(obj, matcher(attrs));
+  }
+
+  // The cornerstone for collection functions, an `each`
+  // implementation, aka `forEach`.
+  // Handles raw objects in addition to array-likes. Treats all
+  // sparse array-likes as if they were dense.
+  function each(obj, iteratee, context) {
+    iteratee = optimizeCb(iteratee, context);
+    var i, length;
+    if (isArrayLike(obj)) {
+      for (i = 0, length = obj.length; i < length; i++) {
+        iteratee(obj[i], i, obj);
+      }
+    } else {
+      var _keys = keys(obj);
+      for (i = 0, length = _keys.length; i < length; i++) {
+        iteratee(obj[_keys[i]], _keys[i], obj);
+      }
+    }
+    return obj;
+  }
+
+  // Return the results of applying the iteratee to each element.
+  function map(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length,
+        results = Array(length);
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      results[index] = iteratee(obj[currentKey], currentKey, obj);
+    }
+    return results;
+  }
+
+  // Internal helper to create a reducing function, iterating left or right.
+  function createReduce(dir) {
+    // Wrap code that reassigns argument variables in a separate function than
+    // the one that accesses `arguments.length` to avoid a perf hit. (#1991)
+    var reducer = function(obj, iteratee, memo, initial) {
+      var _keys = !isArrayLike(obj) && keys(obj),
+          length = (_keys || obj).length,
+          index = dir > 0 ? 0 : length - 1;
+      if (!initial) {
+        memo = obj[_keys ? _keys[index] : index];
+        index += dir;
+      }
+      for (; index >= 0 && index < length; index += dir) {
+        var currentKey = _keys ? _keys[index] : index;
+        memo = iteratee(memo, obj[currentKey], currentKey, obj);
+      }
+      return memo;
+    };
+
+    return function(obj, iteratee, memo, context) {
+      var initial = arguments.length >= 3;
+      return reducer(obj, optimizeCb(iteratee, context, 4), memo, initial);
+    };
+  }
+
+  // **Reduce** builds up a single result from a list of values, aka `inject`,
+  // or `foldl`.
+  var reduce = createReduce(1);
+
+  // The right-associative version of reduce, also known as `foldr`.
+  var reduceRight = createReduce(-1);
+
+  // Return all the elements that pass a truth test.
+  function filter(obj, predicate, context) {
+    var results = [];
+    predicate = cb(predicate, context);
+    each(obj, function(value, index, list) {
+      if (predicate(value, index, list)) results.push(value);
+    });
+    return results;
+  }
+
+  // Return all the elements for which a truth test fails.
+  function reject(obj, predicate, context) {
+    return filter(obj, negate(cb(predicate)), context);
+  }
+
+  // Determine whether all of the elements pass a truth test.
+  function every(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      if (!predicate(obj[currentKey], currentKey, obj)) return false;
+    }
+    return true;
+  }
+
+  // Determine if at least one element in the object passes a truth test.
+  function some(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      if (predicate(obj[currentKey], currentKey, obj)) return true;
+    }
+    return false;
+  }
+
+  // Determine if the array or object contains a given item (using `===`).
+  function contains(obj, item, fromIndex, guard) {
+    if (!isArrayLike(obj)) obj = values(obj);
+    if (typeof fromIndex != 'number' || guard) fromIndex = 0;
+    return indexOf(obj, item, fromIndex) >= 0;
+  }
+
+  // Invoke a method (with arguments) on every item in a collection.
+  var invoke = restArguments(function(obj, path, args) {
+    var contextPath, func;
+    if (isFunction$1(path)) {
+      func = path;
+    } else {
+      path = toPath(path);
+      contextPath = path.slice(0, -1);
+      path = path[path.length - 1];
+    }
+    return map(obj, function(context) {
+      var method = func;
+      if (!method) {
+        if (contextPath && contextPath.length) {
+          context = deepGet(context, contextPath);
+        }
+        if (context == null) return void 0;
+        method = context[path];
+      }
+      return method == null ? method : method.apply(context, args);
+    });
+  });
+
+  // Convenience version of a common use case of `_.map`: fetching a property.
+  function pluck(obj, key) {
+    return map(obj, property(key));
+  }
+
+  // Convenience version of a common use case of `_.filter`: selecting only
+  // objects containing specific `key:value` pairs.
+  function where(obj, attrs) {
+    return filter(obj, matcher(attrs));
+  }
+
+  // Return the maximum element (or element-based computation).
+  function max(obj, iteratee, context) {
+    var result = -Infinity, lastComputed = -Infinity,
+        value, computed;
+    if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+      obj = isArrayLike(obj) ? obj : values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value != null && value > result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      each(obj, function(v, index, list) {
+        computed = iteratee(v, index, list);
+        if (computed > lastComputed || computed === -Infinity && result === -Infinity) {
+          result = v;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  }
+
+  // Return the minimum element (or element-based computation).
+  function min(obj, iteratee, context) {
+    var result = Infinity, lastComputed = Infinity,
+        value, computed;
+    if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+      obj = isArrayLike(obj) ? obj : values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value != null && value < result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      each(obj, function(v, index, list) {
+        computed = iteratee(v, index, list);
+        if (computed < lastComputed || computed === Infinity && result === Infinity) {
+          result = v;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  }
+
+  // Sample **n** random values from a collection using the modern version of the
+  // [Fisher-Yates shuffle](https://en.wikipedia.org/wiki/Fisher–Yates_shuffle).
+  // If **n** is not specified, returns a single random element.
+  // The internal `guard` argument allows it to work with `_.map`.
+  function sample(obj, n, guard) {
+    if (n == null || guard) {
+      if (!isArrayLike(obj)) obj = values(obj);
+      return obj[random(obj.length - 1)];
+    }
+    var sample = isArrayLike(obj) ? clone(obj) : values(obj);
+    var length = getLength(sample);
+    n = Math.max(Math.min(n, length), 0);
+    var last = length - 1;
+    for (var index = 0; index < n; index++) {
+      var rand = random(index, last);
+      var temp = sample[index];
+      sample[index] = sample[rand];
+      sample[rand] = temp;
+    }
+    return sample.slice(0, n);
+  }
+
+  // Shuffle a collection.
+  function shuffle(obj) {
+    return sample(obj, Infinity);
+  }
+
+  // Sort the object's values by a criterion produced by an iteratee.
+  function sortBy(obj, iteratee, context) {
+    var index = 0;
+    iteratee = cb(iteratee, context);
+    return pluck(map(obj, function(value, key, list) {
+      return {
+        value: value,
+        index: index++,
+        criteria: iteratee(value, key, list)
+      };
+    }).sort(function(left, right) {
+      var a = left.criteria;
+      var b = right.criteria;
+      if (a !== b) {
+        if (a > b || a === void 0) return 1;
+        if (a < b || b === void 0) return -1;
+      }
+      return left.index - right.index;
+    }), 'value');
+  }
+
+  // An internal function used for aggregate "group by" operations.
+  function group(behavior, partition) {
+    return function(obj, iteratee, context) {
+      var result = partition ? [[], []] : {};
+      iteratee = cb(iteratee, context);
+      each(obj, function(value, index) {
+        var key = iteratee(value, index, obj);
+        behavior(result, value, key);
+      });
+      return result;
+    };
+  }
+
+  // Groups the object's values by a criterion. Pass either a string attribute
+  // to group by, or a function that returns the criterion.
+  var groupBy = group(function(result, value, key) {
+    if (has$1(result, key)) result[key].push(value); else result[key] = [value];
+  });
+
+  // Indexes the object's values by a criterion, similar to `_.groupBy`, but for
+  // when you know that your index values will be unique.
+  var indexBy = group(function(result, value, key) {
+    result[key] = value;
+  });
+
+  // Counts instances of an object that group by a certain criterion. Pass
+  // either a string attribute to count by, or a function that returns the
+  // criterion.
+  var countBy = group(function(result, value, key) {
+    if (has$1(result, key)) result[key]++; else result[key] = 1;
+  });
+
+  // Split a collection into two arrays: one whose elements all pass the given
+  // truth test, and one whose elements all do not pass the truth test.
+  var partition = group(function(result, value, pass) {
+    result[pass ? 0 : 1].push(value);
+  }, true);
+
+  // Safely create a real, live array from anything iterable.
+  var reStrSymbol = /[^\ud800-\udfff]|[\ud800-\udbff][\udc00-\udfff]|[\ud800-\udfff]/g;
+  function toArray(obj) {
+    if (!obj) return [];
+    if (isArray(obj)) return slice.call(obj);
+    if (isString(obj)) {
+      // Keep surrogate pair characters together.
+      return obj.match(reStrSymbol);
+    }
+    if (isArrayLike(obj)) return map(obj, identity);
+    return values(obj);
+  }
+
+  // Return the number of elements in a collection.
+  function size(obj) {
+    if (obj == null) return 0;
+    return isArrayLike(obj) ? obj.length : keys(obj).length;
+  }
+
+  // Internal `_.pick` helper function to determine whether `key` is an enumerable
+  // property name of `obj`.
+  function keyInObj(value, key, obj) {
+    return key in obj;
+  }
+
+  // Return a copy of the object only containing the allowed properties.
+  var pick = restArguments(function(obj, keys) {
+    var result = {}, iteratee = keys[0];
+    if (obj == null) return result;
+    if (isFunction$1(iteratee)) {
+      if (keys.length > 1) iteratee = optimizeCb(iteratee, keys[1]);
+      keys = allKeys(obj);
+    } else {
+      iteratee = keyInObj;
+      keys = flatten$1(keys, false, false);
+      obj = Object(obj);
+    }
+    for (var i = 0, length = keys.length; i < length; i++) {
+      var key = keys[i];
+      var value = obj[key];
+      if (iteratee(value, key, obj)) result[key] = value;
+    }
+    return result;
+  });
+
+  // Return a copy of the object without the disallowed properties.
+  var omit = restArguments(function(obj, keys) {
+    var iteratee = keys[0], context;
+    if (isFunction$1(iteratee)) {
+      iteratee = negate(iteratee);
+      if (keys.length > 1) context = keys[1];
+    } else {
+      keys = map(flatten$1(keys, false, false), String);
+      iteratee = function(value, key) {
+        return !contains(keys, key);
+      };
+    }
+    return pick(obj, iteratee, context);
+  });
+
+  // Returns everything but the last entry of the array. Especially useful on
+  // the arguments object. Passing **n** will return all the values in
+  // the array, excluding the last N.
+  function initial(array, n, guard) {
+    return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n)));
+  }
+
+  // Get the first element of an array. Passing **n** will return the first N
+  // values in the array. The **guard** check allows it to work with `_.map`.
+  function first(array, n, guard) {
+    if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+    if (n == null || guard) return array[0];
+    return initial(array, array.length - n);
+  }
+
+  // Returns everything but the first entry of the `array`. Especially useful on
+  // the `arguments` object. Passing an **n** will return the rest N values in the
+  // `array`.
+  function rest(array, n, guard) {
+    return slice.call(array, n == null || guard ? 1 : n);
+  }
+
+  // Get the last element of an array. Passing **n** will return the last N
+  // values in the array.
+  function last(array, n, guard) {
+    if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+    if (n == null || guard) return array[array.length - 1];
+    return rest(array, Math.max(0, array.length - n));
+  }
+
+  // Trim out all falsy values from an array.
+  function compact(array) {
+    return filter(array, Boolean);
+  }
+
+  // Flatten out an array, either recursively (by default), or up to `depth`.
+  // Passing `true` or `false` as `depth` means `1` or `Infinity`, respectively.
+  function flatten(array, depth) {
+    return flatten$1(array, depth, false);
+  }
+
+  // Take the difference between one array and a number of other arrays.
+  // Only the elements present in just the first array will remain.
+  var difference = restArguments(function(array, rest) {
+    rest = flatten$1(rest, true, true);
+    return filter(array, function(value){
+      return !contains(rest, value);
+    });
+  });
+
+  // Return a version of the array that does not contain the specified value(s).
+  var without = restArguments(function(array, otherArrays) {
+    return difference(array, otherArrays);
+  });
+
+  // Produce a duplicate-free version of the array. If the array has already
+  // been sorted, you have the option of using a faster algorithm.
+  // The faster algorithm will not work with an iteratee if the iteratee
+  // is not a one-to-one function, so providing an iteratee will disable
+  // the faster algorithm.
+  function uniq(array, isSorted, iteratee, context) {
+    if (!isBoolean(isSorted)) {
+      context = iteratee;
+      iteratee = isSorted;
+      isSorted = false;
+    }
+    if (iteratee != null) iteratee = cb(iteratee, context);
+    var result = [];
+    var seen = [];
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var value = array[i],
+          computed = iteratee ? iteratee(value, i, array) : value;
+      if (isSorted && !iteratee) {
+        if (!i || seen !== computed) result.push(value);
+        seen = computed;
+      } else if (iteratee) {
+        if (!contains(seen, computed)) {
+          seen.push(computed);
+          result.push(value);
+        }
+      } else if (!contains(result, value)) {
+        result.push(value);
+      }
+    }
+    return result;
+  }
+
+  // Produce an array that contains the union: each distinct element from all of
+  // the passed-in arrays.
+  var union = restArguments(function(arrays) {
+    return uniq(flatten$1(arrays, true, true));
+  });
+
+  // Produce an array that contains every item shared between all the
+  // passed-in arrays.
+  function intersection(array) {
+    var result = [];
+    var argsLength = arguments.length;
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var item = array[i];
+      if (contains(result, item)) continue;
+      var j;
+      for (j = 1; j < argsLength; j++) {
+        if (!contains(arguments[j], item)) break;
+      }
+      if (j === argsLength) result.push(item);
+    }
+    return result;
+  }
+
+  // Complement of zip. Unzip accepts an array of arrays and groups
+  // each array's elements on shared indices.
+  function unzip(array) {
+    var length = array && max(array, getLength).length || 0;
+    var result = Array(length);
+
+    for (var index = 0; index < length; index++) {
+      result[index] = pluck(array, index);
+    }
+    return result;
+  }
+
+  // Zip together multiple lists into a single array -- elements that share
+  // an index go together.
+  var zip = restArguments(unzip);
+
+  // Converts lists into objects. Pass either a single array of `[key, value]`
+  // pairs, or two parallel arrays of the same length -- one of keys, and one of
+  // the corresponding values. Passing by pairs is the reverse of `_.pairs`.
+  function object(list, values) {
+    var result = {};
+    for (var i = 0, length = getLength(list); i < length; i++) {
+      if (values) {
+        result[list[i]] = values[i];
+      } else {
+        result[list[i][0]] = list[i][1];
+      }
+    }
+    return result;
+  }
+
+  // Generate an integer Array containing an arithmetic progression. A port of
+  // the native Python `range()` function. See
+  // [the Python documentation](https://docs.python.org/library/functions.html#range).
+  function range(start, stop, step) {
+    if (stop == null) {
+      stop = start || 0;
+      start = 0;
+    }
+    if (!step) {
+      step = stop < start ? -1 : 1;
+    }
+
+    var length = Math.max(Math.ceil((stop - start) / step), 0);
+    var range = Array(length);
+
+    for (var idx = 0; idx < length; idx++, start += step) {
+      range[idx] = start;
+    }
+
+    return range;
+  }
+
+  // Chunk a single array into multiple arrays, each containing `count` or fewer
+  // items.
+  function chunk(array, count) {
+    if (count == null || count < 1) return [];
+    var result = [];
+    var i = 0, length = array.length;
+    while (i < length) {
+      result.push(slice.call(array, i, i += count));
+    }
+    return result;
+  }
+
+  // Helper function to continue chaining intermediate results.
+  function chainResult(instance, obj) {
+    return instance._chain ? _$1(obj).chain() : obj;
+  }
+
+  // Add your own custom functions to the Underscore object.
+  function mixin(obj) {
+    each(functions(obj), function(name) {
+      var func = _$1[name] = obj[name];
+      _$1.prototype[name] = function() {
+        var args = [this._wrapped];
+        push.apply(args, arguments);
+        return chainResult(this, func.apply(_$1, args));
+      };
+    });
+    return _$1;
+  }
+
+  // Add all mutator `Array` functions to the wrapper.
+  each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
+    var method = ArrayProto[name];
+    _$1.prototype[name] = function() {
+      var obj = this._wrapped;
+      if (obj != null) {
+        method.apply(obj, arguments);
+        if ((name === 'shift' || name === 'splice') && obj.length === 0) {
+          delete obj[0];
+        }
+      }
+      return chainResult(this, obj);
+    };
+  });
+
+  // Add all accessor `Array` functions to the wrapper.
+  each(['concat', 'join', 'slice'], function(name) {
+    var method = ArrayProto[name];
+    _$1.prototype[name] = function() {
+      var obj = this._wrapped;
+      if (obj != null) obj = method.apply(obj, arguments);
+      return chainResult(this, obj);
+    };
+  });
+
+  // Named Exports
+
+  var allExports = {
+    __proto__: null,
+    VERSION: VERSION,
+    restArguments: restArguments,
+    isObject: isObject,
+    isNull: isNull,
+    isUndefined: isUndefined,
+    isBoolean: isBoolean,
+    isElement: isElement,
+    isString: isString,
+    isNumber: isNumber,
+    isDate: isDate,
+    isRegExp: isRegExp,
+    isError: isError,
+    isSymbol: isSymbol,
+    isArrayBuffer: isArrayBuffer,
+    isDataView: isDataView$1,
+    isArray: isArray,
+    isFunction: isFunction$1,
+    isArguments: isArguments$1,
+    isFinite: isFinite$1,
+    isNaN: isNaN$1,
+    isTypedArray: isTypedArray$1,
+    isEmpty: isEmpty,
+    isMatch: isMatch,
+    isEqual: isEqual,
+    isMap: isMap,
+    isWeakMap: isWeakMap,
+    isSet: isSet,
+    isWeakSet: isWeakSet,
+    keys: keys,
+    allKeys: allKeys,
+    values: values,
+    pairs: pairs,
+    invert: invert,
+    functions: functions,
+    methods: functions,
+    extend: extend,
+    extendOwn: extendOwn,
+    assign: extendOwn,
+    defaults: defaults,
+    create: create,
+    clone: clone,
+    tap: tap,
+    get: get,
+    has: has,
+    mapObject: mapObject,
+    identity: identity,
+    constant: constant,
+    noop: noop,
+    toPath: toPath$1,
+    property: property,
+    propertyOf: propertyOf,
+    matcher: matcher,
+    matches: matcher,
+    times: times,
+    random: random,
+    now: now,
+    escape: _escape,
+    unescape: _unescape,
+    templateSettings: templateSettings,
+    template: template,
+    result: result,
+    uniqueId: uniqueId,
+    chain: chain,
+    iteratee: iteratee,
+    partial: partial,
+    bind: bind,
+    bindAll: bindAll,
+    memoize: memoize,
+    delay: delay,
+    defer: defer,
+    throttle: throttle,
+    debounce: debounce,
+    wrap: wrap,
+    negate: negate,
+    compose: compose,
+    after: after,
+    before: before,
+    once: once,
+    findKey: findKey,
+    findIndex: findIndex,
+    findLastIndex: findLastIndex,
+    sortedIndex: sortedIndex,
+    indexOf: indexOf,
+    lastIndexOf: lastIndexOf,
+    find: find,
+    detect: find,
+    findWhere: findWhere,
+    each: each,
+    forEach: each,
+    map: map,
+    collect: map,
+    reduce: reduce,
+    foldl: reduce,
+    inject: reduce,
+    reduceRight: reduceRight,
+    foldr: reduceRight,
+    filter: filter,
+    select: filter,
+    reject: reject,
+    every: every,
+    all: every,
+    some: some,
+    any: some,
+    contains: contains,
+    includes: contains,
+    include: contains,
+    invoke: invoke,
+    pluck: pluck,
+    where: where,
+    max: max,
+    min: min,
+    shuffle: shuffle,
+    sample: sample,
+    sortBy: sortBy,
+    groupBy: groupBy,
+    indexBy: indexBy,
+    countBy: countBy,
+    partition: partition,
+    toArray: toArray,
+    size: size,
+    pick: pick,
+    omit: omit,
+    first: first,
+    head: first,
+    take: first,
+    initial: initial,
+    last: last,
+    rest: rest,
+    tail: rest,
+    drop: rest,
+    compact: compact,
+    flatten: flatten,
+    without: without,
+    uniq: uniq,
+    unique: uniq,
+    union: union,
+    intersection: intersection,
+    difference: difference,
+    unzip: unzip,
+    transpose: unzip,
+    zip: zip,
+    object: object,
+    range: range,
+    chunk: chunk,
+    mixin: mixin,
+    'default': _$1
+  };
+
+  // Default Export
+
+  // Add all of the Underscore functions to the wrapper object.
+  var _ = mixin(allExports);
+  // Legacy Node.js API.
+  _._ = _;
+
+  return _;
+
+})));
+//# sourceMappingURL=underscore-umd.js.map
diff --git a/docs/build/html/_static/underscore-1.3.1.js b/docs/build/html/_static/underscore-1.3.1.js
deleted file mode 100644
index 208d4cd..0000000
--- a/docs/build/html/_static/underscore-1.3.1.js
+++ /dev/null
@@ -1,999 +0,0 @@
-//     Underscore.js 1.3.1
-//     (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc.
-//     Underscore is freely distributable under the MIT license.
-//     Portions of Underscore are inspired or borrowed from Prototype,
-//     Oliver Steele's Functional, and John Resig's Micro-Templating.
-//     For all details and documentation:
-//     http://documentcloud.github.com/underscore
-
-(function() {
-
-  // Baseline setup
-  // --------------
-
-  // Establish the root object, `window` in the browser, or `global` on the server.
-  var root = this;
-
-  // Save the previous value of the `_` variable.
-  var previousUnderscore = root._;
-
-  // Establish the object that gets returned to break out of a loop iteration.
-  var breaker = {};
-
-  // Save bytes in the minified (but not gzipped) version:
-  var ArrayProto = Array.prototype, ObjProto = Object.prototype, FuncProto = Function.prototype;
-
-  // Create quick reference variables for speed access to core prototypes.
-  var slice            = ArrayProto.slice,
-      unshift          = ArrayProto.unshift,
-      toString         = ObjProto.toString,
-      hasOwnProperty   = ObjProto.hasOwnProperty;
-
-  // All **ECMAScript 5** native function implementations that we hope to use
-  // are declared here.
-  var
-    nativeForEach      = ArrayProto.forEach,
-    nativeMap          = ArrayProto.map,
-    nativeReduce       = ArrayProto.reduce,
-    nativeReduceRight  = ArrayProto.reduceRight,
-    nativeFilter       = ArrayProto.filter,
-    nativeEvery        = ArrayProto.every,
-    nativeSome         = ArrayProto.some,
-    nativeIndexOf      = ArrayProto.indexOf,
-    nativeLastIndexOf  = ArrayProto.lastIndexOf,
-    nativeIsArray      = Array.isArray,
-    nativeKeys         = Object.keys,
-    nativeBind         = FuncProto.bind;
-
-  // Create a safe reference to the Underscore object for use below.
-  var _ = function(obj) { return new wrapper(obj); };
-
-  // Export the Underscore object for **Node.js**, with
-  // backwards-compatibility for the old `require()` API. If we're in
-  // the browser, add `_` as a global object via a string identifier,
-  // for Closure Compiler "advanced" mode.
-  if (typeof exports !== 'undefined') {
-    if (typeof module !== 'undefined' && module.exports) {
-      exports = module.exports = _;
-    }
-    exports._ = _;
-  } else {
-    root['_'] = _;
-  }
-
-  // Current version.
-  _.VERSION = '1.3.1';
-
-  // Collection Functions
-  // --------------------
-
-  // The cornerstone, an `each` implementation, aka `forEach`.
-  // Handles objects with the built-in `forEach`, arrays, and raw objects.
-  // Delegates to **ECMAScript 5**'s native `forEach` if available.
-  var each = _.each = _.forEach = function(obj, iterator, context) {
-    if (obj == null) return;
-    if (nativeForEach && obj.forEach === nativeForEach) {
-      obj.forEach(iterator, context);
-    } else if (obj.length === +obj.length) {
-      for (var i = 0, l = obj.length; i < l; i++) {
-        if (i in obj && iterator.call(context, obj[i], i, obj) === breaker) return;
-      }
-    } else {
-      for (var key in obj) {
-        if (_.has(obj, key)) {
-          if (iterator.call(context, obj[key], key, obj) === breaker) return;
-        }
-      }
-    }
-  };
-
-  // Return the results of applying the iterator to each element.
-  // Delegates to **ECMAScript 5**'s native `map` if available.
-  _.map = _.collect = function(obj, iterator, context) {
-    var results = [];
-    if (obj == null) return results;
-    if (nativeMap && obj.map === nativeMap) return obj.map(iterator, context);
-    each(obj, function(value, index, list) {
-      results[results.length] = iterator.call(context, value, index, list);
-    });
-    if (obj.length === +obj.length) results.length = obj.length;
-    return results;
-  };
-
-  // **Reduce** builds up a single result from a list of values, aka `inject`,
-  // or `foldl`. Delegates to **ECMAScript 5**'s native `reduce` if available.
-  _.reduce = _.foldl = _.inject = function(obj, iterator, memo, context) {
-    var initial = arguments.length > 2;
-    if (obj == null) obj = [];
-    if (nativeReduce && obj.reduce === nativeReduce) {
-      if (context) iterator = _.bind(iterator, context);
-      return initial ? obj.reduce(iterator, memo) : obj.reduce(iterator);
-    }
-    each(obj, function(value, index, list) {
-      if (!initial) {
-        memo = value;
-        initial = true;
-      } else {
-        memo = iterator.call(context, memo, value, index, list);
-      }
-    });
-    if (!initial) throw new TypeError('Reduce of empty array with no initial value');
-    return memo;
-  };
-
-  // The right-associative version of reduce, also known as `foldr`.
-  // Delegates to **ECMAScript 5**'s native `reduceRight` if available.
-  _.reduceRight = _.foldr = function(obj, iterator, memo, context) {
-    var initial = arguments.length > 2;
-    if (obj == null) obj = [];
-    if (nativeReduceRight && obj.reduceRight === nativeReduceRight) {
-      if (context) iterator = _.bind(iterator, context);
-      return initial ? obj.reduceRight(iterator, memo) : obj.reduceRight(iterator);
-    }
-    var reversed = _.toArray(obj).reverse();
-    if (context && !initial) iterator = _.bind(iterator, context);
-    return initial ? _.reduce(reversed, iterator, memo, context) : _.reduce(reversed, iterator);
-  };
-
-  // Return the first value which passes a truth test. Aliased as `detect`.
-  _.find = _.detect = function(obj, iterator, context) {
-    var result;
-    any(obj, function(value, index, list) {
-      if (iterator.call(context, value, index, list)) {
-        result = value;
-        return true;
-      }
-    });
-    return result;
-  };
-
-  // Return all the elements that pass a truth test.
-  // Delegates to **ECMAScript 5**'s native `filter` if available.
-  // Aliased as `select`.
-  _.filter = _.select = function(obj, iterator, context) {
-    var results = [];
-    if (obj == null) return results;
-    if (nativeFilter && obj.filter === nativeFilter) return obj.filter(iterator, context);
-    each(obj, function(value, index, list) {
-      if (iterator.call(context, value, index, list)) results[results.length] = value;
-    });
-    return results;
-  };
-
-  // Return all the elements for which a truth test fails.
-  _.reject = function(obj, iterator, context) {
-    var results = [];
-    if (obj == null) return results;
-    each(obj, function(value, index, list) {
-      if (!iterator.call(context, value, index, list)) results[results.length] = value;
-    });
-    return results;
-  };
-
-  // Determine whether all of the elements match a truth test.
-  // Delegates to **ECMAScript 5**'s native `every` if available.
-  // Aliased as `all`.
-  _.every = _.all = function(obj, iterator, context) {
-    var result = true;
-    if (obj == null) return result;
-    if (nativeEvery && obj.every === nativeEvery) return obj.every(iterator, context);
-    each(obj, function(value, index, list) {
-      if (!(result = result && iterator.call(context, value, index, list))) return breaker;
-    });
-    return result;
-  };
-
-  // Determine if at least one element in the object matches a truth test.
-  // Delegates to **ECMAScript 5**'s native `some` if available.
-  // Aliased as `any`.
-  var any = _.some = _.any = function(obj, iterator, context) {
-    iterator || (iterator = _.identity);
-    var result = false;
-    if (obj == null) return result;
-    if (nativeSome && obj.some === nativeSome) return obj.some(iterator, context);
-    each(obj, function(value, index, list) {
-      if (result || (result = iterator.call(context, value, index, list))) return breaker;
-    });
-    return !!result;
-  };
-
-  // Determine if a given value is included in the array or object using `===`.
-  // Aliased as `contains`.
-  _.include = _.contains = function(obj, target) {
-    var found = false;
-    if (obj == null) return found;
-    if (nativeIndexOf && obj.indexOf === nativeIndexOf) return obj.indexOf(target) != -1;
-    found = any(obj, function(value) {
-      return value === target;
-    });
-    return found;
-  };
-
-  // Invoke a method (with arguments) on every item in a collection.
-  _.invoke = function(obj, method) {
-    var args = slice.call(arguments, 2);
-    return _.map(obj, function(value) {
-      return (_.isFunction(method) ? method || value : value[method]).apply(value, args);
-    });
-  };
-
-  // Convenience version of a common use case of `map`: fetching a property.
-  _.pluck = function(obj, key) {
-    return _.map(obj, function(value){ return value[key]; });
-  };
-
-  // Return the maximum element or (element-based computation).
-  _.max = function(obj, iterator, context) {
-    if (!iterator && _.isArray(obj)) return Math.max.apply(Math, obj);
-    if (!iterator && _.isEmpty(obj)) return -Infinity;
-    var result = {computed : -Infinity};
-    each(obj, function(value, index, list) {
-      var computed = iterator ? iterator.call(context, value, index, list) : value;
-      computed >= result.computed && (result = {value : value, computed : computed});
-    });
-    return result.value;
-  };
-
-  // Return the minimum element (or element-based computation).
-  _.min = function(obj, iterator, context) {
-    if (!iterator && _.isArray(obj)) return Math.min.apply(Math, obj);
-    if (!iterator && _.isEmpty(obj)) return Infinity;
-    var result = {computed : Infinity};
-    each(obj, function(value, index, list) {
-      var computed = iterator ? iterator.call(context, value, index, list) : value;
-      computed < result.computed && (result = {value : value, computed : computed});
-    });
-    return result.value;
-  };
-
-  // Shuffle an array.
-  _.shuffle = function(obj) {
-    var shuffled = [], rand;
-    each(obj, function(value, index, list) {
-      if (index == 0) {
-        shuffled[0] = value;
-      } else {
-        rand = Math.floor(Math.random() * (index + 1));
-        shuffled[index] = shuffled[rand];
-        shuffled[rand] = value;
-      }
-    });
-    return shuffled;
-  };
-
-  // Sort the object's values by a criterion produced by an iterator.
-  _.sortBy = function(obj, iterator, context) {
-    return _.pluck(_.map(obj, function(value, index, list) {
-      return {
-        value : value,
-        criteria : iterator.call(context, value, index, list)
-      };
-    }).sort(function(left, right) {
-      var a = left.criteria, b = right.criteria;
-      return a < b ? -1 : a > b ? 1 : 0;
-    }), 'value');
-  };
-
-  // Groups the object's values by a criterion. Pass either a string attribute
-  // to group by, or a function that returns the criterion.
-  _.groupBy = function(obj, val) {
-    var result = {};
-    var iterator = _.isFunction(val) ? val : function(obj) { return obj[val]; };
-    each(obj, function(value, index) {
-      var key = iterator(value, index);
-      (result[key] || (result[key] = [])).push(value);
-    });
-    return result;
-  };
-
-  // Use a comparator function to figure out at what index an object should
-  // be inserted so as to maintain order. Uses binary search.
-  _.sortedIndex = function(array, obj, iterator) {
-    iterator || (iterator = _.identity);
-    var low = 0, high = array.length;
-    while (low < high) {
-      var mid = (low + high) >> 1;
-      iterator(array[mid]) < iterator(obj) ? low = mid + 1 : high = mid;
-    }
-    return low;
-  };
-
-  // Safely convert anything iterable into a real, live array.
-  _.toArray = function(iterable) {
-    if (!iterable)                return [];
-    if (iterable.toArray)         return iterable.toArray();
-    if (_.isArray(iterable))      return slice.call(iterable);
-    if (_.isArguments(iterable))  return slice.call(iterable);
-    return _.values(iterable);
-  };
-
-  // Return the number of elements in an object.
-  _.size = function(obj) {
-    return _.toArray(obj).length;
-  };
-
-  // Array Functions
-  // ---------------
-
-  // Get the first element of an array. Passing **n** will return the first N
-  // values in the array. Aliased as `head`. The **guard** check allows it to work
-  // with `_.map`.
-  _.first = _.head = function(array, n, guard) {
-    return (n != null) && !guard ? slice.call(array, 0, n) : array[0];
-  };
-
-  // Returns everything but the last entry of the array. Especcialy useful on
-  // the arguments object. Passing **n** will return all the values in
-  // the array, excluding the last N. The **guard** check allows it to work with
-  // `_.map`.
-  _.initial = function(array, n, guard) {
-    return slice.call(array, 0, array.length - ((n == null) || guard ? 1 : n));
-  };
-
-  // Get the last element of an array. Passing **n** will return the last N
-  // values in the array. The **guard** check allows it to work with `_.map`.
-  _.last = function(array, n, guard) {
-    if ((n != null) && !guard) {
-      return slice.call(array, Math.max(array.length - n, 0));
-    } else {
-      return array[array.length - 1];
-    }
-  };
-
-  // Returns everything but the first entry of the array. Aliased as `tail`.
-  // Especially useful on the arguments object. Passing an **index** will return
-  // the rest of the values in the array from that index onward. The **guard**
-  // check allows it to work with `_.map`.
-  _.rest = _.tail = function(array, index, guard) {
-    return slice.call(array, (index == null) || guard ? 1 : index);
-  };
-
-  // Trim out all falsy values from an array.
-  _.compact = function(array) {
-    return _.filter(array, function(value){ return !!value; });
-  };
-
-  // Return a completely flattened version of an array.
-  _.flatten = function(array, shallow) {
-    return _.reduce(array, function(memo, value) {
-      if (_.isArray(value)) return memo.concat(shallow ? value : _.flatten(value));
-      memo[memo.length] = value;
-      return memo;
-    }, []);
-  };
-
-  // Return a version of the array that does not contain the specified value(s).
-  _.without = function(array) {
-    return _.difference(array, slice.call(arguments, 1));
-  };
-
-  // Produce a duplicate-free version of the array. If the array has already
-  // been sorted, you have the option of using a faster algorithm.
-  // Aliased as `unique`.
-  _.uniq = _.unique = function(array, isSorted, iterator) {
-    var initial = iterator ? _.map(array, iterator) : array;
-    var result = [];
-    _.reduce(initial, function(memo, el, i) {
-      if (0 == i || (isSorted === true ? _.last(memo) != el : !_.include(memo, el))) {
-        memo[memo.length] = el;
-        result[result.length] = array[i];
-      }
-      return memo;
-    }, []);
-    return result;
-  };
-
-  // Produce an array that contains the union: each distinct element from all of
-  // the passed-in arrays.
-  _.union = function() {
-    return _.uniq(_.flatten(arguments, true));
-  };
-
-  // Produce an array that contains every item shared between all the
-  // passed-in arrays. (Aliased as "intersect" for back-compat.)
-  _.intersection = _.intersect = function(array) {
-    var rest = slice.call(arguments, 1);
-    return _.filter(_.uniq(array), function(item) {
-      return _.every(rest, function(other) {
-        return _.indexOf(other, item) >= 0;
-      });
-    });
-  };
-
-  // Take the difference between one array and a number of other arrays.
-  // Only the elements present in just the first array will remain.
-  _.difference = function(array) {
-    var rest = _.flatten(slice.call(arguments, 1));
-    return _.filter(array, function(value){ return !_.include(rest, value); });
-  };
-
-  // Zip together multiple lists into a single array -- elements that share
-  // an index go together.
-  _.zip = function() {
-    var args = slice.call(arguments);
-    var length = _.max(_.pluck(args, 'length'));
-    var results = new Array(length);
-    for (var i = 0; i < length; i++) results[i] = _.pluck(args, "" + i);
-    return results;
-  };
-
-  // If the browser doesn't supply us with indexOf (I'm looking at you, **MSIE**),
-  // we need this function. Return the position of the first occurrence of an
-  // item in an array, or -1 if the item is not included in the array.
-  // Delegates to **ECMAScript 5**'s native `indexOf` if available.
-  // If the array is large and already in sort order, pass `true`
-  // for **isSorted** to use binary search.
-  _.indexOf = function(array, item, isSorted) {
-    if (array == null) return -1;
-    var i, l;
-    if (isSorted) {
-      i = _.sortedIndex(array, item);
-      return array[i] === item ? i : -1;
-    }
-    if (nativeIndexOf && array.indexOf === nativeIndexOf) return array.indexOf(item);
-    for (i = 0, l = array.length; i < l; i++) if (i in array && array[i] === item) return i;
-    return -1;
-  };
-
-  // Delegates to **ECMAScript 5**'s native `lastIndexOf` if available.
-  _.lastIndexOf = function(array, item) {
-    if (array == null) return -1;
-    if (nativeLastIndexOf && array.lastIndexOf === nativeLastIndexOf) return array.lastIndexOf(item);
-    var i = array.length;
-    while (i--) if (i in array && array[i] === item) return i;
-    return -1;
-  };
-
-  // Generate an integer Array containing an arithmetic progression. A port of
-  // the native Python `range()` function. See
-  // [the Python documentation](http://docs.python.org/library/functions.html#range).
-  _.range = function(start, stop, step) {
-    if (arguments.length <= 1) {
-      stop = start || 0;
-      start = 0;
-    }
-    step = arguments[2] || 1;
-
-    var len = Math.max(Math.ceil((stop - start) / step), 0);
-    var idx = 0;
-    var range = new Array(len);
-
-    while(idx < len) {
-      range[idx++] = start;
-      start += step;
-    }
-
-    return range;
-  };
-
-  // Function (ahem) Functions
-  // ------------------
-
-  // Reusable constructor function for prototype setting.
-  var ctor = function(){};
-
-  // Create a function bound to a given object (assigning `this`, and arguments,
-  // optionally). Binding with arguments is also known as `curry`.
-  // Delegates to **ECMAScript 5**'s native `Function.bind` if available.
-  // We check for `func.bind` first, to fail fast when `func` is undefined.
-  _.bind = function bind(func, context) {
-    var bound, args;
-    if (func.bind === nativeBind && nativeBind) return nativeBind.apply(func, slice.call(arguments, 1));
-    if (!_.isFunction(func)) throw new TypeError;
-    args = slice.call(arguments, 2);
-    return bound = function() {
-      if (!(this instanceof bound)) return func.apply(context, args.concat(slice.call(arguments)));
-      ctor.prototype = func.prototype;
-      var self = new ctor;
-      var result = func.apply(self, args.concat(slice.call(arguments)));
-      if (Object(result) === result) return result;
-      return self;
-    };
-  };
-
-  // Bind all of an object's methods to that object. Useful for ensuring that
-  // all callbacks defined on an object belong to it.
-  _.bindAll = function(obj) {
-    var funcs = slice.call(arguments, 1);
-    if (funcs.length == 0) funcs = _.functions(obj);
-    each(funcs, function(f) { obj[f] = _.bind(obj[f], obj); });
-    return obj;
-  };
-
-  // Memoize an expensive function by storing its results.
-  _.memoize = function(func, hasher) {
-    var memo = {};
-    hasher || (hasher = _.identity);
-    return function() {
-      var key = hasher.apply(this, arguments);
-      return _.has(memo, key) ? memo[key] : (memo[key] = func.apply(this, arguments));
-    };
-  };
-
-  // Delays a function for the given number of milliseconds, and then calls
-  // it with the arguments supplied.
-  _.delay = function(func, wait) {
-    var args = slice.call(arguments, 2);
-    return setTimeout(function(){ return func.apply(func, args); }, wait);
-  };
-
-  // Defers a function, scheduling it to run after the current call stack has
-  // cleared.
-  _.defer = function(func) {
-    return _.delay.apply(_, [func, 1].concat(slice.call(arguments, 1)));
-  };
-
-  // Returns a function, that, when invoked, will only be triggered at most once
-  // during a given window of time.
-  _.throttle = function(func, wait) {
-    var context, args, timeout, throttling, more;
-    var whenDone = _.debounce(function(){ more = throttling = false; }, wait);
-    return function() {
-      context = this; args = arguments;
-      var later = function() {
-        timeout = null;
-        if (more) func.apply(context, args);
-        whenDone();
-      };
-      if (!timeout) timeout = setTimeout(later, wait);
-      if (throttling) {
-        more = true;
-      } else {
-        func.apply(context, args);
-      }
-      whenDone();
-      throttling = true;
-    };
-  };
-
-  // Returns a function, that, as long as it continues to be invoked, will not
-  // be triggered. The function will be called after it stops being called for
-  // N milliseconds.
-  _.debounce = function(func, wait) {
-    var timeout;
-    return function() {
-      var context = this, args = arguments;
-      var later = function() {
-        timeout = null;
-        func.apply(context, args);
-      };
-      clearTimeout(timeout);
-      timeout = setTimeout(later, wait);
-    };
-  };
-
-  // Returns a function that will be executed at most one time, no matter how
-  // often you call it. Useful for lazy initialization.
-  _.once = function(func) {
-    var ran = false, memo;
-    return function() {
-      if (ran) return memo;
-      ran = true;
-      return memo = func.apply(this, arguments);
-    };
-  };
-
-  // Returns the first function passed as an argument to the second,
-  // allowing you to adjust arguments, run code before and after, and
-  // conditionally execute the original function.
-  _.wrap = function(func, wrapper) {
-    return function() {
-      var args = [func].concat(slice.call(arguments, 0));
-      return wrapper.apply(this, args);
-    };
-  };
-
-  // Returns a function that is the composition of a list of functions, each
-  // consuming the return value of the function that follows.
-  _.compose = function() {
-    var funcs = arguments;
-    return function() {
-      var args = arguments;
-      for (var i = funcs.length - 1; i >= 0; i--) {
-        args = [funcs[i].apply(this, args)];
-      }
-      return args[0];
-    };
-  };
-
-  // Returns a function that will only be executed after being called N times.
-  _.after = function(times, func) {
-    if (times <= 0) return func();
-    return function() {
-      if (--times < 1) { return func.apply(this, arguments); }
-    };
-  };
-
-  // Object Functions
-  // ----------------
-
-  // Retrieve the names of an object's properties.
-  // Delegates to **ECMAScript 5**'s native `Object.keys`
-  _.keys = nativeKeys || function(obj) {
-    if (obj !== Object(obj)) throw new TypeError('Invalid object');
-    var keys = [];
-    for (var key in obj) if (_.has(obj, key)) keys[keys.length] = key;
-    return keys;
-  };
-
-  // Retrieve the values of an object's properties.
-  _.values = function(obj) {
-    return _.map(obj, _.identity);
-  };
-
-  // Return a sorted list of the function names available on the object.
-  // Aliased as `methods`
-  _.functions = _.methods = function(obj) {
-    var names = [];
-    for (var key in obj) {
-      if (_.isFunction(obj[key])) names.push(key);
-    }
-    return names.sort();
-  };
-
-  // Extend a given object with all the properties in passed-in object(s).
-  _.extend = function(obj) {
-    each(slice.call(arguments, 1), function(source) {
-      for (var prop in source) {
-        obj[prop] = source[prop];
-      }
-    });
-    return obj;
-  };
-
-  // Fill in a given object with default properties.
-  _.defaults = function(obj) {
-    each(slice.call(arguments, 1), function(source) {
-      for (var prop in source) {
-        if (obj[prop] == null) obj[prop] = source[prop];
-      }
-    });
-    return obj;
-  };
-
-  // Create a (shallow-cloned) duplicate of an object.
-  _.clone = function(obj) {
-    if (!_.isObject(obj)) return obj;
-    return _.isArray(obj) ? obj.slice() : _.extend({}, obj);
-  };
-
-  // Invokes interceptor with the obj, and then returns obj.
-  // The primary purpose of this method is to "tap into" a method chain, in
-  // order to perform operations on intermediate results within the chain.
-  _.tap = function(obj, interceptor) {
-    interceptor(obj);
-    return obj;
-  };
-
-  // Internal recursive comparison function.
-  function eq(a, b, stack) {
-    // Identical objects are equal. `0 === -0`, but they aren't identical.
-    // See the Harmony `egal` proposal: http://wiki.ecmascript.org/doku.php?id=harmony:egal.
-    if (a === b) return a !== 0 || 1 / a == 1 / b;
-    // A strict comparison is necessary because `null == undefined`.
-    if (a == null || b == null) return a === b;
-    // Unwrap any wrapped objects.
-    if (a._chain) a = a._wrapped;
-    if (b._chain) b = b._wrapped;
-    // Invoke a custom `isEqual` method if one is provided.
-    if (a.isEqual && _.isFunction(a.isEqual)) return a.isEqual(b);
-    if (b.isEqual && _.isFunction(b.isEqual)) return b.isEqual(a);
-    // Compare `[[Class]]` names.
-    var className = toString.call(a);
-    if (className != toString.call(b)) return false;
-    switch (className) {
-      // Strings, numbers, dates, and booleans are compared by value.
-      case '[object String]':
-        // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
-        // equivalent to `new String("5")`.
-        return a == String(b);
-      case '[object Number]':
-        // `NaN`s are equivalent, but non-reflexive. An `egal` comparison is performed for
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-        // Coerce dates and booleans to numeric primitive values. Dates are compared by their
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-        return a.source == b.source &&
-               a.global == b.global &&
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-          // Ensure commutative equality for sparse arrays.
-          if (!(result = size in a == size in b && eq(a[size], b[size], stack))) break;
-        }
-      }
-    } else {
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-          // Count the expected number of properties.
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-          // Deep compare each member.
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-      }
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-        }
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-      }
-    }
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-    stack.pop();
-    return result;
-  }
-
-  // Perform a deep comparison to check if two objects are equal.
-  _.isEqual = function(a, b) {
-    return eq(a, b, []);
-  };
-
-  // Is a given array, string, or object empty?
-  // An "empty" object has no enumerable own-properties.
-  _.isEmpty = function(obj) {
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-    return true;
-  };
-
-  // Is a given value a DOM element?
-  _.isElement = function(obj) {
-    return !!(obj && obj.nodeType == 1);
-  };
-
-  // Is a given value an array?
-  // Delegates to ECMA5's native Array.isArray
-  _.isArray = nativeIsArray || function(obj) {
-    return toString.call(obj) == '[object Array]';
-  };
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-  // Is a given variable an object?
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-    return obj === Object(obj);
-  };
-
-  // Is a given variable an arguments object?
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-    return toString.call(obj) == '[object Arguments]';
-  };
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-    };
-  }
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-  };
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-  };
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-  // Is a given value a number?
-  _.isNumber = function(obj) {
-    return toString.call(obj) == '[object Number]';
-  };
-
-  // Is the given value `NaN`?
-  _.isNaN = function(obj) {
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-  };
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-  // Is a given value a boolean?
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-    return obj === true || obj === false || toString.call(obj) == '[object Boolean]';
-  };
-
-  // Is a given value a date?
-  _.isDate = function(obj) {
-    return toString.call(obj) == '[object Date]';
-  };
-
-  // Is the given value a regular expression?
-  _.isRegExp = function(obj) {
-    return toString.call(obj) == '[object RegExp]';
-  };
-
-  // Is a given value equal to null?
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-    return obj === null;
-  };
-
-  // Is a given variable undefined?
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-  };
-
-  // Has own property?
-  _.has = function(obj, key) {
-    return hasOwnProperty.call(obj, key);
-  };
-
-  // Utility Functions
-  // -----------------
-
-  // Run Underscore.js in *noConflict* mode, returning the `_` variable to its
-  // previous owner. Returns a reference to the Underscore object.
-  _.noConflict = function() {
-    root._ = previousUnderscore;
-    return this;
-  };
-
-  // Keep the identity function around for default iterators.
-  _.identity = function(value) {
-    return value;
-  };
-
-  // Run a function **n** times.
-  _.times = function (n, iterator, context) {
-    for (var i = 0; i < n; i++) iterator.call(context, i);
-  };
-
-  // Escape a string for HTML interpolation.
-  _.escape = function(string) {
-    return (''+string).replace(/&/g, '&amp;').replace(/</g, '&lt;').replace(/>/g, '&gt;').replace(/"/g, '&quot;').replace(/'/g, '&#x27;').replace(/\//g,'&#x2F;');
-  };
-
-  // Add your own custom functions to the Underscore object, ensuring that
-  // they're correctly added to the OOP wrapper as well.
-  _.mixin = function(obj) {
-    each(_.functions(obj), function(name){
-      addToWrapper(name, _[name] = obj[name]);
-    });
-  };
-
-  // Generate a unique integer id (unique within the entire client session).
-  // Useful for temporary DOM ids.
-  var idCounter = 0;
-  _.uniqueId = function(prefix) {
-    var id = idCounter++;
-    return prefix ? prefix + id : id;
-  };
-
-  // By default, Underscore uses ERB-style template delimiters, change the
-  // following template settings to use alternative delimiters.
-  _.templateSettings = {
-    evaluate    : /<%([\s\S]+?)%>/g,
-    interpolate : /<%=([\s\S]+?)%>/g,
-    escape      : /<%-([\s\S]+?)%>/g
-  };
-
-  // When customizing `templateSettings`, if you don't want to define an
-  // interpolation, evaluation or escaping regex, we need one that is
-  // guaranteed not to match.
-  var noMatch = /.^/;
-
-  // Within an interpolation, evaluation, or escaping, remove HTML escaping
-  // that had been previously added.
-  var unescape = function(code) {
-    return code.replace(/\\\\/g, '\\').replace(/\\'/g, "'");
-  };
-
-  // JavaScript micro-templating, similar to John Resig's implementation.
-  // Underscore templating handles arbitrary delimiters, preserves whitespace,
-  // and correctly escapes quotes within interpolated code.
-  _.template = function(str, data) {
-    var c  = _.templateSettings;
-    var tmpl = 'var __p=[],print=function(){__p.push.apply(__p,arguments);};' +
-      'with(obj||{}){__p.push(\'' +
-      str.replace(/\\/g, '\\\\')
-         .replace(/'/g, "\\'")
-         .replace(c.escape || noMatch, function(match, code) {
-           return "',_.escape(" + unescape(code) + "),'";
-         })
-         .replace(c.interpolate || noMatch, function(match, code) {
-           return "'," + unescape(code) + ",'";
-         })
-         .replace(c.evaluate || noMatch, function(match, code) {
-           return "');" + unescape(code).replace(/[\r\n\t]/g, ' ') + ";__p.push('";
-         })
-         .replace(/\r/g, '\\r')
-         .replace(/\n/g, '\\n')
-         .replace(/\t/g, '\\t')
-         + "');}return __p.join('');";
-    var func = new Function('obj', '_', tmpl);
-    if (data) return func(data, _);
-    return function(data) {
-      return func.call(this, data, _);
-    };
-  };
-
-  // Add a "chain" function, which will delegate to the wrapper.
-  _.chain = function(obj) {
-    return _(obj).chain();
-  };
-
-  // The OOP Wrapper
-  // ---------------
-
-  // If Underscore is called as a function, it returns a wrapped object that
-  // can be used OO-style. This wrapper holds altered versions of all the
-  // underscore functions. Wrapped objects may be chained.
-  var wrapper = function(obj) { this._wrapped = obj; };
-
-  // Expose `wrapper.prototype` as `_.prototype`
-  _.prototype = wrapper.prototype;
-
-  // Helper function to continue chaining intermediate results.
-  var result = function(obj, chain) {
-    return chain ? _(obj).chain() : obj;
-  };
-
-  // A method to easily add functions to the OOP wrapper.
-  var addToWrapper = function(name, func) {
-    wrapper.prototype[name] = function() {
-      var args = slice.call(arguments);
-      unshift.call(args, this._wrapped);
-      return result(func.apply(_, args), this._chain);
-    };
-  };
-
-  // Add all of the Underscore functions to the wrapper object.
-  _.mixin(_);
-
-  // Add all mutator Array functions to the wrapper.
-  each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
-    var method = ArrayProto[name];
-    wrapper.prototype[name] = function() {
-      var wrapped = this._wrapped;
-      method.apply(wrapped, arguments);
-      var length = wrapped.length;
-      if ((name == 'shift' || name == 'splice') && length === 0) delete wrapped[0];
-      return result(wrapped, this._chain);
-    };
-  });
-
-  // Add all accessor Array functions to the wrapper.
-  each(['concat', 'join', 'slice'], function(name) {
-    var method = ArrayProto[name];
-    wrapper.prototype[name] = function() {
-      return result(method.apply(this._wrapped, arguments), this._chain);
-    };
-  });
-
-  // Start chaining a wrapped Underscore object.
-  wrapper.prototype.chain = function() {
-    this._chain = true;
-    return this;
-  };
-
-  // Extracts the result from a wrapped and chained object.
-  wrapper.prototype.value = function() {
-    return this._wrapped;
-  };
-
-}).call(this);
diff --git a/docs/build/html/_static/underscore.js b/docs/build/html/_static/underscore.js
index 5b55f32..cf177d4 100644
--- a/docs/build/html/_static/underscore.js
+++ b/docs/build/html/_static/underscore.js
@@ -1,31 +1,6 @@
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diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html
index 0fd9623..fa39338 100644
--- a/docs/build/html/genindex.html
+++ b/docs/build/html/genindex.html
@@ -1,43 +1,154 @@
+<!DOCTYPE html>
 
 
-<!DOCTYPE html>
 
-<html xmlns="http://www.w3.org/1999/xhtml">
+
+<html lang="en">
   <head>
     <meta charset="utf-8" />
-    <title>Index &#8212; calibration-framework 1.2.1 documentation</title>
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-    <script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
+    <title>Index &mdash; net:cal API Reference</title>
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+    
+<script type="text/javascript">
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+            URL_ROOT:    './',
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+  };
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+    <script type="text/javascript" src="_static/documentation_options.js"></script>
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+                  <input type="hidden" name="area" value="default" />
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+            </li>
+
             
 
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+
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+      </div>
+    </div>
+    
+
+    <!-- container -->
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+
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+<h3><a href="index.html">Table of Contents</a></h3>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.binning.html">netcal.binning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.scaling.html">netcal.scaling</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.regularization.html">netcal.regularization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.metrics.html">netcal.metrics</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.presentation.html">netcal.presentation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.regression.html">netcal.regression</a></li>
+</ul>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html">netcal.AbstractCalibration</a></li>
+</ul>
+
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+            <div class="documentwrapper">
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+                <div class="body">
+                  
+
 <h1 id="index">Index</h1>
 
 <div class="genindex-jumpbox">
@@ -47,22 +158,19 @@ <h1 id="index">Index</h1>
  | <a href="#C"><strong>C</strong></a>
  | <a href="#D"><strong>D</strong></a>
  | <a href="#E"><strong>E</strong></a>
- | <a href="#F"><strong>F</strong></a>
  | <a href="#G"><strong>G</strong></a>
  | <a href="#H"><strong>H</strong></a>
  | <a href="#I"><strong>I</strong></a>
- | <a href="#K"><strong>K</strong></a>
  | <a href="#L"><strong>L</strong></a>
  | <a href="#M"><strong>M</strong></a>
  | <a href="#N"><strong>N</strong></a>
  | <a href="#P"><strong>P</strong></a>
+ | <a href="#Q"><strong>Q</strong></a>
  | <a href="#R"><strong>R</strong></a>
  | <a href="#S"><strong>S</strong></a>
  | <a href="#T"><strong>T</strong></a>
+ | <a href="#U"><strong>U</strong></a>
  | <a href="#V"><strong>V</strong></a>
- | <a href="#W"><strong>W</strong></a>
- | <a href="#X"><strong>X</strong></a>
- | <a href="#Z"><strong>Z</strong></a>
  
 </div>
 <h2 id="_">_</h2>
@@ -74,56 +182,6 @@ <h2 id="_">_</h2>
         <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.__init__">(netcal.regularization.DCAPenalty method)</a>
 </li>
         <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.__init__">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty._get_backward_hooks">_get_backward_hooks() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty._get_backward_hooks">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty._get_backward_hooks">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty._load_from_state_dict">_load_from_state_dict() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty._load_from_state_dict">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty._load_from_state_dict">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty._named_members">_named_members() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty._named_members">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty._named_members">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty._register_load_state_dict_pre_hook">_register_load_state_dict_pre_hook() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty._register_load_state_dict_pre_hook">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty._register_load_state_dict_pre_hook">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty._register_state_dict_hook">_register_state_dict_hook() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty._register_state_dict_hook">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty._register_state_dict_hook">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty._save_to_state_dict">_save_to_state_dict() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty._save_to_state_dict">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty._save_to_state_dict">(netcal.regularization.MMCEPenalty method)</a>
 </li>
       </ul></li>
   </ul></td>
@@ -134,30 +192,16 @@ <h2 id="A">A</h2>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration">AbstractCalibration (class in netcal)</a>
 </li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression (class in netcal.scaling)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP.accuracy">accuracy() (netcal.metrics.PICP method)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE">ACE (class in netcal.metrics)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.add_module">add_module() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.add_module">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.add_module">(netcal.regularization.MMCEPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.AbstractGP.html#netcal.regression.gp.AbstractGP">AbstractGP (class in netcal.regression.gp)</a>
 </li>
-      </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.alphas">alphas() (netcal.scaling.BetaCalibrationDependent property)</a>
+      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression">AbstractLogisticRegression (class in netcal.scaling)</a>
 </li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.apply">apply() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE">ACE (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.apply">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.apply">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ACE.html#netcal.metrics.confidence.ACE">(class in netcal.metrics.confidence)</a>
 </li>
       </ul></li>
   </ul></td>
@@ -170,116 +214,26 @@ <h2 id="B">B</h2>
 </li>
       <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration">BetaCalibration (class in netcal.scaling)</a>
 </li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent">BetaCalibrationDependent (class in netcal.scaling)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.betas">betas() (netcal.scaling.BetaCalibrationDependent property)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.bfloat16">bfloat16() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.bfloat16">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.bfloat16">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE.binning">binning() (netcal.metrics.ACE method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE.binning">(netcal.metrics.ECE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE.binning">(netcal.metrics.MCE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP.binning">(netcal.metrics.PICP method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.buffers">buffers() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.buffers">(netcal.regularization.DCAPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent">BetaCalibrationDependent (class in netcal.scaling)</a>
 </li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.buffers">(netcal.regularization.MMCEPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.BetaLikelihood.html#netcal.regression.gp.likelihood.BetaLikelihood">BetaLikelihood (class in netcal.regression.gp.likelihood)</a>
 </li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
 <h2 id="C">C</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.children">children() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.children">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.children">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.clear">clear() (netcal.AbstractCalibration method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.clear">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.clear">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.clear">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.clear">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.clear">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.clear">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.clear">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.clear">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.clear">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.clear">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.confidence_penalty.html#netcal.regularization.confidence_penalty">confidence_penalty() (in module netcal.regularization)</a>
+      <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.CauchyLikelihood.html#netcal.regression.gp.likelihood.CauchyLikelihood">CauchyLikelihood (class in netcal.regression.gp.likelihood)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty">ConfidencePenalty (class in netcal.regularization)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.to">ConfidencePenalty.to() (in module netcal.regularization)</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.to">[1]</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.to">[2]</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.to">[3]</a>
-</li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.convex">convex() (netcal.scaling.AbstractLogisticRegression method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.convex">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.convex">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.convex">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.convex">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.convex">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.covariances">covariances() (netcal.scaling.LogisticCalibrationDependent property)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.cpu">cpu() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.cpu">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.cpu">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.cuda">cuda() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.cuda">(netcal.regularization.DCAPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.confidence_penalty.html#netcal.regularization.confidence_penalty">confidence_penalty() (in module netcal.regularization)</a>
 </li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.cuda">(netcal.regularization.MMCEPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty">ConfidencePenalty (class in netcal.regularization)</a>
 </li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
@@ -288,18 +242,6 @@ <h2 id="D">D</h2>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty">DCAPenalty (class in netcal.regularization)</a>
 </li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.to">DCAPenalty.to() (in module netcal.regularization)</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.to">[1]</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.to">[2]</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.to">[3]</a>
-</li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.double">double() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.double">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.double">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
@@ -307,171 +249,49 @@ <h2 id="E">E</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE">ECE (class in netcal.metrics)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR">ENIR (class in netcal.binning)</a>
-</li>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.epsilon">epsilon (netcal.AbstractCalibration attribute)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.eval">eval() (netcal.regularization.ConfidencePenalty method)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.eval">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.eval">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.ECE.html#netcal.metrics.confidence.ECE">(class in netcal.metrics.confidence)</a>
 </li>
       </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.extra_repr">extra_repr() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ENCE.html#netcal.metrics.ENCE">ENCE (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.extra_repr">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.extra_repr">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.ENCE.html#netcal.metrics.regression.ENCE">(class in netcal.metrics.regression)</a>
 </li>
       </ul></li>
   </ul></td>
-</tr></table>
-
-<h2 id="F">F</h2>
-<table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.fit">fit() (netcal.AbstractCalibration method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.fit">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.fit">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.fit">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.fit">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.fit">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.fit">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.fit">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.fit">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.fit">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.fit">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.fit_transform">fit_transform() (netcal.AbstractCalibration method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.fit_transform">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.fit_transform">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.fit_transform">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.fit_transform">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.fit_transform">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.fit_transform">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.fit_transform">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.fit_transform">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.fit_transform">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.fit_transform">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.float">float() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.float">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.float">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.forward">forward() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.forward">(netcal.regularization.DCAPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR">ENIR (class in netcal.binning)</a>
 </li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.forward">(netcal.regularization.MMCEPenalty method)</a>
+      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.epsilon">epsilon (netcal.AbstractCalibration attribute)</a>
 </li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
 <h2 id="G">G</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.get_buffer">get_buffer() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.get_buffer">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.get_buffer">(netcal.regularization.MMCEPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_kernel/netcal.regression.gp.kernel.GaussianRBFKernel.html#netcal.regression.gp.kernel.GaussianRBFKernel">GaussianRBFKernel (class in netcal.regression.gp.kernel)</a>
 </li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.get_degrees_of_freedom">get_degrees_of_freedom() (netcal.binning.HistogramBinning method)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.get_parameter">get_parameter() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regression/netcal.regression.GPBeta.html#netcal.regression.GPBeta">GPBeta (class in netcal.regression)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.get_parameter">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.get_parameter">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.get_params">get_params() (netcal.AbstractCalibration method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.get_params">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.get_params">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.get_params">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.get_params">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.get_params">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.get_params">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.get_params">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.get_params">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.get_params">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.get_params">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPBeta.html#netcal.regression.gp.GPBeta">(class in netcal.regression.gp)</a>
 </li>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.get_submodule">get_submodule() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regression/netcal.regression.GPCauchy.html#netcal.regression.GPCauchy">GPCauchy (class in netcal.regression)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.get_submodule">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.get_submodule">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPCauchy.html#netcal.regression.gp.GPCauchy">(class in netcal.regression.gp)</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.guide">guide() (netcal.scaling.AbstractLogisticRegression method)</a>
+      <li><a href="_autosummary/_autosummary_regression/netcal.regression.GPNormal.html#netcal.regression.GPNormal">GPNormal (class in netcal.regression)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.guide">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.guide">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.guide">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.guide">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.guide">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp/netcal.regression.gp.GPNormal.html#netcal.regression.gp.GPNormal">(class in netcal.regression.gp)</a>
 </li>
       </ul></li>
   </ul></td>
@@ -479,16 +299,6 @@ <h2 id="G">G</h2>
 
 <h2 id="H">H</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.half">half() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.half">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.half">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-  </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning">HistogramBinning (class in netcal.binning)</a>
 </li>
@@ -498,72 +308,22 @@ <h2 id="H">H</h2>
 <h2 id="I">I</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.intercept">intercept() (netcal.scaling.BetaCalibration property)</a>
+      <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression">IsotonicRegression (class in netcal.binning)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.intercept">(netcal.scaling.BetaCalibrationDependent property)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.intercept">(netcal.scaling.LogisticCalibration property)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.intercept">(netcal.scaling.LogisticCalibrationDependent property)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.intercept">(netcal.scaling.TemperatureScaling property)</a>
+        <li><a href="_autosummary/_autosummary_regression/netcal.regression.IsotonicRegression.html#netcal.regression.IsotonicRegression">(class in netcal.regression)</a>
 </li>
       </ul></li>
   </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression">IsotonicRegression (class in netcal.binning)</a>
-</li>
-  </ul></td>
-</tr></table>
-
-<h2 id="K">K</h2>
-<table style="width: 100%" class="indextable genindextable"><tr>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.kernel">kernel() (netcal.regularization.MMCEPenalty method)</a>
-</li>
-  </ul></td>
 </tr></table>
 
 <h2 id="L">L</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.load_model">load_model() (netcal.AbstractCalibration method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.load_model">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.load_model">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.load_model">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.load_model">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.load_model">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.load_model">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.load_model">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.load_model">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.load_model">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.load_model">(netcal.scaling.TemperatureScaling method)</a>
+      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration">LogisticCalibration (class in netcal.scaling)</a>
 </li>
-      </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.load_state_dict">load_state_dict() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.load_state_dict">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.load_state_dict">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration">LogisticCalibration (class in netcal.scaling)</a>
-</li>
       <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent">LogisticCalibrationDependent (class in netcal.scaling)</a>
 </li>
   </ul></td>
@@ -572,92 +332,47 @@ <h2 id="L">L</h2>
 <h2 id="M">M</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.mask">mask() (netcal.scaling.AbstractLogisticRegression method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.mask">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.mask">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.mask">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.mask">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.mask">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
       <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE">MCE (class in netcal.metrics)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.mcmc">mcmc() (netcal.scaling.AbstractLogisticRegression method)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.mcmc">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.mcmc">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.mcmc">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.mcmc">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.mcmc">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MCE.html#netcal.metrics.confidence.MCE">(class in netcal.metrics.confidence)</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.means">means() (netcal.scaling.LogisticCalibrationDependent property)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE.measure">measure() (netcal.metrics.ACE method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MMCE.html#netcal.metrics.MMCE">MMCE (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE.measure">(netcal.metrics.ECE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE.measure">(netcal.metrics.MCE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MMCE.html#netcal.metrics.MMCE.measure">(netcal.metrics.MMCE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP.measure">(netcal.metrics.PICP method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.confidence.MMCE.html#netcal.metrics.confidence.MMCE">(class in netcal.metrics.confidence)</a>
 </li>
       </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MMCE.html#netcal.metrics.MMCE">MMCE (class in netcal.metrics)</a>
-</li>
       <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty">MMCEPenalty (class in netcal.regularization)</a>
 </li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.to">MMCEPenalty.to() (in module netcal.regularization)</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.to">[1]</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.to">[2]</a>, <a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.to">[3]</a>
-</li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.model">model() (netcal.scaling.AbstractLogisticRegression method)</a>
+      <li>
+    module
 
       <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.model">(netcal.scaling.BetaCalibration method)</a>
+        <li><a href="index.html#module-netcal">netcal</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.model">(netcal.scaling.BetaCalibrationDependent method)</a>
+        <li><a href="_autosummary/netcal.binning.html#module-netcal.binning">netcal.binning</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.model">(netcal.scaling.LogisticCalibration method)</a>
+        <li><a href="_autosummary/netcal.metrics.html#module-netcal.metrics">netcal.metrics</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.model">(netcal.scaling.LogisticCalibrationDependent method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/netcal.metrics.confidence.html#module-netcal.metrics.confidence">netcal.metrics.confidence</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.model">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.html#module-netcal.metrics.regression">netcal.metrics.regression</a>
 </li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.modules">modules() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.modules">(netcal.regularization.DCAPenalty method)</a>
+        <li><a href="_autosummary/netcal.presentation.html#module-netcal.presentation">netcal.presentation</a>
 </li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.modules">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/netcal.regression.html#module-netcal.regression">netcal.regression</a>
 </li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.momentum">momentum() (netcal.scaling.AbstractLogisticRegression method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.momentum">(netcal.scaling.BetaCalibration method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/netcal.regression.gp.html#module-netcal.regression.gp">netcal.regression.gp</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.momentum">(netcal.scaling.BetaCalibrationDependent method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.html#module-netcal.regression.gp.kernel">netcal.regression.gp.kernel</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.momentum">(netcal.scaling.LogisticCalibration method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.likelihood.html#module-netcal.regression.gp.likelihood">netcal.regression.gp.likelihood</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.momentum">(netcal.scaling.LogisticCalibrationDependent method)</a>
+        <li><a href="_autosummary/netcal.regularization.html#module-netcal.regularization">netcal.regularization</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.momentum">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/netcal.scaling.html#module-netcal.scaling">netcal.scaling</a>
 </li>
       </ul></li>
   </ul></td>
@@ -666,479 +381,231 @@ <h2 id="M">M</h2>
 <h2 id="N">N</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.named_buffers">named_buffers() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.named_buffers">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.named_buffers">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="index.html#module-netcal">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.named_children">named_children() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.binning
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.named_children">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.named_children">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/netcal.binning.html#module-netcal.binning">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.named_modules">named_modules() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.metrics
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.named_modules">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.named_modules">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/netcal.metrics.html#module-netcal.metrics">module</a>
 </li>
       </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.named_parameters">named_parameters() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.metrics.confidence
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.named_parameters">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.named_parameters">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/netcal.metrics.confidence.html#module-netcal.metrics.confidence">module</a>
 </li>
       </ul></li>
-      <li><a href="index.html#module-netcal">netcal (module)</a>
-</li>
-      <li><a href="_autosummary/netcal.binning.html#module-netcal.binning">netcal.binning (module)</a>
-</li>
-      <li><a href="_autosummary/netcal.metrics.html#module-netcal.metrics">netcal.metrics (module)</a>
-</li>
-      <li><a href="_autosummary/netcal.presentation.html#module-netcal.presentation">netcal.presentation (module)</a>
-</li>
-      <li><a href="_autosummary/netcal.regularization.html#module-netcal.regularization">netcal.regularization (module)</a>
-</li>
-      <li><a href="_autosummary/netcal.scaling.html#module-netcal.scaling">netcal.scaling (module)</a>
-</li>
-  </ul></td>
-</tr></table>
-
-<h2 id="P">P</h2>
-<table style="width: 100%" class="indextable genindextable"><tr>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.parameters">parameters() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.metrics.regression
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.parameters">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.parameters">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.html#module-netcal.metrics.regression">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP">PICP (class in netcal.metrics)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html#netcal.presentation.ReliabilityDiagram.plot">plot() (netcal.presentation.ReliabilityDiagram method)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE.prepare">prepare() (netcal.metrics.ACE method)</a>
+      <li>
+    netcal.presentation
 
       <ul>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE.prepare">(netcal.metrics.ECE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE.prepare">(netcal.metrics.MCE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP.prepare">(netcal.metrics.PICP method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.prepare">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.prepare">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.prepare">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.prepare">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.prepare">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.prepare">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.prior">prior() (netcal.scaling.AbstractLogisticRegression method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.prior">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.prior">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.prior">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.prior">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.prior">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/netcal.presentation.html#module-netcal.presentation">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE.process">process() (netcal.metrics.ACE method)</a>
+      <li>
+    netcal.regression
 
       <ul>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE.process">(netcal.metrics.ECE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE.process">(netcal.metrics.MCE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP.process">(netcal.metrics.PICP method)</a>
+        <li><a href="_autosummary/netcal.regression.html#module-netcal.regression">module</a>
 </li>
       </ul></li>
   </ul></td>
-</tr></table>
-
-<h2 id="R">R</h2>
-<table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE.reduce">reduce() (netcal.metrics.ACE method)</a>
+      <li>
+    netcal.regression.gp
 
       <ul>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE.reduce">(netcal.metrics.ECE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE.reduce">(netcal.metrics.MCE method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP.reduce">(netcal.metrics.PICP method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/netcal.regression.gp.html#module-netcal.regression.gp">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.register_backward_hook">register_backward_hook() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.regression.gp.kernel
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.register_backward_hook">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.register_backward_hook">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.html#module-netcal.regression.gp.kernel">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.register_buffer">register_buffer() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.regression.gp.likelihood
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.register_buffer">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.register_buffer">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.likelihood.html#module-netcal.regression.gp.likelihood">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.register_forward_hook">register_forward_hook() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.regularization
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.register_forward_hook">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.register_forward_hook">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/netcal.regularization.html#module-netcal.regularization">module</a>
 </li>
       </ul></li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.register_forward_pre_hook">register_forward_pre_hook() (netcal.regularization.ConfidencePenalty method)</a>
+      <li>
+    netcal.scaling
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.register_forward_pre_hook">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.register_forward_pre_hook">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/netcal.scaling.html#module-netcal.scaling">module</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.register_full_backward_hook">register_full_backward_hook() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.NLL.html#netcal.metrics.NLL">NLL (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.register_full_backward_hook">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.register_full_backward_hook">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.register_parameter">register_parameter() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.register_parameter">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.register_parameter">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html#netcal.presentation.ReliabilityDiagram">ReliabilityDiagram (class in netcal.presentation)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.requires_grad_">requires_grad_() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.requires_grad_">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.requires_grad_">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.NLL.html#netcal.metrics.regression.NLL">(class in netcal.metrics.regression)</a>
 </li>
       </ul></li>
   </ul></td>
 </tr></table>
 
-<h2 id="S">S</h2>
+<h2 id="P">P</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.save_model">save_model() (netcal.AbstractCalibration method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.save_model">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.save_model">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.save_model">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.save_model">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.save_model">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.save_model">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.save_model">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.save_model">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.save_model">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.save_model">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.set_params">set_params() (netcal.AbstractCalibration method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP">PICP (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.set_params">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.set_params">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.set_params">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.set_params">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.set_params">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.set_params">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.set_params">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.set_params">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.set_params">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.set_params">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PICP.html#netcal.metrics.regression.PICP">(class in netcal.metrics.regression)</a>
 </li>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.share_memory">share_memory() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PinballLoss.html#netcal.metrics.PinballLoss">PinballLoss (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.share_memory">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.share_memory">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.squeeze_generic">squeeze_generic() (netcal.AbstractCalibration class method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.squeeze_generic">(netcal.binning.BBQ class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.squeeze_generic">(netcal.binning.ENIR class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.squeeze_generic">(netcal.binning.HistogramBinning class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.squeeze_generic">(netcal.binning.IsotonicRegression class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ACE.html#netcal.metrics.ACE.squeeze_generic">(netcal.metrics.ACE class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.ECE.html#netcal.metrics.ECE.squeeze_generic">(netcal.metrics.ECE class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.MCE.html#netcal.metrics.MCE.squeeze_generic">(netcal.metrics.MCE class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_metric/netcal.metrics.PICP.html#netcal.metrics.PICP.squeeze_generic">(netcal.metrics.PICP class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.squeeze_generic">(netcal.scaling.AbstractLogisticRegression class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.squeeze_generic">(netcal.scaling.BetaCalibration class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.squeeze_generic">(netcal.scaling.BetaCalibrationDependent class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.squeeze_generic">(netcal.scaling.LogisticCalibration class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.squeeze_generic">(netcal.scaling.LogisticCalibrationDependent class method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.squeeze_generic">(netcal.scaling.TemperatureScaling class method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.state_dict">state_dict() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.state_dict">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.state_dict">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.PinballLoss.html#netcal.metrics.regression.PinballLoss">(class in netcal.metrics.regression)</a>
 </li>
       </ul></li>
   </ul></td>
 </tr></table>
 
-<h2 id="T">T</h2>
+<h2 id="Q">Q</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.temperature">temperature() (netcal.scaling.TemperatureScaling property)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling">TemperatureScaling (class in netcal.scaling)</a>
-</li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.to">to() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.QCE.html#netcal.metrics.QCE">QCE (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.to">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.to">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.to">(netcal.scaling.AbstractLogisticRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.to">(netcal.scaling.BetaCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.to">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.to">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.to">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.to">(netcal.scaling.TemperatureScaling method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QCE.html#netcal.metrics.regression.QCE">(class in netcal.metrics.regression)</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.to_empty">to_empty() (netcal.regularization.ConfidencePenalty method)</a>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.QuantileLoss.html#netcal.metrics.QuantileLoss">QuantileLoss (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.to_empty">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.to_empty">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.QuantileLoss.html#netcal.metrics.regression.QuantileLoss">(class in netcal.metrics.regression)</a>
 </li>
       </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.train">train() (netcal.regularization.ConfidencePenalty method)</a>
+  </ul></td>
+</tr></table>
 
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.train">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.train">(netcal.regularization.MMCEPenalty method)</a>
+<h2 id="R">R</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityDiagram.html#netcal.presentation.ReliabilityDiagram">ReliabilityDiagram (class in netcal.presentation)</a>
 </li>
-      </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration.transform">transform() (netcal.AbstractCalibration method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.BBQ.html#netcal.binning.BBQ.transform">(netcal.binning.BBQ method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.ENIR.html#netcal.binning.ENIR.transform">(netcal.binning.ENIR method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.HistogramBinning.html#netcal.binning.HistogramBinning.transform">(netcal.binning.HistogramBinning method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_binning/netcal.binning.IsotonicRegression.html#netcal.binning.IsotonicRegression.transform">(netcal.binning.IsotonicRegression method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.transform">(netcal.scaling.AbstractLogisticRegression method)</a>
+      <li><a href="_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityQCE.html#netcal.presentation.ReliabilityQCE">ReliabilityQCE (class in netcal.presentation)</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.transform">(netcal.scaling.BetaCalibration method)</a>
+      <li><a href="_autosummary/_autosummary_presentation/netcal.presentation.ReliabilityRegression.html#netcal.presentation.ReliabilityRegression">ReliabilityRegression (class in netcal.presentation)</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.transform">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.transform">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.transform">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.transform">(netcal.scaling.TemperatureScaling method)</a>
-</li>
-      </ul></li>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.type">type() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.type">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.type">(netcal.regularization.MMCEPenalty method)</a>
-</li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
-<h2 id="V">V</h2>
+<h2 id="S">S</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.AbstractLogisticRegression.html#netcal.scaling.AbstractLogisticRegression.variational">variational() (netcal.scaling.AbstractLogisticRegression method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.variational">(netcal.scaling.BetaCalibration method)</a>
+      <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood.html#netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood">ScaledMultivariateNormalLikelihood (class in netcal.regression.gp.likelihood)</a>
 </li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibrationDependent.html#netcal.scaling.BetaCalibrationDependent.variational">(netcal.scaling.BetaCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.variational">(netcal.scaling.LogisticCalibration method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibrationDependent.html#netcal.scaling.LogisticCalibrationDependent.variational">(netcal.scaling.LogisticCalibrationDependent method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.variational">(netcal.scaling.TemperatureScaling method)</a>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/_autosummary_regression_gp_likelihood/netcal.regression.gp.likelihood.ScaledNormalLikelihood.html#netcal.regression.gp.likelihood.ScaledNormalLikelihood">ScaledNormalLikelihood (class in netcal.regression.gp.likelihood)</a>
 </li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
-<h2 id="W">W</h2>
+<h2 id="T">T</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.BetaCalibration.html#netcal.scaling.BetaCalibration.weights">weights() (netcal.scaling.BetaCalibration property)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.LogisticCalibration.html#netcal.scaling.LogisticCalibration.weights">(netcal.scaling.LogisticCalibration property)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling.weights">(netcal.scaling.TemperatureScaling property)</a>
+      <li><a href="_autosummary/_autosummary_scaling/netcal.scaling.TemperatureScaling.html#netcal.scaling.TemperatureScaling">TemperatureScaling (class in netcal.scaling)</a>
 </li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
-<h2 id="X">X</h2>
+<h2 id="U">U</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.xpu">xpu() (netcal.regularization.ConfidencePenalty method)</a>
+      <li><a href="_autosummary/_autosummary_metric/netcal.metrics.UCE.html#netcal.metrics.UCE">UCE (class in netcal.metrics)</a>
 
       <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.xpu">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.xpu">(netcal.regularization.MMCEPenalty method)</a>
+        <li><a href="_autosummary/_autosummary_metric_submodules/_autosummary_metric/netcal.metrics.regression.UCE.html#netcal.metrics.regression.UCE">(class in netcal.metrics.regression)</a>
 </li>
       </ul></li>
   </ul></td>
 </tr></table>
 
-<h2 id="Z">Z</h2>
+<h2 id="V">V</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.ConfidencePenalty.html#netcal.regularization.ConfidencePenalty.zero_grad">zero_grad() (netcal.regularization.ConfidencePenalty method)</a>
-
-      <ul>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.DCAPenalty.html#netcal.regularization.DCAPenalty.zero_grad">(netcal.regularization.DCAPenalty method)</a>
-</li>
-        <li><a href="_autosummary/_autosummary_regularization_func/netcal.regularization.MMCEPenalty.html#netcal.regularization.MMCEPenalty.zero_grad">(netcal.regularization.MMCEPenalty method)</a>
+      <li><a href="_autosummary/_autosummary_regression/netcal.regression.VarianceScaling.html#netcal.regression.VarianceScaling">VarianceScaling (class in netcal.regression)</a>
 </li>
-      </ul></li>
   </ul></td>
 </tr></table>
 
 
 
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+                <ul class="dropdown-menu localtoc sp-localtoc" role="menu" aria-labelledby="localToc">
+                <ul>
+<li><a class="reference internal" href="#">API Reference of net:cal</a><ul>
+<li><a class="reference internal" href="#available-packages">Available packages</a></li>
+<li><a class="reference internal" href="#base-class">Base class</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#net-cal-uncertainty-calibration">net:cal - Uncertainty Calibration</a><ul>
+<li><a class="reference internal" href="#table-of-contents">Table of Contents</a></li>
+<li><a class="reference internal" href="#overview">Overview</a><ul>
+<li><a class="reference internal" href="#update-on-version-1-3">Update on version 1.3</a></li>
+<li><a class="reference internal" href="#update-on-version-1-2">Update on version 1.2</a></li>
+<li><a class="reference internal" href="#update-on-version-1-1">Update on version 1.1</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#installation">Installation</a><ul>
+<li><a class="reference internal" href="#requirements">Requirements</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#calibration-metrics">Calibration Metrics</a><ul>
+<li><a class="reference internal" href="#confidence-calibration-metrics">Confidence Calibration Metrics</a></li>
+<li><a class="reference internal" href="#regression-calibration-metrics">Regression Calibration Metrics</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#methods">Methods</a><ul>
+<li><a class="reference internal" href="#confidence-calibration-methods">Confidence Calibration Methods</a><ul>
+<li><a class="reference internal" href="#binning">Binning</a></li>
+<li><a class="reference internal" href="#scaling">Scaling</a></li>
+<li><a class="reference internal" href="#regularization">Regularization</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#regression-calibration-methods">Regression Calibration Methods</a><ul>
+<li><a class="reference internal" href="#non-parametric-calibration">Non-parametric calibration</a></li>
+<li><a class="reference internal" href="#parametric-calibration">Parametric calibration</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#visualization">Visualization</a></li>
+<li><a class="reference internal" href="#examples">Examples</a><ul>
+<li><a class="reference internal" href="#classification">Classification</a><ul>
+<li><a class="reference internal" href="#post-hoc-calibration-for-classification">Post-hoc Calibration for Classification</a></li>
+<li><a class="reference internal" href="#measuring-miscalibration-for-classification">Measuring Miscalibration for Classification</a></li>
+<li><a class="reference internal" href="#visualizing-miscalibration-for-classification">Visualizing Miscalibration for Classification</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#detection-confidence-of-objects">Detection (Confidence of Objects)</a><ul>
+<li><a class="reference internal" href="#post-hoc-calibration-for-detection">Post-hoc Calibration for Detection</a></li>
+<li><a class="reference internal" href="#measuring-miscalibration-for-detection">Measuring Miscalibration for Detection</a></li>
+<li><a class="reference internal" href="#visualizing-miscalibration-for-detection">Visualizing Miscalibration for Detection</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#uncertainty-in-confidence-calibration">Uncertainty in Confidence Calibration</a><ul>
+<li><a class="reference internal" href="#post-hoc-calibration-with-uncertainty">Post-hoc Calibration with Uncertainty</a></li>
+<li><a class="reference internal" href="#measuring-miscalibration-with-uncertainty">Measuring Miscalibration with Uncertainty</a></li>
+</ul>
+</li>
+<li><a class="reference internal" href="#probabilistic-regression">Probabilistic Regression</a><ul>
+<li><a class="reference internal" href="#post-hoc-calibration-parametric">Post-hoc Calibration (Parametric)</a></li>
+<li><a class="reference internal" href="#post-hoc-calibration-non-parametric">Post-hoc Calibration (Non-Parametric)</a></li>
+<li><a class="reference internal" href="#correlation-estimation-and-recalibration">Correlation Estimation and Recalibration</a></li>
+<li><a class="reference internal" href="#measuring-miscalibration-for-regression">Measuring Miscalibration for Regression</a></li>
+<li><a class="reference internal" href="#visualizing-miscalibration-for-regression">Visualizing Miscalibration for Regression</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a class="reference internal" href="#references">References</a></li>
+</ul>
+</li>
+</ul>
+
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-  <span class="target" id="module-netcal"></span><div class="section" id="api-reference">
-<h1><a class="toc-backref" href="#id57">API Reference</a><a class="headerlink" href="#api-reference" title="Permalink to this headline">¶</a></h1>
-<p>This is the detailled API reference for the confidence calibration framework. This framework can be used to
-obtain well-calibrated confidence estimates from biased estimators like Neural Networks.
-The API reference contains a detailled description of all available methods and their parameters. For
+            <li class="visible-xs"><a href="_sources/index.rst.txt" rel="nofollow">Show Source</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.scaling.html">netcal.scaling</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.regularization.html">netcal.regularization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.metrics.html">netcal.metrics</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.presentation.html">netcal.presentation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.regression.html">netcal.regression</a></li>
+</ul>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html">netcal.AbstractCalibration</a></li>
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+  <span class="target" id="module-netcal"></span><section id="api-reference-of-net-cal">
+<h1>API Reference of net:cal<a class="headerlink" href="#api-reference-of-net-cal" title="Permalink to this heading">¶</a></h1>
+<p>This is the detailed API reference for the net:cal calibration framework. This library can be used to
+obtain well-calibrated confidence or uncertainty estimates from biased estimators such as neural networks.
+The API reference contains a detailed description of all available methods and their parameters. For
 miscellaneous examples on how to use these methods, see readme below.</p>
-<p>Available packages</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+<section id="available-packages">
+<h2>Available packages<a class="headerlink" href="#available-packages" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
 <tbody>
 <tr class="row-odd"><td><p><a class="reference internal" href="_autosummary/netcal.binning.html#module-netcal.binning" title="netcal.binning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">binning</span></code></a></p></td>
-<td><p>Binning methods for confidence calibration.</p></td>
+<td><p>Binning Methods for Confidence Calibration
+
+This package consists of several methods for confidence calibration which use binning to approximate
+confidence estimates to the measured accuracy. The most common calibration methods within this package
+are netcal.binning.HistogramBinning and netcal.binning.IsotonicRegression.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="_autosummary/netcal.scaling.html#module-netcal.scaling" title="netcal.scaling"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scaling</span></code></a></p></td>
-<td><p>Scaling methods for confidence calibration.</p></td>
+<td><p>Scaling Methods for Confidence Calibration
+
+This package consists of several methods for confidence calibration which use confidence scaling to approximate
+confidence estimates to observed accuracy. The most common scaling methods are
+netcal.scaling.TemperatureScaling, netcal.scaling.LogisticCalibration, and netcal.scaling.BetaCalibration.
+Note that all methods can also be applied to object detection and are capable of additional influenting factors
+such as object position and/or shape.
+The advanced methods netcal.scaling.LogisticCalibrationDependent and netcal.scaling.BetaCalibrationDependent
+are able to better represent possible correlations as the underlying probability distributions are joint
+multivariate distributions with possible correlations.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="_autosummary/netcal.regularization.html#module-netcal.regularization" title="netcal.regularization"><code class="xref py py-obj docutils literal notranslate"><span class="pre">regularization</span></code></a></p></td>
-<td><p>Regularization methods which are applied during model training.</p></td>
+<td><p>Regularization Methods for Confidence Calibration
+
+Regularization methods which are applied during model training. These methods should achieve a
+confidence calibration during model training. For example, the Confidence Penalty
+penalizes confident predictions and prohibits over-confident estimates.
+Use the functions to obtain the regularization and callback instances with prebuild parameters.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="_autosummary/netcal.metrics.html#module-netcal.metrics" title="netcal.metrics"><code class="xref py py-obj docutils literal notranslate"><span class="pre">metrics</span></code></a></p></td>
-<td><p>Methods for measuring miscalibration.</p></td>
+<td><p>Metrics Package to Measure Miscalibration
+
+Methods for measuring miscalibration in the context of confidence calibration and regression uncertainty calibration.
+
+The common methods for confidence calibration evaluation are given with the
+netcal.metrics.confidence.ECE (ECE), netcal.metrics.confidence.MCE (MCE), and
+netcal.metrics.confidence.ACE (ACE). Each method bins the samples by their confidence and measures the
+accuracy in each bin. The ECE gives the mean gap between confidence and observed accuracy in each bin weighted by the
+number of samples. The MCE returns the highest observed deviation. The ACE is similar to the ECE but weights
+each bin equally.
+
+The common methods for regression uncertainty evaluation are netcal.metrics.regression.PinballLoss (Pinball
+loss), the netcal.metrics.regression.NLL (NLL), and the netcal.metrics.regression.QCE (M-QCE and
+C-QCE). The Pinball loss as well as the Marginal/Conditional Quantile Calibration Error (M-QCE and C-QCE) evaluate
+the quality of the estimated quantiles compared to the observed ground-truth quantile coverage. The NLL is a proper
+scoring rule to measure the overall quality of the predicted probability distributions.
+
+For a detailed description of the available metrics within regression calibration, see the module doc of
+netcal.regression.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="_autosummary/netcal.presentation.html#module-netcal.presentation" title="netcal.presentation"><code class="xref py py-obj docutils literal notranslate"><span class="pre">presentation</span></code></a></p></td>
-<td><p>Methods for the visualization of miscalibration.</p></td>
+<td><p>Visualization Package
+
+Methods for the visualization of miscalibration in the scope of confidence calibration and regression uncertainty
+calibration.
+
+This package consists of a netcal.presentation.ReliabilityDiagram (Reliability Diagram) method used to
+visualize the calibration properties for confidence
+calibration in the scope of classification, object detection (semantic label confidence) or segmentation.
+Similar to the ACE or ECE, this method bins the samples in equally sized bins by their confidence and
+displays the gap between confidence and observed accuracy in each bin.
+
+For regression uncertainty calibration, this package also holds the netcal.presentation.ReliabilityRegression
+method that is able to visualize the quantile calibration properties of probabilistic regression models, e.g., within
+probabilistic regression or object detection (spatial position uncertainty).
+A complementary diagram is the netcal.presentation.ReliabilityQCE that visualizes the computation of the netcal.metrics.regression.QCE (C-QCE) metric.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="_autosummary/netcal.regression.html#module-netcal.regression" title="netcal.regression"><code class="xref py py-obj docutils literal notranslate"><span class="pre">regression</span></code></a></p></td>
+<td><p>Probabilistic Regression Calibration Package
+
+Methods for uncertainty calibration of probabilistic regression tasks.
+A probabilistic regression model does not only provide a continuous estimate but also an according uncertainty
+(commonly a Gaussian standard deviation/variance).
+The methods within this package are able to recalibrate this uncertainty by means of quantile calibration [1],
+distribution calibration [2], or variance calibration [3], [4].
+
+Quantile calibration [1] requires that a predicted quantile for a quantile level t covers
+approx. 100t% of the ground-truth samples.
+
+Methods for quantile calibration:
+
+IsotonicRegression [1].
+
+Distribution calibration [2] requires that a predicted probability distribution should be equal to the observed
+error distribution. This must hold for all statistical moments.
+
+Methods for distribution calibration:
+
+GPBeta [2].
+
+GPNormal [5].
+
+GPCauchy [5].
+
+Variance calibration [3], [4] requires that the predicted variance of a Gaussian distribution should match the
+observed error variance which is equivalent to the root mean squared error.
+
+Methods for variance calibration:
+
+VarianceScaling [3], [4].
+
+GPNormal [5].
+
+References
+
+[1] Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon:
+&quot;Accurate uncertainties for deep learning using calibrated regression.&quot;
+International Conference on Machine Learning. PMLR, 2018.
+Get source online
+
+[2] Hao Song, Tom Diethe, Meelis Kull and Peter Flach:
+&quot;Distribution calibration for regression.&quot;
+International Conference on Machine Learning. PMLR, 2019.
+Get source online
+
+[3] Levi, Dan, et al.:
+&quot;Evaluating and calibrating uncertainty prediction in regression tasks.&quot;
+arXiv preprint arXiv:1905.11659 (2019).
+Get source online
+
+[4] Laves, Max-Heinrich, et al.:
+&quot;Well-calibrated regression uncertainty in medical imaging with deep learning.&quot;
+Medical Imaging with Deep Learning. PMLR, 2020.
+Get source online
+
+[5] Küppers, Fabian, Schneider, Jonas, and Haselhoff, Anselm:
+&quot;Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.&quot;
+ArXiv preprint arXiv:2207.01242, 2022.
+Get source online</p></td>
 </tr>
 </tbody>
 </table>
 <p>Each calibration method must inherit the base class <a class="reference internal" href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractCalibration</span></code></a>. If you want to write your own method and
 include into the framework, include this class as the base class.</p>
-<table class="longtable docutils align-default">
-<colgroup>
-<col style="width: 10%" />
-<col style="width: 90%" />
-</colgroup>
+</section>
+<section id="base-class">
+<h2>Base class<a class="headerlink" href="#base-class" title="Permalink to this heading">¶</a></h2>
+<table class="autosummary longtable docutils align-default">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AbstractCalibration</span></code></a>([detection, …])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="_autosummary_abstract_calibration/netcal.AbstractCalibration.html#netcal.AbstractCalibration" title="netcal.AbstractCalibration"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AbstractCalibration</span></code></a>([detection, ...])</p></td>
 <td><p>Abstract base class for all calibration methods.</p></td>
 </tr>
 </tbody>
 </table>
-</div>
-<div class="section" id="calibration-framework">
-<h1><a class="toc-backref" href="#id58">Calibration Framework</a><a class="headerlink" href="#calibration-framework" title="Permalink to this headline">¶</a></h1>
-<p>Calibration framework in Python 3 for Neural Networks.
-For full API reference documentation, visit <a class="reference external" href="https://fabiankueppers.github.io/calibration-framework">https://fabiankueppers.github.io/calibration-framework</a>.</p>
-<p>Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-AND Elektronische Fahrwerksysteme GmbH, Gaimersheim, Germany</p>
+</section>
+</section>
+<p><img alt="netcal logo" src="_images/logo_long.png" /></p>
+<section id="net-cal-uncertainty-calibration">
+<h1>net:cal - Uncertainty Calibration<a class="headerlink" href="#net-cal-uncertainty-calibration" title="Permalink to this heading">¶</a></h1>
+<div style="text-align: justify">
+<p>The <strong>net:cal</strong> calibration framework is a Python 3 library for measuring and mitigating miscalibration of uncertainty estimates, e.g., by a neural network.
+For full API reference documentation, visit
+<a class="reference external" href="https://fabiankueppers.github.io/calibration-framework">https://fabiankueppers.github.io/calibration-framework</a>.</p>
+<p>Copyright © 2019-2022 Ruhr West University of Applied Sciences,
+Bottrop, Germany AND e:fs TechHub GmbH, Gaimersheim, Germany.</p>
 <p>This Source Code Form is subject to the terms of the Apache License 2.0.
-If a copy of the APL2 was not distributed with this
-file, You can obtain one at <a class="reference external" href="https://www.apache.org/licenses/LICENSE-2.0.txt">https://www.apache.org/licenses/LICENSE-2.0.txt</a>.</p>
-<p><strong>Important: updated references!</strong> If you use this framework (<em>classification or detection</em>) or parts of it for your research, please cite it by:</p>
+If a copy of the APL2 was not distributed with this file, You can obtain
+one at <a class="reference external" href="https://www.apache.org/licenses/LICENSE-2.0.txt">https://www.apache.org/licenses/LICENSE-2.0.txt</a>.</p>
+<p><strong>Important: updated references!</strong> If you use this framework
+(<em>classification or detection</em>) or parts of it for your research, please
+cite it by:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nd">@InProceedings</span><span class="p">{</span><span class="n">Kueppers_2020_CVPR_Workshops</span><span class="p">,</span>
    <span class="n">author</span> <span class="o">=</span> <span class="p">{</span><span class="n">Küppers</span><span class="p">,</span> <span class="n">Fabian</span> <span class="ow">and</span> <span class="n">Kronenberger</span><span class="p">,</span> <span class="n">Jan</span> <span class="ow">and</span> <span class="n">Shantia</span><span class="p">,</span> <span class="n">Amirhossein</span> <span class="ow">and</span> <span class="n">Haselhoff</span><span class="p">,</span> <span class="n">Anselm</span><span class="p">},</span>
    <span class="n">title</span> <span class="o">=</span> <span class="p">{</span><span class="n">Multivariate</span> <span class="n">Confidence</span> <span class="n">Calibration</span> <span class="k">for</span> <span class="n">Object</span> <span class="n">Detection</span><span class="p">},</span>
@@ -103,187 +406,505 @@ <h1><a class="toc-backref" href="#id58">Calibration Framework</a><a class="heade
 <span class="p">}</span>
 </pre></div>
 </div>
-<p><em>If you use Bayesian calibration methods with uncertainty, please cite it by</em>:</p>
+<p><em>If you use Bayesian calibration methods with uncertainty, please cite
+it by</em>:</p>
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nd">@InProceedings</span><span class="p">{</span><span class="n">Kueppers_2021_IV</span><span class="p">,</span>
-       <span class="n">author</span> <span class="o">=</span> <span class="p">{</span><span class="n">Küppers</span><span class="p">,</span> <span class="n">Fabian</span> <span class="ow">and</span> <span class="n">Kronenberger</span><span class="p">,</span> <span class="n">Jan</span> <span class="ow">and</span> <span class="n">Schneider</span><span class="p">,</span> <span class="n">Jonas</span> <span class="ow">and</span> <span class="n">Haselhoff</span><span class="p">,</span> <span class="n">Anselm</span><span class="p">},</span>
-       <span class="n">title</span> <span class="o">=</span> <span class="p">{</span><span class="n">Bayesian</span> <span class="n">Confidence</span> <span class="n">Calibration</span> <span class="k">for</span> <span class="n">Epistemic</span> <span class="n">Uncertainty</span> <span class="n">Modelling</span><span class="p">},</span>
-       <span class="n">booktitle</span> <span class="o">=</span> <span class="p">{</span><span class="n">Proceedings</span> <span class="n">of</span> <span class="n">the</span> <span class="n">IEEE</span> <span class="n">Intelligent</span> <span class="n">Vehicles</span> <span class="n">Symposium</span> <span class="p">(</span><span class="n">IV</span><span class="p">)},</span>
-       <span class="n">month</span> <span class="o">=</span> <span class="p">{</span><span class="n">July</span><span class="p">},</span>
-       <span class="n">year</span> <span class="o">=</span> <span class="p">{</span><span class="mi">2021</span><span class="p">},</span>
-    <span class="p">}</span>
+   <span class="n">author</span> <span class="o">=</span> <span class="p">{</span><span class="n">Küppers</span><span class="p">,</span> <span class="n">Fabian</span> <span class="ow">and</span> <span class="n">Kronenberger</span><span class="p">,</span> <span class="n">Jan</span> <span class="ow">and</span> <span class="n">Schneider</span><span class="p">,</span> <span class="n">Jonas</span> <span class="ow">and</span> <span class="n">Haselhoff</span><span class="p">,</span> <span class="n">Anselm</span><span class="p">},</span>
+   <span class="n">title</span> <span class="o">=</span> <span class="p">{</span><span class="n">Bayesian</span> <span class="n">Confidence</span> <span class="n">Calibration</span> <span class="k">for</span> <span class="n">Epistemic</span> <span class="n">Uncertainty</span> <span class="n">Modelling</span><span class="p">},</span>
+   <span class="n">booktitle</span> <span class="o">=</span> <span class="p">{</span><span class="n">Proceedings</span> <span class="n">of</span> <span class="n">the</span> <span class="n">IEEE</span> <span class="n">Intelligent</span> <span class="n">Vehicles</span> <span class="n">Symposium</span> <span class="p">(</span><span class="n">IV</span><span class="p">)},</span>
+   <span class="n">month</span> <span class="o">=</span> <span class="p">{</span><span class="n">July</span><span class="p">},</span>
+   <span class="n">year</span> <span class="o">=</span> <span class="p">{</span><span class="mi">2021</span><span class="p">},</span>
+<span class="p">}</span>
 </pre></div>
 </div>
-<div class="contents topic" id="table-of-contents">
-<p class="topic-title">Table of Contents</p>
+<p><em>If you use Regression calibration methods, please cite it by</em>:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nd">@InProceedings</span><span class="p">{</span><span class="n">Kueppers_2022_ECCV_Workshops</span><span class="p">,</span>
+  <span class="n">author</span>    <span class="o">=</span> <span class="p">{</span><span class="n">Küppers</span><span class="p">,</span> <span class="n">Fabian</span> <span class="ow">and</span> <span class="n">Schneider</span><span class="p">,</span> <span class="n">Jonas</span> <span class="ow">and</span> <span class="n">Haselhoff</span><span class="p">,</span> <span class="n">Anselm</span><span class="p">},</span>
+  <span class="n">title</span>     <span class="o">=</span> <span class="p">{</span><span class="n">Parametric</span> <span class="ow">and</span> <span class="n">Multivariate</span> <span class="n">Uncertainty</span> <span class="n">Calibration</span> <span class="k">for</span> <span class="n">Regression</span> <span class="ow">and</span> <span class="n">Object</span> <span class="n">Detection</span><span class="p">},</span>
+  <span class="n">booktitle</span> <span class="o">=</span> <span class="p">{</span><span class="n">European</span> <span class="n">Conference</span> <span class="n">on</span> <span class="n">Computer</span> <span class="n">Vision</span> <span class="p">(</span><span class="n">ECCV</span><span class="p">)</span> <span class="n">Workshops</span><span class="p">},</span>
+  <span class="n">year</span>      <span class="o">=</span> <span class="p">{</span><span class="mi">2022</span><span class="p">},</span>
+  <span class="n">month</span>     <span class="o">=</span> <span class="p">{</span><span class="n">October</span><span class="p">},</span>
+  <span class="n">publisher</span> <span class="o">=</span> <span class="p">{</span><span class="n">Springer</span><span class="p">},</span>
+<span class="p">}</span>
+</pre></div>
+</div>
+<section id="table-of-contents">
+<h2>Table of Contents<a class="headerlink" href="#table-of-contents" title="Permalink to this heading">¶</a></h2>
 <ul class="simple">
-<li><p><a class="reference internal" href="#api-reference" id="id57">API Reference</a></p></li>
-<li><p><a class="reference internal" href="#calibration-framework" id="id58">Calibration Framework</a></p></li>
-<li><p><a class="reference internal" href="#overview" id="id59">Overview</a></p>
+<li><p><span class="xref myst">Overview</span></p>
 <ul>
-<li><p><a class="reference internal" href="#update-on-version-1-2" id="id60">Update on version 1.2</a></p></li>
-<li><p><a class="reference internal" href="#update-on-version-1-1" id="id61">Update on version 1.1</a></p></li>
+<li><p><span class="xref myst">Update on version 1.3</span></p></li>
+<li><p><span class="xref myst">Update on version 1.2</span></p></li>
+<li><p><span class="xref myst">Update on version 1.1</span></p></li>
 </ul>
 </li>
-<li><p><a class="reference internal" href="#installation" id="id62">Installation</a></p>
+<li><p><span class="xref myst">Installation</span></p></li>
+<li><p><span class="xref myst">Requirements</span></p></li>
+<li><p><span class="xref myst">Calibration Metrics</span></p>
 <ul>
-<li><p><a class="reference internal" href="#requirements" id="id63">Requirements</a></p></li>
+<li><p><span class="xref myst">Confidence Calibration Metrics</span></p></li>
+<li><p><span class="xref myst">Regression Calibration Metrics</span></p></li>
 </ul>
 </li>
-<li><p><a class="reference internal" href="#calibration-metrics" id="id64">Calibration Metrics</a></p></li>
-<li><p><a class="reference internal" href="#methods" id="id65">Methods</a></p>
+<li><p><span class="xref myst">Methods</span></p>
+<ul>
+<li><p><span class="xref myst">Confidence Calibration Methods</span></p>
 <ul>
-<li><p><a class="reference internal" href="#binning" id="id66">Binning</a></p></li>
-<li><p><a class="reference internal" href="#scaling" id="id67">Scaling</a></p></li>
-<li><p><a class="reference internal" href="#regularization" id="id68">Regularization</a></p></li>
+<li><p><span class="xref myst">Binning</span></p></li>
+<li><p><span class="xref myst">Scaling</span></p></li>
+<li><p><span class="xref myst">Regularization</span></p></li>
 </ul>
 </li>
-<li><p><a class="reference internal" href="#visualization" id="id69">Visualization</a></p></li>
-<li><p><a class="reference internal" href="#examples" id="id70">Examples</a></p>
+<li><p><span class="xref myst">Regression Calibration Methods</span></p>
 <ul>
-<li><p><a class="reference internal" href="#classification" id="id71">Classification</a></p></li>
-<li><p><a class="reference internal" href="#detection" id="id72">Detection</a></p></li>
-<li><p><a class="reference internal" href="#uncertainty-in-calibration" id="id73">Uncertainty in Calibration</a></p></li>
+<li><p><span class="xref myst">Non-parametric calibration</span></p></li>
+<li><p><span class="xref myst">Parametric calibration</span></p></li>
 </ul>
 </li>
-<li><p><a class="reference internal" href="#references" id="id74">References</a></p></li>
 </ul>
-</div>
-</div>
-<div class="section" id="overview">
-<h1><a class="toc-backref" href="#id59">Overview</a><a class="headerlink" href="#overview" title="Permalink to this headline">¶</a></h1>
-<p>This framework is designed to calibrate the confidence estimates of classifiers like neural networks. Modern neural networks are likely to be overconfident with their predictions. However, reliable confidence estimates of such classifiers are crucial especially in safety-critical applications.</p>
-<p>For example: given 100 predictions with a confidence of 80% of each prediction, the observed accuracy should also match 80% (neither more nor less). This behaviour is achievable with several calibration methods.</p>
-<div class="section" id="update-on-version-1-2">
-<h2><a class="toc-backref" href="#id60">Update on version 1.2</a><a class="headerlink" href="#update-on-version-1-2" title="Permalink to this headline">¶</a></h2>
-<p>TL;DR:
-- Bayesian confidence calibration: train and infer scaling methods using variational inference (VI) and MCMC sampling
-- New metrics: MMCE <a class="footnote-reference brackets" href="#id54" id="id1">13</a> and PICP <a class="footnote-reference brackets" href="#id55" id="id2">14</a> (<em>netcal.metrics.MMCE</em> and <em>netcal.metrics.PICP</em>)
-- New regularization methods: MMCE <a class="footnote-reference brackets" href="#id54" id="id3">13</a> and DCA <a class="footnote-reference brackets" href="#id56" id="id4">15</a> (<em>netcal.regularization.MMCEPenalty</em> and <em>netcal.regularization.DCAPenalty</em>)
-- Updated examples
-- Switched license from MPL2 to APL2</p>
-<p>Now you can also use Bayesian methods to obtain uncertainty within a calibration mapping mainly in the <em>netcal.scaling</em> package. We adapted Markov-Chain Monte-Carlo sampling (MCMC) as well as Variational Inference (VI) on common calibration methods.
-It is also easily possible to bring the scaling methods to CUDA in order to speed-up the computations. We further provide new metrics to evaluate confidence calibration (MMCE) and to evaluate the quality of prediction intervals (PICP).
-Finally, we updated our framework by new regularization methods that can be used during model training (MMCE and DCA).</p>
-</div>
-<div class="section" id="update-on-version-1-1">
-<h2><a class="toc-backref" href="#id61">Update on version 1.1</a><a class="headerlink" href="#update-on-version-1-1" title="Permalink to this headline">¶</a></h2>
-<p>This framework can also be used to calibrate object detection models. It has recently been shown that calibration on object detection also depends on the position and/or scale of a predicted object <a class="footnote-reference brackets" href="#id53" id="id5">12</a>. We provide calibration methods to perform confidence calibration w.r.t. the additional box regression branch.
-For this purpose, we extended the commonly used Histogram Binning <a class="footnote-reference brackets" href="#id44" id="id6">3</a>, Logistic Calibration alias Platt scaling <a class="footnote-reference brackets" href="#id51" id="id7">10</a> and the Beta Calibration method <a class="footnote-reference brackets" href="#id43" id="id8">2</a> to also include the bounding box information into a calibration mapping.
-Furthermore, we provide two new methods called the <em>Dependent Logistic Calibration</em> and the <em>Dependent Beta Calibration</em> that are not only able to perform a calibration mapping
-w.r.t. additional bounding box information but also to model correlations and dependencies between all given quantities <a class="footnote-reference brackets" href="#id53" id="id9">12</a>. Those methods should be preffered over their counterparts in object detection mode.</p>
+</li>
+<li><p><span class="xref myst">Visualization</span></p></li>
+<li><p><span class="xref myst">Examples</span></p>
+<ul>
+<li><p><span class="xref myst">Classification</span></p>
+<ul>
+<li><p><span class="xref myst">Post-hoc Calibration for Classification</span></p></li>
+<li><p><span class="xref myst">Measuring Miscalibration for Classification</span></p></li>
+<li><p><span class="xref myst">Visualizing Miscalibration for Classification</span></p></li>
+</ul>
+</li>
+<li><p><span class="xref myst">Detection (Confidence of Objects)</span></p>
+<ul>
+<li><p><span class="xref myst">Post-hoc Calibration for Detection</span></p></li>
+<li><p><span class="xref myst">Measuring Miscalibration for Detection</span></p></li>
+<li><p><span class="xref myst">Visualizing Miscalibration for Detection</span></p></li>
+</ul>
+</li>
+<li><p><span class="xref myst">Uncertainty in Confidence Calibration</span></p>
+<ul>
+<li><p><span class="xref myst">Post-hoc Calibration with Uncertainty</span></p></li>
+<li><p><span class="xref myst">Measuing Miscalibration with Uncertainty</span></p></li>
+</ul>
+</li>
+<li><p><span class="xref myst">Probabilistic Regression</span></p>
+<ul>
+<li><p><span class="xref myst">Post-hoc Calibration (Parametric)</span></p></li>
+<li><p><span class="xref myst">Post-hoc Calibration (Non-Parametric)</span></p></li>
+<li><p><span class="xref myst">Correlation Estimation and Recalibration</span></p></li>
+<li><p><span class="xref myst">Measuring Miscalibration for Regression</span></p></li>
+<li><p><span class="xref myst">Visualizing Miscalibration for Regression</span></p></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><p><span class="xref myst">References</span></p></li>
+</ul>
+</section>
+<section id="overview">
+<h2>Overview<a class="headerlink" href="#overview" title="Permalink to this heading">¶</a></h2>
+<p>This framework is designed to calibrate the confidence estimates of
+classifiers like neural networks. Modern neural networks are likely to
+be overconfident with their predictions. However, reliable confidence
+estimates of such classifiers are crucial especially in safety-critical
+applications.</p>
+<p>For example: given 100 predictions with a confidence of 80% of each
+prediction, the observed accuracy should also match 80% (neither more
+nor less). This behaviour is achievable with several calibration
+methods.</p>
+<section id="update-on-version-1-3">
+<h3>Update on version 1.3<a class="headerlink" href="#update-on-version-1-3" title="Permalink to this heading">¶</a></h3>
+<p>TL;DR:</p>
+<ul class="simple">
+<li><p>Regression calibration methods: train and infer methods to rescale the uncertainty of probabilistic regression models</p></li>
+<li><p>New package: <em>netcal.regression</em> with regression calibration methods:</p>
+<ul>
+<li><p>Isotonic Regression (<em>netcal.regression.IsotonicRegression</em>)</p></li>
+<li><p>Variance Scaling (<em>netcal.regression.VarianceScaling</em>)</p></li>
+<li><p>GP-Beta (<em>netcal.regression.GPBeta</em>)</p></li>
+<li><p>GP-Normal (<em>netcal.regression.GPNormal</em>)</p></li>
+<li><p>GP-Cauchy (<em>netcal.regression.GPCauchy</em>)</p></li>
+</ul>
+</li>
+<li><p>Implement <em>netcal.regression.GPNormal</em> method with correlation estimation and recalibration</p></li>
+<li><p>Restructured <em>netcal.metrics</em> package to distinguish between (semantic) confidence calibration in <em>netcal.confidence</em> and regression uncertainty calibration in <em>netcal.regression</em>:</p>
+<ul>
+<li><p>Expected Calibration Error (ECE - <em>netcal.confidence.ECE</em>)</p></li>
+<li><p>Maximum Calibration Error (MCE - <em>netcal.confidence.MCE</em>)</p></li>
+<li><p>Average Calibration Error (ACE - <em>netcal.confidence.ACE</em>)</p></li>
+<li><p>Maximum Mean Calibration Error (MMCE - <em>netcal.confidence.MMCE</em>)</p></li>
+<li><p>Negative Log Likelihood (NLL - <em>netcal.regression.NLL</em>)</p></li>
+<li><p>Prediction Interval Coverage Probability (PICP - <em>netcal.regression.PICP</em>)</p></li>
+<li><p>Pinball loss (<em>netcal.regression.PinballLoss</em>)</p></li>
+<li><p>Uncertainty Calibration Error (UCE - <em>netcal.regression.UCE</em>)</p></li>
+<li><p>Expected Normalized Calibration Error (ENCE - <em>netcal.regression.ENCE</em>)</p></li>
+<li><p>Quantile Calibration Error (QCE - <em>netcal.regression.QCE</em>)</p></li>
+</ul>
+</li>
+<li><p>Added new types of reliability diagrams to visualize regression calibration properties:</p>
+<ul>
+<li><p>Reliability Regression diagram to visualize calibration for different quantile levels (preferred - <em>netcal.presentation.ReliabilityRegression</em>)</p></li>
+<li><p>Reliability QCE diagram to visualize QCE over stddev (<em>netcal.presentation.QCE</em>)</p></li>
+</ul>
+</li>
+<li><p>Updated examples</p></li>
+<li><p>Minor bugfixes</p></li>
+<li><p>Use library <a class="reference external" href="https://github.com/texworld/tikzplotlib">tikzplotlib</a> within the <em>netcal.presentation</em> package to enable a direct conversion of <em>matplotlib.Figure</em> objects to Tikz-Code (e.g., can be used for LaTeX figures)</p></li>
+</ul>
+<p>Within this release, we provide a new package <em>netcal.regression</em> to
+enable recalibration of probabilistic regression tasks. Within
+probabilistic regression, a regression model does not output a single
+score for each prediction but rather a probability distribution (e.g.,
+Gaussian with mean/variance) that targets the true output score. Similar
+to (semantic) confidence calibration, regression calibration requires
+that the estimated uncertainty matches the observed error distribution.
+There exist several definitions for regression calibration which the
+provided calibration methods aim to mitigate (cf. README within the
+<em>netcal.regression</em> package). We distinguish the provided calibration
+methods into non-parametric and parametric methods. Non-parametric
+calibration methods take a probability distribution as input and apply
+recalibration in terms of quantiles on the cumulative (CDF). This leads
+to a recalibrated probability distribution that, however, has no
+analytical representation but is given by certain points defining a CDF
+distribution. Non-parametric calibration methods are
+<em>netcal.regression.IsotonicRegression</em> and <em>netcal.regression.GPBeta</em>.</p>
+<p>In contrast, parametric calibration methods also take a probability
+distribution as input and provide a recalibrated distribution that has
+an analytical expression (e.g., Gaussian). Parametric calibration
+methods are <em>netcal.regression.VarianceScaling</em>,
+<em>netcal.regression.GPNormal</em>, and <em>netcal.regression.GPCauchy</em>.</p>
+<p>The calibration methods are designed to also work with multiple
+independent dimensions. The methods
+<em>netcal.regression.IsotonicRegression</em> and
+<em>netcal.regression.VarianceScaling</em> apply a recalibration of each
+dimension independently of each other. In contrast, the GP methods
+<em>netcal.regression.GPBeta</em>, <em>netcal.regression.GPNormal</em>, and
+<em>netcal.regression.GPCauchy</em> use a single GP to apply recalibration.
+Furthermore, the GP-Normal <em>netcal.regression.GPNormal</em> is can model
+possible correlations within the training data to transform multiple
+univariate probability distributions of a single sample to a joint
+multivariate (normal) distribution with possible correlations. This
+calibration scheme is denoted as <em>correlation estimation</em>. Additionally,
+the GP-Normal is also able to take a multivariate (normal) distribution
+with correlations as input and applies a recalibration of the whole
+covariance matrix. This is referred to as <em>correlation recalibration</em>.</p>
+<p>Besides the recalibration methods, we restructured the <em>netcal.metrics</em>
+package which now also holds several metrics for regression calibration
+(cf. <em>netcal.metrics</em> package documentation for detailed information).
+Finally, we provide several ways to visualize regression miscalibration
+within the <em>netcal.presentation</em> package.</p>
+<p>All plot-methods within the <em>netcal.presentation</em> package now support
+the option “tikz=True” which switches from standard
+<em>matplotlib.Figure</em> objects to strings with Tikz-Code. Tikz-code can be
+directly used for LaTeX documents to render images as vector graphics
+with high quality. Thus, this option helps to improve the quality of
+your reliability diagrams if you are planning to use this library for
+any type of publication/document</p>
+</section>
+<section id="update-on-version-1-2">
+<h3>Update on version 1.2<a class="headerlink" href="#update-on-version-1-2" title="Permalink to this heading">¶</a></h3>
+<p>TL;DR:</p>
+<ul class="simple">
+<li><p>Bayesian confidence calibration: train and infer scaling methods using variational inference (VI) and MCMC sampling</p></li>
+<li><p>New metrics: MMCE <span class="xref myst">[13]</span> and PICP <span class="xref myst">[14]</span> (<em>netcal.metrics.MMCE</em> and <em>netcal.metrics.PICP</em>)</p></li>
+<li><p>New regularization methods: MMCE <span class="xref myst">[13]</span> and DCA <span class="xref myst">[15]</span> (<em>netcal.regularization.MMCEPenalty</em> and <em>netcal.regularization.DCAPenalty</em>)</p></li>
+<li><p>Updated examples</p></li>
+<li><p>Switched license from MPL2 to APL2</p></li>
+</ul>
+<p>Now you can also use Bayesian methods to obtain uncertainty within a
+calibration mapping mainly in the <em>netcal.scaling</em> package. We adapted
+Markov-Chain Monte-Carlo sampling (MCMC) as well as Variational
+Inference (VI) on common calibration methods. It is also easily possible
+to bring the scaling methods to CUDA in order to speed-up the
+computations. We further provide new metrics to evaluate confidence
+calibration (MMCE) and to evaluate the quality of prediction intervals
+(PICP). Finally, we updated our framework by new regularization methods
+that can be used during model training (MMCE and DCA).</p>
+</section>
+<section id="update-on-version-1-1">
+<h3>Update on version 1.1<a class="headerlink" href="#update-on-version-1-1" title="Permalink to this heading">¶</a></h3>
+<p>This framework can also be used to calibrate object detection models. It
+has recently been shown that calibration on object detection also
+depends on the position and/or scale of a predicted object <span class="xref myst">[12]</span>. We
+provide calibration methods to perform confidence calibration w.r.t. the
+additional box regression branch. For this purpose, we extended the
+commonly used Histogram Binning <span class="xref myst">[3]</span>, Logistic Calibration alias Platt
+scaling <span class="xref myst">[10]</span> and the Beta Calibration method <span class="xref myst">[2]</span> to also include the
+bounding box information into a calibration mapping. Furthermore, we
+provide two new methods called the <em>Dependent Logistic Calibration</em> and
+the <em>Dependent Beta Calibration</em> that are not only able to perform a
+calibration mapping w.r.t. additional bounding box information but also
+to model correlations and dependencies between all given quantities <span class="xref myst">[12]</span>.
+Those methods should be preffered over their counterparts in object
+detection mode.</p>
 <p>The framework is structured as follows:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">netcal</span>
-  <span class="o">.</span><span class="n">binning</span>         <span class="c1"># binning methods</span>
-  <span class="o">.</span><span class="n">scaling</span>         <span class="c1"># scaling methods</span>
-  <span class="o">.</span><span class="n">regularization</span>  <span class="c1"># regularization methods</span>
-  <span class="o">.</span><span class="n">presentation</span>    <span class="c1"># presentation methods</span>
-  <span class="o">.</span><span class="n">metrics</span>         <span class="c1"># metrics for measuring miscalibration</span>
-
-<span class="n">examples</span>           <span class="c1"># example code snippets</span>
+<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>netcal
+  .binning         # binning methods (confidence calibration)
+  .scaling         # scaling methods (confidence calibration)
+  .regularization  # regularization methods (confidence calibration)
+  .presentation    # presentation methods (confidence/regression calibration)
+  .metrics         # metrics for measuring miscalibration (confidence/regression calibration)
+  .regression      # methods for regression uncertainty calibration (regression calibration)
+
+examples           # example code snippets
 </pre></div>
 </div>
-</div>
-</div>
-<div class="section" id="installation">
-<h1><a class="toc-backref" href="#id62">Installation</a><a class="headerlink" href="#installation" title="Permalink to this headline">¶</a></h1>
-<p>The installation of the calibration suite is quite easy with setuptools. You can either install this framework using PIP:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pip3</span> <span class="n">install</span> <span class="n">netcal</span>
+</section>
+</section>
+<section id="installation">
+<h2>Installation<a class="headerlink" href="#installation" title="Permalink to this heading">¶</a></h2>
+<p>The installation of the calibration suite is quite easy as it registered
+in the Python Package Index (PyPI). You can either install this
+framework using PIP:</p>
+<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>    $ python3 -m pip install netcal
 </pre></div>
 </div>
-<p>Or simply invoke the following command to install the calibration suite:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">python3</span> <span class="n">setup</span><span class="o">.</span><span class="n">py</span> <span class="n">install</span>
+<p>Or simply invoke the following command to install the calibration suite when installing from source:</p>
+<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>    $ git clone https://github.com/fabiankueppers/calibration-framework.git
+    $ <span class="nb">cd</span> calibration-framework
+    $ python3 -m pip install .
 </pre></div>
 </div>
-<div class="section" id="requirements">
-<h2><a class="toc-backref" href="#id63">Requirements</a><a class="headerlink" href="#requirements" title="Permalink to this headline">¶</a></h2>
+<p>Note: with update 1.3, we switched from <em>setup.py</em> to <em>pyproject.toml</em>
+according to PEP-518. The <em>setup.py</em> is only for backwards
+compatibility.</p>
+<section id="requirements">
+<h3>Requirements<a class="headerlink" href="#requirements" title="Permalink to this heading">¶</a></h3>
+<p>According to <em>requierments.txt</em>:</p>
 <ul class="simple">
-<li><p>numpy&gt;=1.17</p></li>
-<li><p>scipy&gt;=1.3</p></li>
-<li><p>matplotlib&gt;=3.1</p></li>
-<li><p>scikit-learn&gt;=0.21</p></li>
-<li><p>torch&gt;=1.4</p></li>
-<li><p>torchvision&gt;=0.5.0</p></li>
+<li><p>numpy&gt;=1.18</p></li>
+<li><p>scipy&gt;=1.4</p></li>
+<li><p>matplotlib&gt;=3.3</p></li>
+<li><p>scikit-learn&gt;=0.24</p></li>
+<li><p>torch&gt;=1.9</p></li>
+<li><p>torchvision&gt;=0.10.0</p></li>
 <li><p>tqdm&gt;=4.40</p></li>
-<li><p>pyro-ppl&gt;=1.3</p></li>
+<li><p>pyro-ppl&gt;=1.8</p></li>
 <li><p>tikzplotlib&gt;=0.9.8</p></li>
 <li><p>tensorboard&gt;=2.2</p></li>
+<li><p>gpytorch&gt;=1.5.1</p></li>
 </ul>
-</div>
-</div>
-<div class="section" id="calibration-metrics">
-<h1><a class="toc-backref" href="#id64">Calibration Metrics</a><a class="headerlink" href="#calibration-metrics" title="Permalink to this headline">¶</a></h1>
-<p>The most common metric to determine miscalibration in the scope of classification is the <em>Expected Calibration Error</em> (ECE) <a class="footnote-reference brackets" href="#id42" id="id10">1</a>. This metric divides the confidence space into several bins and measures the observed accuracy in each bin. The bin gaps between observed accuracy and bin confidence are summed up and weighted by the amount of samples in each bin. The <em>Maximum Calibration Error</em> (MCE) denotes the highest gap over all bins. The <em>Average Calibration Error</em> (ACE) <a class="footnote-reference brackets" href="#id52" id="id11">11</a> denotes the average miscalibration where each bin gets weighted equally.
-For object detection, we implemented the <em>Detection Calibration Error</em> (D-ECE) <a class="footnote-reference brackets" href="#id53" id="id12">12</a> that is the natural extension of the ECE to object detection tasks. The miscalibration is determined w.r.t. the bounding box information provided (e.g. box location and/or scale). For this purpose, all available information gets binned in a multidimensional histogram. The accuracy is then calculated in each bin separately to determine the mean deviation between confidence and accuracy.</p>
+</section>
+</section>
+<section id="calibration-metrics">
+<h2>Calibration Metrics<a class="headerlink" href="#calibration-metrics" title="Permalink to this heading">¶</a></h2>
+<p>We further distinguish between <em>onfidence calibration</em> which aims to
+recalibrate confidence estimates in the [0, 1] interval, and
+<em>regression uncertainty calibration</em> which addresses the problem of
+calibration in probabilistic regression settings.</p>
+<section id="confidence-calibration-metrics">
+<h3>Confidence Calibration Metrics<a class="headerlink" href="#confidence-calibration-metrics" title="Permalink to this heading">¶</a></h3>
+<p>The most common metric to determine miscalibration in the scope of
+classification is the <em>Expected Calibration Error</em> (ECE) <span class="xref myst">[1]</span>. This
+metric divides the confidence space into several bins and measures the
+observed accuracy in each bin. The bin gaps between observed accuracy
+and bin confidence are summed up and weighted by the amount of samples
+in each bin. The <em>Maximum Calibration Error</em> (MCE) denotes the highest
+gap over all bins. The <em>Average Calibration Error</em> (ACE) <span class="xref myst">[11]</span> denotes
+the average miscalibration where each bin gets weighted equally. For
+object detection, we implemented the <em>Detection Calibration Error</em>
+(D-ECE) <span class="xref myst">[12]</span> that is the natural extension of the ECE to object
+detection tasks. The miscalibration is determined w.r.t. the bounding
+box information provided (e.g. box location and/or scale). For this
+purpose, all available information gets binned in a multidimensional
+histogram. The accuracy is then calculated in each bin separately to
+determine the mean deviation between confidence and accuracy.</p>
 <ul class="simple">
-<li><p>(Detection) Expected Calibration Error <a class="footnote-reference brackets" href="#id42" id="id13">1</a>, <a class="footnote-reference brackets" href="#id53" id="id14">12</a> (<em>netcal.metrics.ECE</em>)</p></li>
-<li><p>(Detection) Maximum Calibration Error <a class="footnote-reference brackets" href="#id42" id="id15">1</a>, <a class="footnote-reference brackets" href="#id53" id="id16">12</a>  (<em>netcal.metrics.MCE</em>)</p></li>
-<li><p>(Detection) Average Calibration Error <a class="footnote-reference brackets" href="#id52" id="id17">11</a>, <a class="footnote-reference brackets" href="#id53" id="id18">12</a> (<em>netcal.metrics.ACE</em>)</p></li>
-<li><p>Maximum Mean Calibration Error (MMCE) <a class="footnote-reference brackets" href="#id54" id="id19">13</a> (<em>netcal.metrics.MMCE</em>) (no position-dependency)</p></li>
-<li><p>Prediction interval coverage probability (PICP) (<em>netcal.metrics.PICP</em>) - this score is not a direct measure of confidence calibration but rather to measure the quality of uncertainty prediction intervals.</p></li>
+<li><p>(Detection) Expected Calibration Error <span class="xref myst">[1]</span>, <span class="xref myst">[12]</span> (<em>netcal.metrics.ECE</em>)</p></li>
+<li><p>(Detection) Maximum Calibration Error <span class="xref myst">[1]</span>, <span class="xref myst">[12]</span>  (<em>netcal.metrics.MCE</em>)</p></li>
+<li><p>(Detection) Average Calibration Error <span class="xref myst">[11]</span>, <span class="xref myst">[12]</span> (<em>netcal.metrics.ACE</em>)</p></li>
+<li><p>Maximum Mean Calibration Error (MMCE) <span class="xref myst">[13]</span> (<em>netcal.metrics.MMCE</em>) (no position-dependency)</p></li>
 </ul>
-</div>
-<div class="section" id="methods">
-<h1><a class="toc-backref" href="#id65">Methods</a><a class="headerlink" href="#methods" title="Permalink to this headline">¶</a></h1>
-<p>The post-hoc calibration methods are separated into binning and scaling methods. The binning methods divide the available information into several bins (like ECE or D-ECE) and perform calibration on each bin. The scaling methods scale the confidence estimates or logits directly to calibrated confidence estimates - on detection calibration, this is done w.r.t. the additional regression branch of a network.</p>
-<p>Important: if you use the detection mode, you need to specifiy the flag “detection=True” in the constructor of the according method (this is not necessary for <em>netcal.scaling.LogisticCalibrationDependent</em> and <em>netcal.scaling.BetaCalibrationDependent</em>).</p>
-<p>Most of the calibration methods are designed for binary classification tasks. For binning methods, multi-class calibration is performed in “one vs. all” by default.</p>
-<p>Some methods like “Isotonic Regression” utilize methods from the scikit-learn API <a class="footnote-reference brackets" href="#id50" id="id20">9</a>.</p>
-<p>Another group are the regularization tools which are added to the loss during the training of a Neural Network.</p>
-<div class="section" id="binning">
-<h2><a class="toc-backref" href="#id66">Binning</a><a class="headerlink" href="#binning" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="regression-calibration-metrics">
+<h3>Regression Calibration Metrics<a class="headerlink" href="#regression-calibration-metrics" title="Permalink to this heading">¶</a></h3>
+<p>In regression calibration, the most common metric is the <em>Negative Log
+Likelihood</em> (NLL) to measure the quality of a predicted probability
+distribution w.r.t. the ground-truth:</p>
+<ul class="simple">
+<li><p>Negative Log Likelihood (NLL) (<em>netcal.metrics.NLL</em>)</p></li>
+</ul>
+<p>The metrics <em>Pinball Loss</em>, <em>Prediction Interval Coverage Probability</em>
+(PICP), and <em>Quantile Calibration Error</em> (QCE) evaluate the estimated
+distributions by means of the predicted quantiles. For example, if a
+forecaster makes 100 predictions using a probability distribution for
+each estimate targeting the true ground-truth, we can measure the
+coverage of the ground-truth samples for a certain quantile level (e.g.,
+95% quantile). If the relative amount of ground-truth samples falling
+into a certain predicted quantile is above or below the specified
+quantile level, a forecaster is told to be miscalibrated in terms of
+<em>quantile calibration</em>. Appropriate metrics in this context are</p>
+<ul class="simple">
+<li><p>Pinball Loss (<em>netcal.metrics.PinballLoss</em>)</p></li>
+<li><p>Prediction Interval Coverage Probability (PICP) <span class="xref myst">[14]</span> (<em>netcal.metrics.PICP</em>)</p></li>
+<li><p>Quantile Calibration Error (QCE) <span class="xref myst">[15]</span> (<em>netcal.metrics.QCE</em>)</p></li>
+</ul>
+<p>Finally, if we work with normal distributions, we can measure the
+quality of the predicted variance/stddev estimates. For <em>variance
+calibration</em>, it is required that the predicted variance mathes the
+observed error variance which is equivalent to then Mean Squared Error
+(MSE). Metrics for <em>variance calibration</em> are</p>
+<ul class="simple">
+<li><p>Expected Normalized Calibration Error (ENCE) <span class="xref myst">[17]</span> (<em>netcal.metrics.ENCE</em>)</p></li>
+<li><p>Uncertainty Calibration Error (UCE) <span class="xref myst">[18]</span> (<em>netcal.metrics.UCE</em>)</p></li>
+</ul>
+</section>
+</section>
+<section id="methods">
+<h2>Methods<a class="headerlink" href="#methods" title="Permalink to this heading">¶</a></h2>
+<p>We further give an overview about the post-hoc calibration methods for
+(semantic) confidence calibration as well as about the methods for
+regression uncertainty calibration.</p>
+<section id="confidence-calibration-methods">
+<h3>Confidence Calibration Methods<a class="headerlink" href="#confidence-calibration-methods" title="Permalink to this heading">¶</a></h3>
+<p>The post-hoc calibration methods are separated into binning and scaling
+methods. The binning methods divide the available information into
+several bins (like ECE or D-ECE) and perform calibration on each bin.
+The scaling methods scale the confidence estimates or logits directly to
+calibrated confidence estimates - on detection calibration, this is done
+w.r.t. the additional regression branch of a network.</p>
+<p>Important: if you use the detection mode, you need to specifiy the flag
+“detection=True” in the constructor of the according method (this is
+not necessary for <em>netcal.scaling.LogisticCalibrationDependent</em> and
+<em>netcal.scaling.BetaCalibrationDependent</em>).</p>
+<p>Most of the calibration methods are designed for binary classification
+tasks. For binning methods, multi-class calibration is performed in
+“one vs. all” by default.</p>
+<p>Some methods such as “Isotonic Regression” utilize methods from the
+scikit-learn API <span class="xref myst">[9]</span>.</p>
+<p>Another group are the regularization tools which are added to the loss
+during the training of a Neural Network.</p>
+<section id="binning">
+<h4>Binning<a class="headerlink" href="#binning" title="Permalink to this heading">¶</a></h4>
 <p>Implemented binning methods are:</p>
 <ul class="simple">
-<li><p>Histogram Binning for classification <a class="footnote-reference brackets" href="#id44" id="id21">3</a>, <a class="footnote-reference brackets" href="#id45" id="id22">4</a> and object detection <a class="footnote-reference brackets" href="#id53" id="id23">12</a> (<em>netcal.binning.HistogramBinning</em>)</p></li>
-<li><p>Isotonic Regression <a class="footnote-reference brackets" href="#id45" id="id24">4</a>, <a class="footnote-reference brackets" href="#id46" id="id25">5</a> (<em>netcal.binning.IsotonicRegression</em>)</p></li>
-<li><p>Bayesian Binning into Quantiles (BBQ) <a class="footnote-reference brackets" href="#id42" id="id26">1</a> (<em>netcal.binning.BBQ</em>)</p></li>
-<li><p>Ensemble of Near Isotonic Regression (ENIR) <a class="footnote-reference brackets" href="#id47" id="id27">6</a> (<em>netcal.binning.ENIR</em>)</p></li>
+<li><p>Histogram Binning for classification <span class="xref myst">[3]</span>, <span class="xref myst">[4]</span> and object detection <span class="xref myst">[12]</span> (<em>netcal.binning.HistogramBinning</em>)</p></li>
+<li><p>Isotonic Regression <span class="xref myst">[4]</span>,<span class="xref myst">[5]</span> (<em>netcal.binning.IsotonicRegression</em>)</p></li>
+<li><p>Bayesian Binning into Quantiles (BBQ) <span class="xref myst">[1]</span> (<em>netcal.binning.BBQ</em>)</p></li>
+<li><p>Ensemble of Near Isotonic Regression (ENIR) <span class="xref myst">[6]</span> (<em>netcal.binning.ENIR</em>)</p></li>
 </ul>
-</div>
-<div class="section" id="scaling">
-<h2><a class="toc-backref" href="#id67">Scaling</a><a class="headerlink" href="#scaling" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="scaling">
+<h4>Scaling<a class="headerlink" href="#scaling" title="Permalink to this heading">¶</a></h4>
 <p>Implemented scaling methods are:</p>
 <ul class="simple">
-<li><p>Logistic Calibration/Platt Scaling for classification <a class="footnote-reference brackets" href="#id51" id="id28">10</a>, <a class="footnote-reference brackets" href="#id53" id="id29">12</a> and object detection <a class="footnote-reference brackets" href="#id53" id="id30">12</a> (<em>netcal.scaling.LogisticCalibration</em>)</p></li>
-<li><p>Dependent Logistic Calibration for object detection <a class="footnote-reference brackets" href="#id53" id="id31">12</a> (<em>netcal.scaling.LogisticCalibrationDependent</em>) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Logistic Calibration for object detection</p></li>
-<li><p>Temperature Scaling for classification <a class="footnote-reference brackets" href="#id48" id="id32">7</a> and object detection <a class="footnote-reference brackets" href="#id53" id="id33">12</a> (<em>netcal.scaling.TemperatureScaling</em>)</p></li>
-<li><p>Beta Calibration for classification <a class="footnote-reference brackets" href="#id43" id="id34">2</a> and object detection <a class="footnote-reference brackets" href="#id53" id="id35">12</a> (<em>netcal.scaling.BetaCalibration</em>)</p></li>
-<li><p>Dependent Beta Calibration for object detection <a class="footnote-reference brackets" href="#id53" id="id36">12</a> (<em>netcal.scaling.BetaCalibrationDependent</em>) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Beta Calibration for object detection</p></li>
-</ul>
-<p><strong>New on version 1.2:</strong>: you can provide a parameter named “method” to the constructor of each scaling method. This parameter could be one of the following:
-- ‘mle’: use the method feed-forward with maximum likelihood estimates on the calibration parameters (standard)
-- ‘momentum’: use non-convex momentum optimization (e.g. default on dependent beta calibration)
-- ‘mcmc’: use Markov-Chain Monte-Carlo sampling to obtain multiple parameter sets in order to quantify uncertainty in the calibration
-- ‘variational’: use Variational Inference to obtain multiple parameter sets in order to quantify uncertainty in the calibration</p>
-</div>
-<div class="section" id="regularization">
-<h2><a class="toc-backref" href="#id68">Regularization</a><a class="headerlink" href="#regularization" title="Permalink to this headline">¶</a></h2>
-<p>With some effort, it is also possible to push the model training towards calibrated confidences by regularization. Implemented regularization methods are:</p>
+<li><p>Logistic Calibration/Platt Scaling for classification <span class="xref myst">[10]</span> and object detection <span class="xref myst">[12]</span> (<em>netcal.scaling.LogisticCalibration</em>)</p></li>
+<li><p>Dependent Logistic Calibration for object detection <span class="xref myst">[12]</span> (<em>netcal.scaling.LogisticCalibrationDependent</em>) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Logistic Calibration for object detection</p></li>
+<li><p>Temperature Scaling for classification <span class="xref myst">[7]</span> and object detection <span class="xref myst">[12]</span> (<em>netcal.scaling.TemperatureScaling</em>)</p></li>
+<li><p>Beta Calibration for classification <span class="xref myst">[2]</span> and object detection <span class="xref myst">[12]</span> (<em>netcal.scaling.BetaCalibration</em>)</p></li>
+<li><p>Dependent Beta Calibration for object detection <span class="xref myst">[12]</span> (<em>netcal.scaling.BetaCalibrationDependent</em>) - on detection, this method is able to capture correlations between all input quantities and should be preferred over Beta Calibration for object detection</p></li>
+</ul>
+<p><strong>New on version 1.2:</strong> you can provide a parameter named “method” to
+the constructor of each scaling method. This parameter could be one of
+the following: - ‘mle’: use the method feed-forward with maximum
+likelihood estimates on the calibration parameters (standard) -
+‘momentum’: use non-convex momentum optimization (e.g. default on
+dependent beta calibration) - ‘mcmc’: use Markov-Chain Monte-Carlo
+sampling to obtain multiple parameter sets in order to quantify
+uncertainty in the calibration - ‘variational’: use Variational
+Inference to obtain multiple parameter sets in order to quantify
+uncertainty in the calibration</p>
+</section>
+<section id="regularization">
+<h4>Regularization<a class="headerlink" href="#regularization" title="Permalink to this heading">¶</a></h4>
+<p>With some effort, it is also possible to push the model training towards
+calibrated confidences by regularization. Implemented regularization
+methods are:</p>
 <ul class="simple">
-<li><p>Confidence Penalty <a class="footnote-reference brackets" href="#id49" id="id37">8</a> (<em>netcal.regularization.confidence_penalty</em> and <em>netcal.regularization.ConfidencePenalty</em> - the latter one is a PyTorch implementation that might be used as a regularization term)</p></li>
-<li><p>Maximum Mean Calibration Error (MMCE) <a class="footnote-reference brackets" href="#id54" id="id38">13</a> (<em>netcal.regularization.MMCEPenalty</em> - PyTorch regularization module)</p></li>
-<li><p>DCA <a class="footnote-reference brackets" href="#id56" id="id39">15</a> (<em>netcal.regularization.DCAPenalty</em> - PyTorch regularization module)</p></li>
+<li><p>Confidence Penalty <span class="xref myst">[8]</span> (<em>netcal.regularization.confidence_penalty</em> and <em>netcal.regularization.ConfidencePenalty</em> - the latter one is a PyTorch implementation that might be used as a regularization term)</p></li>
+<li><p>Maximum Mean Calibration Error (MMCE) <span class="xref myst">[13]</span> (<em>netcal.regularization.MMCEPenalty</em> - PyTorch regularization module)</p></li>
+<li><p>DCA <span class="xref myst">[15]</span> (<em>netcal.regularization.DCAPenalty</em> - PyTorch regularization module)</p></li>
 </ul>
-</div>
-</div>
-<div class="section" id="visualization">
-<h1><a class="toc-backref" href="#id69">Visualization</a><a class="headerlink" href="#visualization" title="Permalink to this headline">¶</a></h1>
-<p>For visualization of miscalibration, one can use a Confidence Histograms &amp; Reliability Diagrams. These diagrams are similar to ECE, the output space is divided into equally spaced bins. The calibration gap between bin accuracy and bin confidence is visualized as a histogram.</p>
-<p>On detection calibration, the miscalibration can be visualized either along one additional box information (e.g. the x-position of the predictions) or distributed over two additional box information in terms of a heatmap.</p>
+</section>
+</section>
+<section id="regression-calibration-methods">
+<h3>Regression Calibration Methods<a class="headerlink" href="#regression-calibration-methods" title="Permalink to this heading">¶</a></h3>
+<p>The <em>netcal</em> library provides post-hoc methods to recalibrate the
+uncertainty of probabilistic regression tasks. We distinguish the
+calibration methods into non-parametric and parametric methods.
+Non-parametric calibration methods take a probability distribution as
+input and apply recalibration in terms of quantiles on the cumulative
+(CDF). This leads to a recalibrated probability distribution that,
+however, has no analytical representation but is given by certain points
+defining a CDF distribution. In contrast, parametric calibration methods
+also take a probability distribution as input and provide a recalibrated
+distribution that has an analytical expression (e.g., Gaussian).</p>
+<section id="non-parametric-calibration">
+<h4>Non-parametric calibration<a class="headerlink" href="#non-parametric-calibration" title="Permalink to this heading">¶</a></h4>
+<p>The common non-parametric recalibration methods use the predicted
+cumulative (CDF) distribution functions to learn a mapping from the
+uncalibrated quantiles to the observed quantile coverage. Using a
+recalibrated CDF, it is possible to derive the respective density
+functions (PDF) or to extract statistical moments such as mean and
+variance. Non-parametric calibration methods within the
+<em>netcal.regression</em> package are</p>
 <ul class="simple">
-<li><p>Reliability Diagram <a class="footnote-reference brackets" href="#id42" id="id40">1</a>, <a class="footnote-reference brackets" href="#id53" id="id41">12</a> (<em>netcal.presentation.ReliabilityDiagram</em>)</p></li>
+<li><p>Isotonic Regression <span class="xref myst">[19]</span> which applies a (marginal) recalibration of the CDF (<em>netcal.regression.IsotonicRegression</em>)</p></li>
+<li><p>GP-Beta <span class="xref myst">[20]</span> which applies an input-dependent recalibration of the CDF using a Gaussian process for parameter estimation (<em>netcal.regression.GPBeta</em>)</p></li>
 </ul>
-</div>
-<div class="section" id="examples">
-<h1><a class="toc-backref" href="#id70">Examples</a><a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h1>
-<p>The calibration methods work with the predicted confidence estimates of a neural network and on detection also with the bounding box regression branch.</p>
-<div class="section" id="classification">
-<h2><a class="toc-backref" href="#id71">Classification</a><a class="headerlink" href="#classification" title="Permalink to this headline">¶</a></h2>
-<p>This is a basic example which uses softmax predictions of a classification task with 10 classes and the given NumPy arrays:</p>
+</section>
+<section id="parametric-calibration">
+<h4>Parametric calibration<a class="headerlink" href="#parametric-calibration" title="Permalink to this heading">¶</a></h4>
+<p>The parametric recalibration methods apply a recalibration of the
+estimated distributions so that the resulting distribution is given in
+terms of a distribution with an analytical expression (e.g., a
+Gaussian). These methods are suitable for applications where a
+parametric distribution is required for subsequent applications, e.g.,
+within Kalman filtering. We implemented the following parametric
+calibration methods:</p>
+<ul class="simple">
+<li><p>Variance Scaling <span class="xref myst">[17]</span>, <span class="xref myst">[18]</span> which is nothing else but a temperature scaling for the predicted variance (<em>netcal.regression.VarianceScaling</em>)</p></li>
+<li><p>GP-Normal <span class="xref myst">[16]</span> which applies an input-dependent rescaling of the predicted variance (<em>netcal.regression.GPNormal</em>). Note: this method is also able to capture correlations between multiple input dimensions and can return a joint multivariate normal distribution as calibration output (cf. examples section).</p></li>
+<li><p>GP-Cauchy <span class="xref myst">[16]</span> is similar to GP-Normal but utilizes a Cauchy distribution as calibration output (<em>netcal.regression.GPCauchy</em>)</p></li>
+</ul>
+</section>
+</section>
+</section>
+<section id="visualization">
+<h2>Visualization<a class="headerlink" href="#visualization" title="Permalink to this heading">¶</a></h2>
+<p>For visualization of miscalibration, one can use a Confidence Histograms
+&amp; Reliability Diagrams for (semantic) confidence calibration as well as
+for regression uncertainty calibration. Within confidence calibration,
+these diagrams are similar to ECE. The output space is divided into
+equally spaced bins. The calibration gap between bin accuracy and bin
+confidence is visualized as a histogram.</p>
+<p>For detection calibration, the miscalibration can be visualized either
+along one additional box information (e.g. the x-position of the
+predictions) or distributed over two additional box information in terms
+of a heatmap.</p>
+<p>For regression uncertainty calibration, the reliability diagram shows
+the relative prediction interval coverage of the ground-truth samples
+for different quantile levels.</p>
+<ul class="simple">
+<li><p>Reliability Diagram <span class="xref myst">[1]</span>, <span class="xref myst">[12]</span> (<em>netcal.presentation.ReliabilityDiagram</em>)</p></li>
+<li><p>Reliability Diagram for regression calibration (<em>netcal.presentation.ReliabilityRegression</em>)</p></li>
+<li><p>Reliability QCE Diagram <span class="xref myst">[16]</span> shows the Quantile Calibration Error (QCE) for different variance levels (<em>netcal.presentation.ReliabilityQCE</em>)</p></li>
+</ul>
+<p><strong>New on version 1.3:</strong> All plot-methods within the
+<em>netcal.presentation</em> package now support the option “tikz=True” which
+switches from standard <em>matplotlib.Figure</em> objects to strings with
+Tikz-Code. Tikz-code can be directly used for LaTeX documents to render
+images as vector graphics with high quality. Thus, this option helps to
+improve the quality of your reliability diagrams if you are planning to
+use this library for any type of publication/document</p>
+</section>
+<section id="examples">
+<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this heading">¶</a></h2>
+<p>The calibration methods work with the predicted confidence estimates of
+a neural network and on detection also with the bounding box regression
+branch.</p>
+<section id="classification">
+<h3>Classification<a class="headerlink" href="#classification" title="Permalink to this heading">¶</a></h3>
+<p>This is a basic example which uses softmax predictions of a
+classification task with 10 classes and the given NumPy arrays:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">ground_truth</span>  <span class="c1"># this is a NumPy 1-D array with ground truth digits between 0-9 - shape: (n_samples,)</span>
 <span class="n">confidences</span>   <span class="c1"># this is a NumPy 2-D array with confidence estimates between 0-1 - shape: (n_samples, n_classes)</span>
 </pre></div>
 </div>
-<p>This is an example for <em>netcal.scaling.TemperatureScaling</em> but also works for every calibration method (remind different constructor parameters):</p>
+<section id="post-hoc-calibration-for-classification">
+<h4>Post-hoc Calibration for Classification<a class="headerlink" href="#post-hoc-calibration-for-classification" title="Permalink to this heading">¶</a></h4>
+<p>This is an example for <em>netcal.scaling.TemperatureScaling</em> but also
+works for every calibration method (remind different constructor
+parameters):</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">from</span> <span class="nn">netcal.scaling</span> <span class="kn">import</span> <span class="n">TemperatureScaling</span>
 
@@ -292,16 +913,22 @@ <h2><a class="toc-backref" href="#id71">Classification</a><a class="headerlink"
 <span class="n">calibrated</span> <span class="o">=</span> <span class="n">temperature</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">confidences</span><span class="p">)</span>
 </pre></div>
 </div>
+</section>
+<section id="measuring-miscalibration-for-classification">
+<h4>Measuring Miscalibration for Classification<a class="headerlink" href="#measuring-miscalibration-for-classification" title="Permalink to this heading">¶</a></h4>
 <p>The miscalibration can be determined with the ECE:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.metrics</span> <span class="kn">import</span> <span class="n">ECE</span>
 
 <span class="n">n_bins</span> <span class="o">=</span> <span class="mi">10</span>
 
 <span class="n">ece</span> <span class="o">=</span> <span class="n">ECE</span><span class="p">(</span><span class="n">n_bins</span><span class="p">)</span>
-<span class="n">uncalibrated_score</span> <span class="o">=</span> <span class="n">ece</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">confidences</span><span class="p">)</span>
-<span class="n">calibrated_score</span> <span class="o">=</span> <span class="n">ece</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">calibrated</span><span class="p">)</span>
+<span class="n">uncalibrated_score</span> <span class="o">=</span> <span class="n">ece</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">confidences</span><span class="p">,</span> <span class="n">ground_truth</span><span class="p">)</span>
+<span class="n">calibrated_score</span> <span class="o">=</span> <span class="n">ece</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">calibrated</span><span class="p">,</span> <span class="n">ground_truth</span><span class="p">)</span>
 </pre></div>
 </div>
+</section>
+<section id="visualizing-miscalibration-for-classification">
+<h4>Visualizing Miscalibration for Classification<a class="headerlink" href="#visualizing-miscalibration-for-classification" title="Permalink to this heading">¶</a></h4>
 <p>The miscalibration can be visualized with a Reliability Diagram:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.presentation</span> <span class="kn">import</span> <span class="n">ReliabilityDiagram</span>
 
@@ -310,18 +937,31 @@ <h2><a class="toc-backref" href="#id71">Classification</a><a class="headerlink"
 <span class="n">diagram</span> <span class="o">=</span> <span class="n">ReliabilityDiagram</span><span class="p">(</span><span class="n">n_bins</span><span class="p">)</span>
 <span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">confidences</span><span class="p">,</span> <span class="n">ground_truth</span><span class="p">)</span>  <span class="c1"># visualize miscalibration of uncalibrated</span>
 <span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">calibrated</span><span class="p">,</span> <span class="n">ground_truth</span><span class="p">)</span>   <span class="c1"># visualize miscalibration of calibrated</span>
+
+<span class="c1"># you can also use this method to create a tikz file with tikz code</span>
+<span class="c1"># that can be directly used within LaTeX documents:</span>
+<span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">confidences</span><span class="p">,</span> <span class="n">ground_truth</span><span class="p">,</span> <span class="n">tikz</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">filename</span><span class="o">=</span><span class="s2">&quot;diagram.tikz&quot;</span><span class="p">)</span>
 </pre></div>
 </div>
-</div>
-<div class="section" id="detection">
-<h2><a class="toc-backref" href="#id72">Detection</a><a class="headerlink" href="#detection" title="Permalink to this headline">¶</a></h2>
-<p>In this example we use confidence predictions of an object detection model with the according x-position of the predicted bounding boxes. Our ground-truth provided to the calibration algorithm denotes if a bounding box has matched a ground-truth box with a certain IoU and the correct class label.</p>
+</section>
+</section>
+<section id="detection-confidence-of-objects">
+<h3>Detection (Confidence of Objects)<a class="headerlink" href="#detection-confidence-of-objects" title="Permalink to this heading">¶</a></h3>
+<p>In this example we use confidence predictions of an object detection
+model with the according x-position of the predicted bounding boxes. Our
+ground-truth provided to the calibration algorithm denotes if a bounding
+box has matched a ground-truth box with a certain IoU and the correct
+class label.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">matched</span>                <span class="c1"># binary NumPy 1-D array (0, 1) that indicates if a bounding box has matched a ground truth at a certain IoU with the right label - shape: (n_samples,)</span>
 <span class="n">confidences</span>            <span class="c1"># NumPy 1-D array with confidence estimates between 0-1 - shape: (n_samples,)</span>
 <span class="n">relative_x_position</span>    <span class="c1"># NumPy 1-D array with relative center-x position between 0-1 of each prediction - shape: (n_samples,)</span>
 </pre></div>
 </div>
-<p>This is an example for <em>netcal.scaling.LogisticCalibration</em> and <em>netcal.scaling.LogisticCalibrationDependent</em> but also works for every calibration method (remind different constructor parameters):</p>
+<section id="post-hoc-calibration-for-detection">
+<h4>Post-hoc Calibration for Detection<a class="headerlink" href="#post-hoc-calibration-for-detection" title="Permalink to this heading">¶</a></h4>
+<p>This is an example for <em>netcal.scaling.LogisticCalibration</em> and
+<em>netcal.scaling.LogisticCalibrationDependent</em> but also works for every
+calibration method (remind different constructor parameters):</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">from</span> <span class="nn">netcal.scaling</span> <span class="kn">import</span> <span class="n">LogisticCalibration</span><span class="p">,</span> <span class="n">LogisticCalibrationDependent</span>
 
@@ -336,6 +976,9 @@ <h2><a class="toc-backref" href="#id72">Detection</a><a class="headerlink" href=
 <span class="n">calibrated</span> <span class="o">=</span> <span class="n">lr_dependent</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
 </pre></div>
 </div>
+</section>
+<section id="measuring-miscalibration-for-detection">
+<h4>Measuring Miscalibration for Detection<a class="headerlink" href="#measuring-miscalibration-for-detection" title="Permalink to this heading">¶</a></h4>
 <p>The miscalibration can be determined with the D-ECE:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.metrics</span> <span class="kn">import</span> <span class="n">ECE</span>
 
@@ -347,6 +990,9 @@ <h2><a class="toc-backref" href="#id72">Detection</a><a class="headerlink" href=
 <span class="n">calibrated_score</span> <span class="o">=</span> <span class="n">ece</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">input_calibrated</span><span class="p">,</span> <span class="n">matched</span><span class="p">)</span>
 </pre></div>
 </div>
+</section>
+<section id="visualizing-miscalibration-for-detection">
+<h4>Visualizing Miscalibration for Detection<a class="headerlink" href="#visualizing-miscalibration-for-detection" title="Permalink to this heading">¶</a></h4>
 <p>The miscalibration can be visualized with a Reliability Diagram:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.presentation</span> <span class="kn">import</span> <span class="n">ReliabilityDiagram</span>
 
@@ -355,18 +1001,30 @@ <h2><a class="toc-backref" href="#id72">Detection</a><a class="headerlink" href=
 <span class="n">diagram</span> <span class="o">=</span> <span class="n">ReliabilityDiagram</span><span class="p">(</span><span class="n">n_bins</span><span class="p">,</span> <span class="n">detection</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>    <span class="c1"># flag &#39;detection=True&#39; is mandatory for this method</span>
 <span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">matched</span><span class="p">)</span>                <span class="c1"># visualize miscalibration of uncalibrated</span>
 <span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">input_calibrated</span><span class="p">,</span> <span class="n">matched</span><span class="p">)</span>     <span class="c1"># visualize miscalibration of calibrated</span>
+
+<span class="c1"># you can also use this method to create a tikz file with tikz code</span>
+<span class="c1"># that can be directly used within LaTeX documents:</span>
+<span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">matched</span><span class="p">,</span> <span class="n">tikz</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">filename</span><span class="o">=</span><span class="s2">&quot;diagram.tikz&quot;</span><span class="p">)</span>
 </pre></div>
 </div>
-</div>
-<div class="section" id="uncertainty-in-calibration">
-<h2><a class="toc-backref" href="#id73">Uncertainty in Calibration</a><a class="headerlink" href="#uncertainty-in-calibration" title="Permalink to this headline">¶</a></h2>
-<p>We can also quantify the uncertainty in a calibration mapping if we use a Bayesian view on the calibration models. We can sample multiple parameter sets using MCMC sampling or VI. In this example, we reuse the data of the previous detection example.</p>
+</section>
+</section>
+<section id="uncertainty-in-confidence-calibration">
+<h3>Uncertainty in Confidence Calibration<a class="headerlink" href="#uncertainty-in-confidence-calibration" title="Permalink to this heading">¶</a></h3>
+<p>We can also quantify the uncertainty in a calibration mapping if we use
+a Bayesian view on the calibration models. We can sample multiple
+parameter sets using MCMC sampling or VI. In this example, we reuse the
+data of the previous detection example.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">matched</span>                <span class="c1"># binary NumPy 1-D array (0, 1) that indicates if a bounding box has matched a ground truth at a certain IoU with the right label - shape: (n_samples,)</span>
 <span class="n">confidences</span>            <span class="c1"># NumPy 1-D array with confidence estimates between 0-1 - shape: (n_samples,)</span>
 <span class="n">relative_x_position</span>    <span class="c1"># NumPy 1-D array with relative center-x position between 0-1 of each prediction - shape: (n_samples,)</span>
 </pre></div>
 </div>
-<p>This is an example for <em>netcal.scaling.LogisticCalibration</em> and <em>netcal.scaling.LogisticCalibrationDependent</em> but also works for every calibration method (remind different constructor parameters):</p>
+<section id="post-hoc-calibration-with-uncertainty">
+<h4>Post-hoc Calibration with Uncertainty<a class="headerlink" href="#post-hoc-calibration-with-uncertainty" title="Permalink to this heading">¶</a></h4>
+<p>This is an example for <em>netcal.scaling.LogisticCalibration</em> and
+<em>netcal.scaling.LogisticCalibrationDependent</em> but also works for every
+calibration method (remind different constructor parameters):</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">from</span> <span class="nn">netcal.scaling</span> <span class="kn">import</span> <span class="n">LogisticCalibration</span><span class="p">,</span> <span class="n">LogisticCalibrationDependent</span>
 
@@ -393,7 +1051,11 @@ <h2><a class="toc-backref" href="#id73">Uncertainty in Calibration</a><a class="
 <span class="n">calibrated</span> <span class="o">=</span> <span class="n">lr_dependent</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
 </pre></div>
 </div>
-<p>You can directly pass the output to the D-ECE and PICP instance to measure miscalibration and mask quality:</p>
+</section>
+<section id="measuring-miscalibration-with-uncertainty">
+<h4>Measuring Miscalibration with Uncertainty<a class="headerlink" href="#measuring-miscalibration-with-uncertainty" title="Permalink to this heading">¶</a></h4>
+<p>You can directly pass the output to the D-ECE and PICP instance to
+measure miscalibration and mask quality:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.metrics</span> <span class="kn">import</span> <span class="n">ECE</span>
 <span class="kn">from</span> <span class="nn">netcal.metrics</span> <span class="kn">import</span> <span class="n">PICP</span>
 
@@ -406,14 +1068,15 @@ <h2><a class="toc-backref" href="#id73">Uncertainty in Calibration</a><a class="
 <span class="n">miscalibration</span> <span class="o">=</span> <span class="n">ece</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">calibrated</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">matched</span><span class="p">)</span>
 
 <span class="c1"># now determine uncertainty quality</span>
-<span class="n">uncertainty</span> <span class="o">=</span> <span class="n">picp</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">calibrated</span><span class="p">,</span> <span class="n">matched</span><span class="p">,</span> <span class="n">uncertainty</span><span class="o">=</span><span class="s2">&quot;mean&quot;</span><span class="p">)</span>
+<span class="n">uncertainty</span> <span class="o">=</span> <span class="n">picp</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">calibrated</span><span class="p">,</span> <span class="n">matched</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s2">&quot;confidence&quot;</span><span class="p">)</span>
 
 <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;D-ECE:&quot;</span><span class="p">,</span> <span class="n">miscalibration</span><span class="p">)</span>
 <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;PICP:&quot;</span><span class="p">,</span> <span class="n">uncertainty</span><span class="o">.</span><span class="n">picp</span><span class="p">)</span> <span class="c1"># prediction coverage probability</span>
 <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;MPIW:&quot;</span><span class="p">,</span> <span class="n">uncertainty</span><span class="o">.</span><span class="n">mpiw</span><span class="p">)</span> <span class="c1"># mean prediction interval width</span>
 </pre></div>
 </div>
-<p>If we want to measure miscalibration and uncertainty quality by means of the relative x position, we need to broadcast the according information:</p>
+<p>If we want to measure miscalibration and uncertainty quality by means of
+the relative x position, we need to broadcast the according information:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># broadcast and stack x information to calibrated information</span>
 <span class="n">broadcasted</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">broadcast_to</span><span class="p">(</span><span class="n">relative_x_position</span><span class="p">,</span> <span class="n">calibrated</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
 <span class="n">calibrated</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">((</span><span class="n">calibrated</span><span class="p">,</span> <span class="n">broadcasted</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
@@ -434,139 +1097,268 @@ <h2><a class="toc-backref" href="#id73">Uncertainty in Calibration</a><a class="
 <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;MPIW:&quot;</span><span class="p">,</span> <span class="n">uncertainty</span><span class="o">.</span><span class="n">mpiw</span><span class="p">)</span> <span class="c1"># mean prediction interval width</span>
 </pre></div>
 </div>
+</section>
+</section>
+<section id="probabilistic-regression">
+<h3>Probabilistic Regression<a class="headerlink" href="#probabilistic-regression" title="Permalink to this heading">¶</a></h3>
+<p>The following example shows how to use the post-hoc calibration methods
+for probabilistic regression tasks. Within probabilistic regression, a
+forecaster (e.g. with Gaussian prior) outputs a mean and a variance
+targeting the true ground-truth score. Thus, the following information
+is required to construct the calibration methods:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">mean</span>          <span class="c1"># NumPy n-D array holding the estimated mean of shape (n, d) with n samples and d dimensions</span>
+<span class="n">stddev</span>        <span class="c1"># NumPy n-D array holding the estimated stddev (independent) of shape (n, d) with n samples and d dimensions</span>
+<span class="n">ground_truth</span>  <span class="c1"># NumPy n-D array holding the ground-truth scores of shape (n, d) with n samples and d dimensions</span>
+</pre></div>
 </div>
+<section id="post-hoc-calibration-parametric">
+<h4>Post-hoc Calibration (Parametric)<a class="headerlink" href="#post-hoc-calibration-parametric" title="Permalink to this heading">¶</a></h4>
+<p>These information might result e.g. from object detection where the
+position information of the objects (bounding boxes) are parametrized by
+normal distributions. We start by using parametric calibration methods
+such as Variance Scaling:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.regression</span> <span class="kn">import</span> <span class="n">VarianceScaling</span><span class="p">,</span> <span class="n">GPNormal</span>
+
+<span class="c1"># the initialization of the Variance Scaling method is pretty simple</span>
+<span class="n">varscaling</span> <span class="o">=</span> <span class="n">VarianceScaling</span><span class="p">()</span>
+
+<span class="c1"># the GP-Normal requires a little bit more parameters to parametrize the underlying GP</span>
+<span class="n">gpnormal</span> <span class="o">=</span> <span class="n">GPNormal</span><span class="p">(</span>
+    <span class="n">n_inducing_points</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span>    <span class="c1"># number of inducing points</span>
+    <span class="n">n_random_samples</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>    <span class="c1"># random samples used for likelihood</span>
+    <span class="n">n_epochs</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>            <span class="c1"># optimization epochs</span>
+    <span class="n">use_cuda</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>          <span class="c1"># can also use CUDA for computations</span>
+<span class="p">)</span>
+
+<span class="c1"># fit the Variance Scaling</span>
+<span class="c1"># note that we need to pass the first argument as tuple as the input distributions</span>
+<span class="c1"># are parametrized by mean and variance</span>
+<span class="n">varscaling</span><span class="o">.</span><span class="n">fit</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">)</span>
+
+<span class="c1"># fit GP-Normal - similar parameters here!</span>
+<span class="n">gpnormal</span><span class="o">.</span><span class="n">fit</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">)</span>
+
+<span class="c1"># transform distributions to obtain recalibrated stddevs</span>
+<span class="n">stddev_varscaling</span> <span class="o">=</span> <span class="n">varscaling</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">))</span>  <span class="c1"># NumPy array with stddev - has shape (n, d)</span>
+<span class="n">stddev_gpnormal</span> <span class="o">=</span> <span class="n">gpnormal</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">))</span>  <span class="c1"># NumPy array with stddev - has shape (n, d)</span>
+</pre></div>
 </div>
-<div class="section" id="references">
-<h1><a class="toc-backref" href="#id74">References</a><a class="headerlink" href="#references" title="Permalink to this headline">¶</a></h1>
-<dl class="footnote brackets">
-<dt class="label" id="id42"><span class="brackets">1</span><span class="fn-backref">(<a href="#id10">1</a>,<a href="#id13">2</a>,<a href="#id15">3</a>,<a href="#id26">4</a>,<a href="#id40">5</a>)</span></dt>
-<dd><p>Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht: “Obtaining well calibrated probabilities using bayesian binning.” Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.</p>
-</dd>
-<dt class="label" id="id43"><span class="brackets">2</span><span class="fn-backref">(<a href="#id8">1</a>,<a href="#id34">2</a>)</span></dt>
-<dd><p>Kull, Meelis, Telmo Silva Filho, and Peter Flach: “Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers.” Artificial Intelligence and Statistics, PMLR 54:623-631, 2017.</p>
-</dd>
-<dt class="label" id="id44"><span class="brackets">3</span><span class="fn-backref">(<a href="#id6">1</a>,<a href="#id21">2</a>)</span></dt>
-<dd><p>Zadrozny, Bianca and Elkan, Charles: “Obtaining calibrated probability estimates from decision trees and naive bayesian classifiers.” In ICML, pp. 609–616, 2001.</p>
-</dd>
-<dt class="label" id="id45"><span class="brackets">4</span><span class="fn-backref">(<a href="#id22">1</a>,<a href="#id24">2</a>)</span></dt>
-<dd><p>Zadrozny, Bianca and Elkan, Charles: “Transforming classifier scores into accurate multiclass probability estimates.” In KDD, pp. 694–699, 2002.</p>
-</dd>
-<dt class="label" id="id46"><span class="brackets"><a class="fn-backref" href="#id25">5</a></span></dt>
-<dd><p>Ryan J Tibshirani, Holger Hoefling, and Robert Tibshirani: “Nearly-isotonic regression.” Technometrics, 53(1):54–61, 2011.</p>
-</dd>
-<dt class="label" id="id47"><span class="brackets"><a class="fn-backref" href="#id27">6</a></span></dt>
-<dd><p>Naeini, Mahdi Pakdaman, and Gregory F. Cooper: “Binary classifier calibration using an ensemble of near isotonic regression models.” 2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE, 2016.</p>
-</dd>
-<dt class="label" id="id48"><span class="brackets"><a class="fn-backref" href="#id32">7</a></span></dt>
-<dd><p>Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger: “On Calibration of Modern Neural Networks.” Proceedings of the 34th International Conference on Machine Learning, 2017.</p>
-</dd>
-<dt class="label" id="id49"><span class="brackets"><a class="fn-backref" href="#id37">8</a></span></dt>
-<dd><p>Pereyra, G., Tucker, G., Chorowski, J., Kaiser, L. and Hinton, G.: “Regularizing neural networks by penalizing confident output distributions.” CoRR, 2017.</p>
-</dd>
-<dt class="label" id="id50"><span class="brackets"><a class="fn-backref" href="#id20">9</a></span></dt>
-<dd><p>Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. and Duchesnay, E.: “Scikit-learn: Machine Learning in Python.” In Journal of Machine Learning Research, volume 12 pp 2825-2830, 2011.</p>
-</dd>
-<dt class="label" id="id51"><span class="brackets">10</span><span class="fn-backref">(<a href="#id7">1</a>,<a href="#id28">2</a>)</span></dt>
-<dd><p>Platt, John: “Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods.” Advances in large margin classifiers, 10(3): 61–74, 1999.</p>
-</dd>
-<dt class="label" id="id52"><span class="brackets">11</span><span class="fn-backref">(<a href="#id11">1</a>,<a href="#id17">2</a>)</span></dt>
-<dd><p>Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi: “Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection.” Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.</p>
-</dd>
-<dt class="label" id="id53"><span class="brackets">12</span><span class="fn-backref">(<a href="#id5">1</a>,<a href="#id9">2</a>,<a href="#id12">3</a>,<a href="#id14">4</a>,<a href="#id16">5</a>,<a href="#id18">6</a>,<a href="#id23">7</a>,<a href="#id29">8</a>,<a href="#id30">9</a>,<a href="#id31">10</a>,<a href="#id33">11</a>,<a href="#id35">12</a>,<a href="#id36">13</a>,<a href="#id41">14</a>)</span></dt>
-<dd><p>Fabian Küppers, Jan Kronenberger, Amirhossein Shantia and Anselm Haselhoff: “Multivariate Confidence Calibration for Object Detection”.” The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020</p>
-</dd>
-<dt class="label" id="id54"><span class="brackets">13</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id3">2</a>,<a href="#id19">3</a>,<a href="#id38">4</a>)</span></dt>
-<dd><p>Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain: “Trainable calibration measures for neural networks from _kernel mean embeddings.” International Conference on Machine Learning. 2018</p>
-</dd>
-<dt class="label" id="id55"><span class="brackets"><a class="fn-backref" href="#id2">14</a></span></dt>
-<dd><p>Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez: “Quality of Uncertainty Quantification for Bayesian Neural Network Inference.” Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019</p>
-</dd>
-<dt class="label" id="id56"><span class="brackets">15</span><span class="fn-backref">(<a href="#id4">1</a>,<a href="#id39">2</a>)</span></dt>
-<dd><p>Liang, Gongbo, et al.: “Improved trainable calibration method for neural networks on medical imaging classification.” arXiv preprint arXiv:2009.04057 (2020)</p>
-</dd>
-</dl>
+</section>
+<section id="post-hoc-calibration-non-parametric">
+<h4>Post-hoc Calibration (Non-Parametric)<a class="headerlink" href="#post-hoc-calibration-non-parametric" title="Permalink to this heading">¶</a></h4>
+<p>We can also use non-parametric calibration methods. In this case, the
+calibrated distributions are defined by their density (PDF) and
+cumulative (CDF) functions:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.regression</span> <span class="kn">import</span> <span class="n">IsotonicRegression</span><span class="p">,</span> <span class="n">GPBeta</span>
+
+<span class="c1"># the initialization of the Isotonic Regression method is pretty simple</span>
+<span class="n">isotonic</span> <span class="o">=</span> <span class="n">IsotonicRegression</span><span class="p">()</span>
+
+<span class="c1"># the GP-Normal requires a little bit more parameters to parametrize the underlying GP</span>
+<span class="n">gpbeta</span> <span class="o">=</span> <span class="n">GPBeta</span><span class="p">(</span>
+    <span class="n">n_inducing_points</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span>    <span class="c1"># number of inducing points</span>
+    <span class="n">n_random_samples</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>    <span class="c1"># random samples used for likelihood</span>
+    <span class="n">n_epochs</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>            <span class="c1"># optimization epochs</span>
+    <span class="n">use_cuda</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>          <span class="c1"># can also use CUDA for computations</span>
+<span class="p">)</span>
+
+<span class="c1"># fit the Isotonic Regression</span>
+<span class="c1"># note that we need to pass the first argument as tuple as the input distributions</span>
+<span class="c1"># are parametrized by mean and variance</span>
+<span class="n">isotonic</span><span class="o">.</span><span class="n">fit</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">)</span>
+
+<span class="c1"># fit GP-Beta - similar parameters here!</span>
+<span class="n">gpbeta</span><span class="o">.</span><span class="n">fit</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">)</span>
+
+<span class="c1"># transform distributions to obtain recalibrated distributions</span>
+<span class="n">t_isotonic</span><span class="p">,</span> <span class="n">pdf_isotonic</span><span class="p">,</span> <span class="n">cdf_isotonic</span> <span class="o">=</span> <span class="n">varscaling</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">))</span>
+<span class="n">t_gpbeta</span><span class="p">,</span> <span class="n">pdf_gpbeta</span><span class="p">,</span> <span class="n">cdf_gpbeta</span> <span class="o">=</span> <span class="n">gpbeta</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">))</span>
+
+<span class="c1"># Note: the transformation results are NumPy n-d arrays with shape (t, n, d)</span>
+<span class="c1"># with t as the number of points that define the PDF/CDF,</span>
+<span class="c1"># with n as the number of samples, and</span>
+<span class="c1"># with d as the number of dimensions.</span>
+
+<span class="c1"># The resulting variables can be interpreted as follows:</span>
+<span class="c1"># - t_isotonic/t_gpbeta: x-values of the PDF/CDF with shape (t, n, d)</span>
+<span class="c1"># - pdf_isotonic/pdf_gpbeta: y-values of the PDF with shape (t, n, d)</span>
+<span class="c1"># - cdf_isotonic/cdf_gpbeta: y-values of the CDF with shape (t, n, d)</span>
+</pre></div>
 </div>
+<p>You can visualize the non-parametric distribution of a single sample
+within a single dimension using Matplotlib:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
+
+<span class="n">fig</span><span class="p">,</span> <span class="p">(</span><span class="n">ax1</span><span class="p">,</span> <span class="n">ax2</span><span class="p">)</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+
+<span class="c1"># plot the recalibrated PDF within a single axis after calibration</span>
+<span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span>
+    <span class="n">t_isotonic</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">pdf_isotonic</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+    <span class="n">t_gpbeta</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">pdf_gpbeta</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+<span class="p">)</span>
 
+<span class="c1"># plot the recalibrated PDF within a single axis after calibration</span>
+<span class="n">ax2</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span>
+    <span class="n">t_isotonic</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">cdf_isotonic</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+    <span class="n">t_gpbeta</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">cdf_gpbeta</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+<span class="p">)</span>
 
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<p>We provide a method to extract the statistical moments expectation and
+variance from the recalibrated cumulative (CDF). Note that we advise to
+use one of the parametric calibration methods if you need e.g. a
+Gaussian for subsequent applications such as Kalman filtering.</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal</span> <span class="kn">import</span> <span class="n">cumulative_moments</span>
+
+<span class="c1"># extract the expectation (mean) and the variance from the recalibrated CDF</span>
+<span class="n">ymean_isotonic</span><span class="p">,</span> <span class="n">yvar_isotonic</span> <span class="o">=</span> <span class="n">cumulative_moments</span><span class="p">(</span><span class="n">t_isotonic</span><span class="p">,</span> <span class="n">cdf_isotonic</span><span class="p">)</span>
+<span class="n">ymean_gpbeta</span><span class="p">,</span> <span class="n">yvar_gpbeta</span> <span class="o">=</span> <span class="n">cumulative_moments</span><span class="p">(</span><span class="n">t_gpbeta</span><span class="p">,</span> <span class="n">cdf_gpbeta</span><span class="p">)</span>
+
+<span class="c1"># each of these variables has shape (n, d) and holds the</span>
+<span class="c1"># mean/variance for each sample and in each dimension</span>
+</pre></div>
+</div>
+</section>
+<section id="correlation-estimation-and-recalibration">
+<h4>Correlation Estimation and Recalibration<a class="headerlink" href="#correlation-estimation-and-recalibration" title="Permalink to this heading">¶</a></h4>
+<p>With the GP-Normal <em>netcal.regression.GPNormal</em>, it is also possible to
+detect possible correlations between multiple input dimensions that have
+originally been trained/modelled independently from each other:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.regression</span> <span class="kn">import</span> <span class="n">GPNormal</span>
+
+<span class="c1"># the GP-Normal requires a little bit more parameters to parametrize the underlying GP</span>
+<span class="n">gpnormal</span> <span class="o">=</span> <span class="n">GPNormal</span><span class="p">(</span>
+    <span class="n">n_inducing_points</span><span class="o">=</span><span class="mi">12</span><span class="p">,</span>    <span class="c1"># number of inducing points</span>
+    <span class="n">n_random_samples</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>    <span class="c1"># random samples used for likelihood</span>
+    <span class="n">n_epochs</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>            <span class="c1"># optimization epochs</span>
+    <span class="n">use_cuda</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>          <span class="c1"># can also use CUDA for computations</span>
+    <span class="n">correlations</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>       <span class="c1"># enable correlation capturing between the input dimensions</span>
+<span class="p">)</span>
+
+<span class="c1"># fit GP-Normal</span>
+<span class="c1"># note that we need to pass the first argument as tuple as the input distributions</span>
+<span class="c1"># are parametrized by mean and variance</span>
+<span class="n">gpnormal</span><span class="o">.</span><span class="n">fit</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">)</span>
+
+<span class="c1"># transform distributions to obtain recalibrated covariance matrices</span>
+<span class="n">cov</span> <span class="o">=</span> <span class="n">gpnormal</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">))</span>  <span class="c1"># NumPy array with covariance - has shape (n, d, d)</span>
+
+<span class="c1"># note: if the input is already given by multivariate normal distributions</span>
+<span class="c1"># (stddev is covariance and has shape (n, d, d)), the methods works similar</span>
+<span class="c1"># and simply applies a covariance recalibration of the input</span>
+</pre></div>
+</div>
+</section>
+<section id="measuring-miscalibration-for-regression">
+<h4>Measuring Miscalibration for Regression<a class="headerlink" href="#measuring-miscalibration-for-regression" title="Permalink to this heading">¶</a></h4>
+<p>Measuring miscalibration is as simple as the training of the methods:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">netcal.metrics</span> <span class="kn">import</span> <span class="n">NLL</span><span class="p">,</span> <span class="n">PinballLoss</span><span class="p">,</span> <span class="n">QCE</span>
+
+<span class="c1"># define the quantile levels that are used to evaluate the pinball loss and the QCE</span>
+<span class="n">quantiles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mi">9</span><span class="p">)</span>
+
+<span class="c1"># initialize NLL, Pinball, and QCE objects</span>
+<span class="n">nll</span> <span class="o">=</span> <span class="n">NLL</span><span class="p">()</span>
+<span class="n">pinball</span> <span class="o">=</span> <span class="n">PinballLoss</span><span class="p">()</span>
+<span class="n">qce</span> <span class="o">=</span> <span class="n">QCE</span><span class="p">(</span><span class="n">marginal</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># if &quot;marginal=False&quot;, we can also measure the QCE by means of the predicted variance levels (realized by binning the variance space)</span>
+
+<span class="c1"># measure miscalibration with the initialized metrics</span>
+<span class="c1"># Note: the parameter &quot;reduction&quot; has a major influence to the return shape of the metrics</span>
+<span class="c1"># see the method docstrings for detailed information</span>
+<span class="n">nll</span><span class="o">.</span><span class="n">measure</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">,</span> <span class="n">reduction</span><span class="o">=</span><span class="s2">&quot;mean&quot;</span><span class="p">)</span>
+<span class="n">pinball</span><span class="o">.</span><span class="n">measure</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">,</span> <span class="n">q</span><span class="o">=</span><span class="n">quantiles</span><span class="p">,</span> <span class="n">reduction</span><span class="o">=</span><span class="s2">&quot;mean&quot;</span><span class="p">)</span>
+<span class="n">qce</span><span class="o">.</span><span class="n">measure</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">,</span> <span class="n">q</span><span class="o">=</span><span class="n">quantiles</span><span class="p">,</span> <span class="n">reduction</span><span class="o">=</span><span class="s2">&quot;mean&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+</section>
+<section id="visualizing-miscalibration-for-regression">
+<h4>Visualizing Miscalibration for Regression<a class="headerlink" href="#visualizing-miscalibration-for-regression" title="Permalink to this heading">¶</a></h4>
+<p>Example visualization code block using the
+<em>netcal.presentation.ReliabilityRegression</em> class:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">netcal.presentation</span> <span class="kn">import</span> <span class="n">ReliabilityRegression</span>
+
+<span class="c1"># define the quantile levels that are used for the quantile evaluation</span>
+<span class="n">quantiles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mi">9</span><span class="p">)</span>
+
+<span class="c1"># initialize the diagram object</span>
+<span class="n">diagram</span> <span class="o">=</span> <span class="n">ReliabilityRegression</span><span class="p">(</span><span class="n">quantiles</span><span class="o">=</span><span class="n">quantiles</span><span class="p">)</span>
+
+<span class="c1"># visualize miscalibration with the initialized object</span>
+<span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">)</span>
+
+<span class="c1"># you can also use this method to create a tikz file with tikz code</span>
+<span class="c1"># that can be directly used within LaTeX documents:</span>
+<span class="n">diagram</span><span class="o">.</span><span class="n">plot</span><span class="p">((</span><span class="n">mean</span><span class="p">,</span> <span class="n">stddev</span><span class="p">),</span> <span class="n">ground_truth</span><span class="p">,</span> <span class="n">tikz</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">filename</span><span class="o">=</span><span class="s2">&quot;diagram.tikz&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</section>
+</section>
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this heading">¶</a></h2>
+<p><a name="ref1">[1]</a> Naeini, Mahdi Pakdaman, Gregory Cooper, and Milos Hauskrecht: “Obtaining well calibrated probabilities using bayesian binning.” Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.</p>
+<p><a name="ref2">[2]</a> Kull, Meelis, Telmo Silva Filho, and Peter Flach: “Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers.” Artificial Intelligence and Statistics, PMLR 54:623-631, 2017.</p>
+<p><a name="ref3">[3]</a> Zadrozny, Bianca and Elkan, Charles: “Obtaining calibrated probability estimates from decision trees and naive bayesian classifiers.” In ICML, pp. 609–616, 2001.</p>
+<p><a name="ref4">[4]</a> Zadrozny, Bianca and Elkan, Charles: “Transforming classifier scores into accurate multiclass probability estimates.” In KDD, pp. 694–699, 2002.</p>
+<p><a name="ref5">[5]</a> Ryan J Tibshirani, Holger Hoefling, and Robert Tibshirani: “Nearly-isotonic regression.” Technometrics, 53(1):54–61, 2011.</p>
+<p><a name="ref6">[6]</a> Naeini, Mahdi Pakdaman, and Gregory F. Cooper: “Binary classifier calibration using an ensemble of near isotonic regression models.” 2016 IEEE 16th International Conference on Data Mining (ICDM). IEEE, 2016.</p>
+<p><a name="ref7">[7]</a> Chuan Guo, Geoff Pleiss, Yu Sun and Kilian Q. Weinberger: “On Calibration of Modern Neural Networks.” Proceedings of the 34th International Conference on Machine Learning, 2017.</p>
+<p><a name="ref8">[8]</a> Pereyra, G., Tucker, G., Chorowski, J., Kaiser, L. and Hinton, G.: “Regularizing neural networks by penalizing confident output distributions.” CoRR, 2017.</p>
+<p><a name="ref9">[9]</a> Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. and Duchesnay, E.: “Scikit-learn: Machine Learning in Python.” In Journal of Machine Learning Research, volume 12 pp 2825-2830, 2011.</p>
+<p><a name="ref10">[10]</a> Platt, John: “Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods.” Advances in large margin classifiers, 10(3): 61–74, 1999.</p>
+<p><a name="ref11">[11]</a> Neumann, Lukas, Andrew Zisserman, and Andrea Vedaldi: “Relaxed Softmax: Efficient Confidence Auto-Calibration for Safe Pedestrian Detection.” Conference on Neural Information Processing Systems (NIPS) Workshop MLITS, 2018.</p>
+<p><a name="ref12">[12]</a> Fabian Küppers, Jan Kronenberger, Amirhossein Shantia, and Anselm Haselhoff: “Multivariate Confidence Calibration for Object Detection”.” The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2020</p>
+<p><a name="ref13">[13]</a> Kumar, Aviral, Sunita Sarawagi, and Ujjwal Jain: “Trainable calibration measures for neural networks from _kernel mean embeddings.” International Conference on Machine Learning. 2018</p>
+<p><a name="ref14">[14]</a> Jiayu  Yao,  Weiwei  Pan,  Soumya  Ghosh,  and  Finale  Doshi-Velez: “Quality of Uncertainty Quantification for Bayesian Neural Network Inference.” Workshop on Uncertainty and Robustness in Deep Learning, ICML, 2019</p>
+<p><a name="ref15">[15]</a> Liang, Gongbo, et al.: “Improved trainable calibration method for neural networks on medical imaging classification.” arXiv preprint arXiv:2009.04057 (2020)</p>
+<p><a name="ref16">[16]</a> Fabian Küppers, Jonas Schneider, Jonas, and Anselm Haselhoff: “Parametric and Multivariate Uncertainty Calibration for Regression and Object Detection.” In: Proceedings of the European Conference on Computer Vision (ECCV) Workshops, Springer, October 2022</p>
+<p><a name="ref17">[17]</a> Levi, Dan, et al.: “Evaluating and calibrating uncertainty prediction in regression tasks.” arXiv preprint arXiv:1905.11659 (2019).</p>
+<p><a name="ref18">[18]</a> Laves, Max-Heinrich, et al.: “Well-calibrated regression uncertainty in medical imaging with deep learning.” Medical Imaging with Deep Learning. PMLR, 2020.</p>
+<p><a name="ref19">[19]</a> Volodymyr Kuleshov, Nathan Fenner, and Stefano Ermon: “Accurate uncertainties for deep learning using calibrated regression.” International Conference on Machine Learning. PMLR, 2018.</p>
+<p><a name="ref20">[20]</a> Hao Song, Tom Diethe, Meelis Kull and Peter Flach: “Distribution calibration for regression.” International Conference on Machine Learning. PMLR, 2019.</p>
+</section>
+</section>
+
+
+                </div>
+              </div>
+            </div>
           </div>
         </div>
-      </div>
-      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
-        <div class="sphinxsidebarwrapper">
-  <h3><a href="#">Table of Contents</a></h3>
-  <ul>
-<li><a class="reference internal" href="#">API Reference</a><ul>
-</ul>
-</li>
-<li><a class="reference internal" href="#calibration-framework">Calibration Framework</a></li>
-<li><a class="reference internal" href="#overview">Overview</a><ul>
-<li><a class="reference internal" href="#update-on-version-1-2">Update on version 1.2</a></li>
-<li><a class="reference internal" href="#update-on-version-1-1">Update on version 1.1</a></li>
-</ul>
-</li>
-<li><a class="reference internal" href="#installation">Installation</a><ul>
-<li><a class="reference internal" href="#requirements">Requirements</a></li>
-</ul>
-</li>
-<li><a class="reference internal" href="#calibration-metrics">Calibration Metrics</a></li>
-<li><a class="reference internal" href="#methods">Methods</a><ul>
-<li><a class="reference internal" href="#binning">Binning</a></li>
-<li><a class="reference internal" href="#scaling">Scaling</a></li>
-<li><a class="reference internal" href="#regularization">Regularization</a></li>
-</ul>
-</li>
-<li><a class="reference internal" href="#visualization">Visualization</a></li>
-<li><a class="reference internal" href="#examples">Examples</a><ul>
-<li><a class="reference internal" href="#classification">Classification</a></li>
-<li><a class="reference internal" href="#detection">Detection</a></li>
-<li><a class="reference internal" href="#uncertainty-in-calibration">Uncertainty in Calibration</a></li>
-</ul>
-</li>
-<li><a class="reference internal" href="#references">References</a></li>
-</ul>
+        
+        
+      </div><!-- /row -->
 
-  <h4>Next topic</h4>
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+++ b/docs/build/html/py-modindex.html
@@ -1,45 +1,157 @@
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+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.scaling.html">netcal.scaling</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.regularization.html">netcal.regularization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.metrics.html">netcal.metrics</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.presentation.html">netcal.presentation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.regression.html">netcal.regression</a></li>
+</ul>
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+
    <h1>Python Module Index</h1>
 
    <div class="modindex-jumpbox">
@@ -66,11 +178,41 @@ <h1>Python Module Index</h1>
        <td>&#160;&#160;&#160;
        <a href="_autosummary/netcal.metrics.html#module-netcal.metrics"><code class="xref">netcal.metrics</code></a></td><td>
        <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="_autosummary/_autosummary_metric_submodules/netcal.metrics.confidence.html#module-netcal.metrics.confidence"><code class="xref">netcal.metrics.confidence</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="_autosummary/_autosummary_metric_submodules/netcal.metrics.regression.html#module-netcal.metrics.regression"><code class="xref">netcal.metrics.regression</code></a></td><td>
+       <em></em></td></tr>
      <tr class="cg-1">
        <td></td>
        <td>&#160;&#160;&#160;
        <a href="_autosummary/netcal.presentation.html#module-netcal.presentation"><code class="xref">netcal.presentation</code></a></td><td>
        <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="_autosummary/netcal.regression.html#module-netcal.regression"><code class="xref">netcal.regression</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="_autosummary/_autosummary_regression_gp/netcal.regression.gp.html#module-netcal.regression.gp"><code class="xref">netcal.regression.gp</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.kernel.html#module-netcal.regression.gp.kernel"><code class="xref">netcal.regression.gp.kernel</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="_autosummary/_autosummary_regression_gp/_autosummary_regression_gp_submodules/netcal.regression.gp.likelihood.html#module-netcal.regression.gp.likelihood"><code class="xref">netcal.regression.gp.likelihood</code></a></td><td>
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+<li class="toctree-l1"><a class="reference internal" href="_autosummary/netcal.presentation.html">netcal.presentation</a></li>
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10, 15, 16, 17, 18, 21, 28, 52, 53, 55, 57, 64], "boolean": [0, 1, 2, 3, 52, 53, 54, 55, 56, 57, 64], "probabl": [0, 1, 2, 3, 5, 7, 8, 9, 10, 12, 13, 16, 17, 18, 20, 21, 23, 24, 27, 28, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 47, 52, 53, 54, 55, 56, 57, 59, 61, 63, 64, 65], "independ": [0, 1, 2, 3, 29, 30, 33, 34, 35, 36, 39, 40, 52, 53, 54, 55, 56, 57, 64, 65], "other": [0, 1, 2, 3, 30, 34, 35, 36, 52, 53, 54, 55, 56, 57, 64, 65], "sigmoid": [0, 1, 2, 3, 31, 37, 41, 52, 53, 54, 55, 56, 57, 64], "refer": [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 17, 18, 19, 21, 23, 25, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57], "naeini": [0, 1, 5, 7, 16, 17, 65], "mahdi": [0, 1, 5, 7, 16, 17, 65], "pakdaman": [0, 1, 5, 7, 16, 17, 65], "gregori": [0, 1, 5, 7, 16, 17, 65], "cooper": [0, 1, 5, 7, 16, 17, 65], "milo": [0, 5, 7, 16, 17, 65], "hauskrecht": [0, 5, 7, 16, 17, 65], "twenti": [0, 5, 7, 16, 17, 65], "ninth": [0, 5, 7, 16, 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37, 65], "regress": [1, 2, 3, 4, 6, 9, 10, 11, 12, 13, 14, 15, 28, 29, 30, 52, 53, 54, 55, 56, 57, 59, 60], "initi": [1, 3, 65], "allow": [1, 52], "contrast": [1, 33, 36, 39, 47, 52, 65], "standard": [1, 6, 9, 12, 19, 20, 23, 27, 33, 34, 35, 36, 39, 41, 42, 43, 44, 53, 55, 57, 61, 65], "isotonicregress": [1, 58, 61, 65], "violat": 1, "monotoni": 1, "restrict": [1, 31, 36, 37, 47, 56], "modifi": 1, "pool": 1, "adjac": 1, "algorithm": [1, 12, 23, 65], "mpava": 1, "build": 1, "them": 1, "certain": [1, 8, 12, 13, 18, 23, 24, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 47, 65], "quick": 1, "nir": 1, "consecut": 1, "valu": [1, 28, 51, 57, 64, 65], "group": [1, 4, 5, 7, 15, 16, 17, 65], "directli": [1, 41, 50, 52, 56, 65], "f": [1, 34, 36, 53, 54, 55, 56, 65], "binari": [1, 2, 31, 37, 41, 51, 53, 54, 55, 56, 57, 65], "classifi": [1, 2, 3, 8, 18, 31, 37, 41, 53, 54, 55, 56, 57, 65], "an": [1, 4, 5, 6, 7, 10, 12, 13, 14, 15, 16, 17, 19, 21, 23, 24, 25, 32, 36, 38, 52, 53, 54, 55, 56, 61, 65], "2016": [1, 65], "ieee": [1, 2, 4, 5, 7, 15, 16, 17, 28, 52, 53, 54, 55, 56, 57, 65], "16th": [1, 65], "intern": [1, 8, 10, 12, 18, 21, 23, 28, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 47, 50, 55, 57, 61, 65], "mine": [1, 65], "icdm": [1, 65], "union": [2, 4, 5, 6, 7, 10, 14, 15, 16, 17, 19, 21, 25, 28, 29, 30, 36, 52], "int": [2, 4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 52, 53, 54, 55, 56, 57], "iter": [2, 4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 28, 29, 30, 54], "10": [2, 4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 28, 29, 55, 65], "simpl": [2, 65], "histogram": [2, 28, 65], "assign": [2, 48, 51], "its": [2, 35], "work": [2, 35, 36, 53, 65], "classif": [2, 4, 5, 7, 15, 16, 17, 28, 31, 37, 49, 51, 53, 54, 55, 56, 57, 60], "For": [2, 11, 22, 27, 34, 35, 36, 48, 49, 50, 53, 54, 55, 56, 57, 59, 60, 62, 65], "multiclass": [2, 3, 53, 55, 57, 65], "appli": [2, 6, 12, 14, 19, 23, 25, 27, 31, 33, 35, 37, 39, 41, 42, 43, 44, 48, 51, 53, 54, 55, 56, 57, 62, 63, 65], "v": [2, 10, 21, 53, 56, 65], "manner": 2, "boundari": [2, 3, 34], "chosen": 2, "interv": [2, 10, 21, 31, 37, 65], "On": [2, 4, 5, 7, 10, 15, 16, 17, 21, 28, 34, 35, 36, 52, 53, 55, 57, 65], "object": [2, 4, 5, 7, 12, 15, 16, 17, 23, 28, 29, 32, 33, 35, 38, 39, 42, 43, 44, 47, 52, 53, 54, 55, 56, 60, 61, 63], "multidimension": [2, 65], "includ": [2, 4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 65], "addit": [2, 28, 41, 44, 53, 54, 55, 56, 57, 63, 65], "branch": [2, 65], "3": [2, 12, 23, 28, 31, 32, 33, 36, 37, 38, 39, 41, 47, 53, 54, 55, 56, 61], "mode": [2, 4, 5, 7, 8, 10, 15, 16, 17, 18, 21, 28, 32, 38, 42, 53, 55, 65], "dimens": [2, 4, 5, 6, 7, 9, 10, 12, 14, 15, 16, 17, 19, 20, 21, 23, 25, 28, 29, 34, 35, 36, 40, 41, 42, 43, 44, 53, 54, 55, 56, 57, 65], "nx1": [2, 4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 28, 29], "nx2": [2, 4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 28, 29], "zadrozni": [2, 3, 65], "bianca": [2, 3, 65], "elkan": [2, 3, 65], "charl": [2, 3, 65], "from": [2, 8, 12, 18, 23, 31, 32, 33, 36, 37, 38, 39, 41, 50, 52, 55, 64, 65], "decis": [2, 65], "tree": [2, 65], "naiv": [2, 65], "In": [2, 3, 9, 10, 12, 20, 21, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 47, 52, 65], "icml": [2, 10, 21, 65], "pp": [2, 3, 12, 23, 28, 36, 40, 41, 54, 65], "609": [2, 65], "616": [2, 65], "2001": [2, 65], "transform": [2, 3, 33, 39, 65], "accur": [2, 3, 10, 21, 31, 34, 37, 47, 61, 65], "kdd": [2, 3, 65], "694": [2, 3, 65], "699": [2, 3, 65], "2002": [2, 3, 65], "fabian": [2, 4, 5, 7, 12, 15, 16, 17, 23, 28, 29, 32, 33, 38, 39, 42, 43, 44, 47, 52, 53, 54, 55, 56, 57, 61, 65], "k\u00fcpper": [2, 4, 5, 7, 12, 15, 16, 17, 23, 28, 29, 32, 33, 38, 39, 42, 43, 44, 47, 52, 53, 54, 55, 56, 57, 61, 65], "jan": [2, 4, 5, 7, 15, 16, 17, 28, 52, 53, 54, 55, 56, 57, 65], "kronenberg": [2, 4, 5, 7, 15, 16, 17, 28, 52, 53, 54, 55, 56, 57, 65], "amirhossein": [2, 4, 5, 7, 15, 16, 17, 28, 53, 54, 55, 56, 65], "shantia": [2, 4, 5, 7, 15, 16, 17, 28, 53, 54, 55, 56, 65], "anselm": [2, 4, 5, 7, 12, 15, 16, 17, 23, 28, 29, 32, 33, 38, 39, 42, 43, 44, 47, 52, 53, 54, 55, 56, 57, 61, 65], "haselhoff": [2, 4, 5, 7, 12, 15, 16, 17, 23, 28, 29, 32, 33, 38, 39, 42, 43, 44, 47, 52, 53, 54, 55, 56, 57, 61, 65], "multivari": [2, 4, 5, 7, 9, 12, 15, 16, 17, 20, 23, 28, 29, 30, 32, 33, 36, 38, 39, 42, 43, 44, 47, 53, 54, 55, 56, 61, 63, 65], "cvf": [2, 4, 5, 7, 15, 16, 17, 53, 54, 55, 56, 65], "vision": [2, 4, 5, 7, 12, 15, 16, 17, 23, 28, 29, 32, 33, 38, 39, 42, 43, 44, 53, 54, 55, 56, 65], "pattern": [2, 4, 5, 7, 15, 16, 17, 28, 53, 54, 55, 56, 65], "recognit": [2, 4, 5, 7, 15, 16, 17, 28, 53, 54, 55, 56, 65], "cvpr": [2, 4, 5, 7, 15, 16, 17, 28, 53, 54, 55, 56, 65], "workshop": [2, 4, 5, 7, 10, 12, 15, 16, 17, 21, 23, 28, 29, 32, 33, 38, 39, 42, 43, 44, 53, 54, 55, 56, 65], "2020": [2, 4, 5, 7, 14, 15, 16, 17, 25, 28, 32, 33, 35, 38, 39, 49, 53, 54, 55, 56, 61, 65], "similar": [3, 6, 12, 14, 19, 23, 25, 26, 31, 32, 37, 38, 59, 60, 65], "dynam": 3, "size": [3, 5, 8, 16, 18, 31, 32, 33, 36, 37, 38, 39, 53, 54, 55, 56, 57, 60], "A": [3, 6, 12, 14, 19, 23, 25, 26, 28, 34, 35, 36, 40, 60, 61, 65], "piecewis": [3, 34], "constant": [3, 34], "fit": [3, 33, 34, 35, 39, 65], "bin": [4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 26, 27, 28, 29, 59, 60], "sample_threshold": [4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 28], "averag": [4, 5, 7, 12, 15, 16, 17, 23, 28, 36, 65], "error": [4, 5, 6, 7, 8, 12, 14, 15, 16, 17, 18, 19, 23, 25, 26, 27, 29, 33, 35, 39, 50, 59, 61, 65], "segment": [4, 5, 7, 15, 16, 17, 60], "task": [4, 5, 6, 15, 16, 19, 32, 33, 35, 38, 39, 53, 54, 55, 56, 57, 61, 65], "measur": [4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 50, 58], "between": [4, 5, 6, 7, 12, 14, 15, 16, 17, 19, 23, 25, 26, 28, 31, 32, 33, 36, 37, 38, 39, 49, 52, 53, 55, 59, 60, 65], "accuraci": [4, 5, 7, 10, 15, 16, 17, 21, 26, 28, 49, 58, 59, 60, 63, 65], "b": [4, 5, 6, 7, 12, 14, 15, 16, 17, 19, 23, 25, 31, 36, 37, 40, 41, 53, 54, 65], "frac": [4, 5, 6, 8, 12, 14, 15, 16, 18, 19, 23, 25, 31, 35, 37, 40, 41, 52, 53, 54, 55, 56], "text": [4, 5, 6, 7, 9, 12, 13, 14, 15, 16, 17, 19, 20, 23, 24, 25, 32, 33, 38, 39, 41, 42, 52, 53, 54, 55, 56], "acc": [4, 5, 7, 15, 16, 17], "conf": [4, 5, 7, 15, 16, 17], "where": [4, 5, 6, 7, 12, 14, 15, 16, 17, 19, 23, 25, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 47, 53, 54, 65], "th": [4, 5, 7, 15, 16, 17], "main": [4, 15], "ec": [4, 6, 8, 12, 14, 15, 18, 19, 23, 25, 26, 28, 59, 60, 65], "below": [4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 65], "threshold": [4, 5, 6, 7, 10, 12, 14, 15, 16, 17, 19, 21, 23, 25, 48, 51], "miscalibr": [4, 5, 6, 7, 12, 14, 15, 16, 17, 19, 23, 25, 26, 27, 28, 53, 54, 55, 56, 57, 60], "neumann": [4, 15, 65], "luka": [4, 15, 65], "andrew": [4, 15, 65], "zisserman": [4, 15, 65], "andrea": [4, 15, 65], "vedaldi": [4, 15, 65], "relax": [4, 15, 65], "effici": [4, 15, 65], "auto": [4, 15, 65], "safe": [4, 15, 65], "pedestrian": [4, 15, 65], "neural": [4, 8, 10, 15, 18, 21, 28, 48, 49, 50, 51, 55, 57, 65], "process": [4, 10, 15, 21, 31, 32, 33, 36, 37, 38, 39, 41, 42, 45, 46, 47, 65], "system": [4, 15, 65], "nip": [4, 15, 65], "mlit": [4, 15, 65], "2018": [4, 8, 10, 15, 18, 21, 31, 34, 37, 47, 50, 61, 65], "expect": [5, 6, 8, 12, 16, 18, 19, 23, 34, 35, 65], "precis": [5, 16], "so": [5, 12, 16, 23, 31, 32, 33, 36, 37, 38, 39, 41, 42, 43, 44, 65], "n_b": [5, 12, 14, 16, 23, 25], "evalu": [6, 10, 12, 14, 19, 21, 23, 25, 26, 27, 32, 33, 35, 38, 39, 52, 59, 61, 65], "test": [6, 12, 13, 14, 19, 23, 24, 25, 27], "varianc": [6, 12, 14, 19, 23, 25, 27, 32, 33, 35, 36, 38, 39, 41, 42, 44, 47, 55, 61, 65], "probabilist": [6, 9, 13, 14, 19, 20, 24, 25, 27, 29, 30, 32, 33, 34, 35, 36, 38, 39, 55, 60], "take": [6, 14, 19, 25, 65], "output": [6, 9, 13, 14, 19, 20, 24, 25, 33, 34, 35, 36, 39, 47, 48, 51, 53, 54, 55, 56, 57, 65], "mean": [6, 8, 10, 12, 14, 18, 19, 21, 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"process": 61, "optim": 61, "function": 62, "abstractcalibr": 64, "api": 65, "net": 65, "cal": 65, "base": 65, "tabl": 65, "content": 65, "overview": 65, "updat": 65, "version": 65, "1": 65, "3": 65, "2": 65, "instal": 65, "requir": 65, "non": 65, "parametr": 65, "exampl": 65, "classif": 65, "post": 65, "hoc": 65, "detect": 65, "object": 65, "correl": 65, "estim": 65, "recalibr": 65}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx": 57}, "alltitles": {"netcal.binning.BBQ": [[0, "netcal-binning-bbq"]], "netcal.binning.ENIR": [[1, "netcal-binning-enir"]], "netcal.binning.HistogramBinning": [[2, "netcal-binning-histogrambinning"]], "netcal.binning.IsotonicRegression": [[3, "netcal-binning-isotonicregression"]], "netcal.metrics.ACE": [[4, "netcal-metrics-ace"]], "netcal.metrics.ECE": [[5, "netcal-metrics-ece"]], "netcal.metrics.ENCE": [[6, "netcal-metrics-ence"]], "netcal.metrics.MCE": [[7, "netcal-metrics-mce"]], "netcal.metrics.MMCE": [[8, "netcal-metrics-mmce"]], "netcal.metrics.NLL": [[9, "netcal-metrics-nll"]], "netcal.metrics.PICP": [[10, "netcal-metrics-picp"]], "netcal.metrics.PinballLoss": [[11, "netcal-metrics-pinballloss"]], "netcal.metrics.QCE": [[12, "netcal-metrics-qce"]], "netcal.metrics.QuantileLoss": [[13, "netcal-metrics-quantileloss"]], "netcal.metrics.UCE": [[14, "netcal-metrics-uce"]], "netcal.metrics.confidence.ACE": [[15, "netcal-metrics-confidence-ace"]], "netcal.metrics.confidence.ECE": [[16, "netcal-metrics-confidence-ece"]], "netcal.metrics.confidence.MCE": [[17, "netcal-metrics-confidence-mce"]], "netcal.metrics.confidence.MMCE": [[18, "netcal-metrics-confidence-mmce"]], "netcal.metrics.regression.ENCE": [[19, "netcal-metrics-regression-ence"]], "netcal.metrics.regression.NLL": [[20, "netcal-metrics-regression-nll"]], "netcal.metrics.regression.PICP": [[21, "netcal-metrics-regression-picp"]], "netcal.metrics.regression.PinballLoss": [[22, "netcal-metrics-regression-pinballloss"]], "netcal.metrics.regression.QCE": [[23, "netcal-metrics-regression-qce"]], "netcal.metrics.regression.QuantileLoss": [[24, "netcal-metrics-regression-quantileloss"]], "netcal.metrics.regression.UCE": [[25, "netcal-metrics-regression-uce"]], "netcal.metrics.confidence": [[26, "module-netcal.metrics.confidence"]], "Metrics for Confidence Calibration": [[26, "metrics-for-confidence-calibration"]], "Available classes": [[26, "available-classes"], [27, "available-classes"], [45, "available-classes"], [46, "available-classes"], [47, "available-classes"], [58, "available-classes"], [59, "available-classes"], [60, "available-classes"], [61, "available-classes"], [63, "available-classes"]], "netcal.metrics.regression": [[27, "module-netcal.metrics.regression"]], "Metrics for Regression Uncertainty Calibration": [[27, "metrics-for-regression-uncertainty-calibration"]], "netcal.presentation.ReliabilityDiagram": [[28, "netcal-presentation-reliabilitydiagram"]], "netcal.presentation.ReliabilityQCE": [[29, "netcal-presentation-reliabilityqce"]], "netcal.presentation.ReliabilityRegression": [[30, "netcal-presentation-reliabilityregression"]], "netcal.regression.GPBeta": [[31, "netcal-regression-gpbeta"]], "netcal.regression.GPCauchy": [[32, "netcal-regression-gpcauchy"]], "netcal.regression.GPNormal": [[33, "netcal-regression-gpnormal"]], "netcal.regression.IsotonicRegression": [[34, "netcal-regression-isotonicregression"]], "netcal.regression.VarianceScaling": [[35, "netcal-regression-variancescaling"]], "netcal.regression.gp.AbstractGP": [[36, "netcal-regression-gp-abstractgp"]], "netcal.regression.gp.GPBeta": [[37, "netcal-regression-gp-gpbeta"]], "netcal.regression.gp.GPCauchy": [[38, "netcal-regression-gp-gpcauchy"]], "netcal.regression.gp.GPNormal": [[39, "netcal-regression-gp-gpnormal"]], "netcal.regression.gp.kernel.GaussianRBFKernel": [[40, "netcal-regression-gp-kernel-gaussianrbfkernel"]], "netcal.regression.gp.likelihood.BetaLikelihood": [[41, "netcal-regression-gp-likelihood-betalikelihood"]], "netcal.regression.gp.likelihood.CauchyLikelihood": [[42, "netcal-regression-gp-likelihood-cauchylikelihood"]], "netcal.regression.gp.likelihood.ScaledMultivariateNormalLikelihood": [[43, "netcal-regression-gp-likelihood-scaledmultivariatenormallikelihood"]], "netcal.regression.gp.likelihood.ScaledNormalLikelihood": [[44, "netcal-regression-gp-likelihood-scalednormallikelihood"]], "netcal.regression.gp.kernel": [[45, "module-netcal.regression.gp.kernel"]], "Kernels for GP": [[45, "kernels-for-gp"]], "netcal.regression.gp.likelihood": [[46, "module-netcal.regression.gp.likelihood"]], "Likelihoods for GP": [[46, "likelihoods-for-gp"]], "netcal.regression.gp": [[47, "module-netcal.regression.gp"]], "Regression GP Calibration Package": [[47, "regression-gp-calibration-package"]], "References": [[47, "references"], [61, "references"], [65, "references"]], "Packages": [[47, "packages"], [59, "packages"]], "netcal.regularization.ConfidencePenalty": [[48, "netcal-regularization-confidencepenalty"]], "netcal.regularization.DCAPenalty": [[49, "netcal-regularization-dcapenalty"]], "netcal.regularization.MMCEPenalty": [[50, "netcal-regularization-mmcepenalty"]], "netcal.regularization.confidence_penalty": [[51, "netcal-regularization-confidence-penalty"]], "netcal.scaling.AbstractLogisticRegression": [[52, "netcal-scaling-abstractlogisticregression"]], "netcal.scaling.BetaCalibration": [[53, "netcal-scaling-betacalibration"]], "netcal.scaling.BetaCalibrationDependent": [[54, "netcal-scaling-betacalibrationdependent"]], "netcal.scaling.LogisticCalibration": [[55, "netcal-scaling-logisticcalibration"]], "netcal.scaling.LogisticCalibrationDependent": [[56, "netcal-scaling-logisticcalibrationdependent"]], "netcal.scaling.TemperatureScaling": [[57, "netcal-scaling-temperaturescaling"]], "netcal.binning": [[58, "module-netcal.binning"]], "Binning Methods for Confidence Calibration": [[58, "binning-methods-for-confidence-calibration"]], "netcal.metrics": [[59, "module-netcal.metrics"]], "Metrics Package to Measure Miscalibration": [[59, "metrics-package-to-measure-miscalibration"]], "netcal.presentation": [[60, "module-netcal.presentation"]], "Visualization Package": [[60, "visualization-package"]], "netcal.regression": [[61, "module-netcal.regression"]], "Probabilistic Regression Calibration Package": [[61, "probabilistic-regression-calibration-package"]], "Package for Gaussian process optimization": [[61, "package-for-gaussian-process-optimization"]], "netcal.scaling": [[63, "module-netcal.scaling"]], "Scaling Methods for Confidence Calibration": [[63, "scaling-methods-for-confidence-calibration"]], "netcal.AbstractCalibration": [[64, "netcal-abstractcalibration"]], "API Reference of net:cal": [[65, "api-reference-of-net-cal"]], "Available packages": [[65, "available-packages"]], "Base class": [[65, "base-class"]], "net:cal - Uncertainty Calibration": [[65, "net-cal-uncertainty-calibration"]], "Table of Contents": [[65, "table-of-contents"]], "Overview": [[65, "overview"]], "Update on version 1.3": [[65, "update-on-version-1-3"]], "Update on version 1.2": [[65, "update-on-version-1-2"]], "Update on version 1.1": [[65, "update-on-version-1-1"]], "Installation": [[65, "installation"]], "Requirements": [[65, "requirements"]], "Calibration Metrics": [[65, "calibration-metrics"]], "Confidence Calibration Metrics": [[65, "confidence-calibration-metrics"]], "Regression Calibration Metrics": [[65, "regression-calibration-metrics"]], "Methods": [[65, "methods"]], "Confidence Calibration Methods": [[65, "confidence-calibration-methods"]], "Binning": [[65, "binning"]], "Scaling": [[65, "scaling"]], "Regularization": [[65, "regularization"]], "Regression Calibration Methods": [[65, "regression-calibration-methods"]], "Non-parametric calibration": [[65, "non-parametric-calibration"]], "Parametric calibration": [[65, "parametric-calibration"]], "Visualization": [[65, "visualization"]], "Examples": [[65, "examples"]], "Classification": [[65, "classification"]], "Post-hoc Calibration for Classification": [[65, "post-hoc-calibration-for-classification"]], "Measuring Miscalibration for Classification": [[65, "measuring-miscalibration-for-classification"]], "Visualizing Miscalibration for Classification": [[65, "visualizing-miscalibration-for-classification"]], "Detection (Confidence of Objects)": [[65, "detection-confidence-of-objects"]], "Post-hoc Calibration for Detection": [[65, "post-hoc-calibration-for-detection"]], "Measuring Miscalibration for Detection": [[65, "measuring-miscalibration-for-detection"]], "Visualizing Miscalibration for Detection": [[65, "visualizing-miscalibration-for-detection"]], "Uncertainty in Confidence Calibration": [[65, "uncertainty-in-confidence-calibration"]], "Post-hoc Calibration with Uncertainty": [[65, "post-hoc-calibration-with-uncertainty"]], "Measuring Miscalibration with Uncertainty": [[65, "measuring-miscalibration-with-uncertainty"]], "Probabilistic Regression": [[65, "probabilistic-regression"]], "Post-hoc Calibration (Parametric)": [[65, "post-hoc-calibration-parametric"]], "Post-hoc Calibration (Non-Parametric)": [[65, "post-hoc-calibration-non-parametric"]], "Correlation Estimation and Recalibration": [[65, "correlation-estimation-and-recalibration"]], "Measuring Miscalibration for Regression": [[65, "measuring-miscalibration-for-regression"]], "Visualizing Miscalibration for Regression": [[65, "visualizing-miscalibration-for-regression"]], "netcal.regularization": [[62, "module-netcal.regularization"]], "Regularization Methods for Confidence Calibration": [[62, "regularization-methods-for-confidence-calibration"]], "Available functions": [[62, "available-functions"]]}, "indexentries": {"module": [[62, "module-netcal.regularization"], [65, "module-netcal"]], "netcal.regularization": [[62, "module-netcal.regularization"]], "netcal": [[65, "module-netcal"]]}})
\ No newline at end of file

From db47441fbef168453e216f1619c08fa2ca84665c Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 10:13:02 +0200
Subject: [PATCH 13/21] Update copyright in classification examples.

---
 examples/classification/CIFAR.py      | 4 ++--
 examples/classification/Evaluation.py | 4 ++--
 examples/classification/__init__.py   | 4 ++--
 examples/classification/utils.py      | 4 ++--
 4 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/examples/classification/CIFAR.py b/examples/classification/CIFAR.py
index 92588aa..923bc37 100644
--- a/examples/classification/CIFAR.py
+++ b/examples/classification/CIFAR.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/examples/classification/Evaluation.py b/examples/classification/Evaluation.py
index 108646a..ead93bd 100644
--- a/examples/classification/Evaluation.py
+++ b/examples/classification/Evaluation.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/examples/classification/__init__.py b/examples/classification/__init__.py
index 9b42fae..19003ba 100644
--- a/examples/classification/__init__.py
+++ b/examples/classification/__init__.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/examples/classification/utils.py b/examples/classification/utils.py
index a1a6846..af11996 100644
--- a/examples/classification/utils.py
+++ b/examples/classification/utils.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerksysteme GmbH, Gaimersheim Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this

From c8052b9c9a49a2359880b657b5974f5e7870a537 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 10:19:13 +0200
Subject: [PATCH 14/21] Update detection example by a Bayesian confidence
 calibration option.

---
 examples/detection/Calibration.py |  55 ++---
 examples/detection/Evaluation.py  | 321 ++++++++++++++++++++++--------
 examples/detection/Features.py    |   4 +-
 examples/detection/Helper.py      |   4 +-
 examples/detection/__init__.py    |   4 +-
 5 files changed, 274 insertions(+), 114 deletions(-)

diff --git a/examples/detection/Calibration.py b/examples/detection/Calibration.py
index 995320c..20cded8 100644
--- a/examples/detection/Calibration.py
+++ b/examples/detection/Calibration.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -22,7 +22,7 @@
     raise ImportError("Need detectron2 to evaluate object detection calibration. You can get the latest version at https://github.com/facebookresearch/detectron2")
 
 
-def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str], ious: List[float], train_ids: List):
+def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str], ious: List[float], train_ids: List, bayesian: bool):
     """
     Perform calibration of the given frames (as list of dicts) for a dedicated dataset with dedicated train_ids.
     The trained models are stored at "calibration/<network>/models/".
@@ -48,7 +48,7 @@ def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str],
     """
 
     meta = MetadataCatalog.get(dataset)
-    model_dir = os.path.join("calibration", network, "models")
+    model_dir = os.path.join("calibration" if not bayesian else "bayesian_calibration", network, "models")
     os.makedirs(model_dir, exist_ok=True)
 
     # reverse mapping of category ids to network class ids (e.g. for COCO dataset)
@@ -80,13 +80,6 @@ def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str],
         print("Training: category %d: %d samples" % (category_id, features.shape[0]))
         for iou, m in zip(ious, matched):
 
-            # initialize calibration methods
-            histogram = HistogramBinning(bins=bins, detection=True)
-            lr = LogisticCalibration(detection=True)
-            lr_dependent = LogisticCalibrationDependent()
-            betacal = BetaCalibration(detection=True)
-            betacal_dependent = BetaCalibrationDependent(momentum_epochs=500)
-
             # if only negative (or positive) examples are given, calibration is not applicable
             unique = np.unique(m)
             print("Different labels:", unique)
@@ -94,24 +87,30 @@ def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str],
                 print("Calibration failed for cls %d as there are only negative samples" % i)
                 continue
 
-            # fit and save calibration models
-            print("Fit and save histogram binning")
-            histogram.fit(features, m)
-            histogram.save_model(os.path.join(model_dir, "histogram_%s_iou%.2f_cls-%02d.pkl" % (''.join(subset), iou, i)))
+            if not bayesian:
+                # fit and save calibration models
+                print("Fit and save histogram binning")
+                histogram = HistogramBinning(bins=bins, detection=True)
+                histogram.fit(features, m)
+                histogram.save_model(os.path.join(model_dir, "histogram_%s_iou%.2f_cls-%02d.pkl" % (''.join(subset), iou, i)))
 
             print("Fit independent logistic calibration")
+            lr = LogisticCalibration(detection=True, method="variational" if bayesian else "mle", vi_epochs=1000, use_cuda=True)
             lr.fit(features, m)
             lr.save_model(os.path.join(model_dir, "lr_%s_iou%.2f_cls-%02d.pkl" % (''.join(subset), iou, i)))
 
             print("Fit dependent logistic calibration")
+            lr_dependent = LogisticCalibrationDependent(method="variational" if bayesian else "mle", vi_epochs=1000, use_cuda=True)
             lr_dependent.fit(features, m)
             lr_dependent.save_model(os.path.join(model_dir, "lr_dependent_%s_iou%.2f_cls-%02d.pkl" % (''.join(subset), iou, i)))
 
             print("Fit independent beta calibration")
+            betacal = BetaCalibration(detection=True, method="variational" if bayesian else "mle", vi_epochs=1000, use_cuda=True)
             betacal.fit(features, m)
             betacal.save_model(os.path.join(model_dir, "betacal_%s_iou%.2f_cls-%02d.pkl" % (''.join(subset), iou, i)))
 
             print("Fit dependent beta calibration")
+            betacal_dependent = BetaCalibrationDependent(method="variational" if bayesian else "momentum", momentum_epochs=500, vi_epochs=1000, use_cuda=True)
             betacal_dependent.fit(features, m)
             betacal_dependent.save_model(os.path.join(model_dir, "betacal_dependent_%s_iou%.2f_cls-%02d.pkl" % (''.join(subset), iou, i)))
 
@@ -121,22 +120,25 @@ def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str],
     # to use this script, perform inference of neural network using Detectron2 first. The predictions are stored as
     # a JSON file in COCO annotations format. This JSON file is understood by the methods in this script.
 
+    # set 'bayesian' to true if you want to use stochastic variational inference for calibration training
+    bayesian = True
+
     # COCO data - Faster RCNN
-    filename = "./data/faster-rcnn-coco/inference/coco_instances_results.json"
-    network = "COCO-faster-rcnn-threshold-%.f"
+    # filename = "./data/faster-rcnn-coco/inference/coco_instances_results.json"
+    # network = "COCO-faster-rcnn-threshold-%.2f"
 
     # COCO data - RetinaNet
     # filename = "./data/retinanet-coco/inference/coco_instances_results.json"
-    # network = "COCO-retinanet-threshold-%.f"
+    # network = "COCO-retinanet-threshold-%.2f"
 
-    dataset = "coco_2017_val"
-    train_ids, val_ids = read_image_ids("image_ids_coco.json")
+    # dataset = "coco_2017_val"
+    # train_ids, val_ids = read_image_ids("image_ids_coco.json")
 
     # Cityscapes data
-    # filename = "./data/mask-rcnn-cityscapes/inference/coco_instances_results.json"
-    # dataset = "cityscapes_fine_instance_seg_val"
-    # network = "Cityscapes-mask-rcnn-threshold-%.f"
-    # train_ids, val_ids = read_image_ids("image_ids_cityscapes.json")
+    filename = "./data/mask-rcnn-cityscapes/inference/coco_instances_results.json"
+    dataset = "cityscapes_fine_instance_seg_val"
+    network = "Cityscapes-mask-rcnn-threshold-%.2f"
+    train_ids, val_ids = read_image_ids("image_ids_cityscapes.json")
 
     # score threshold used for calibration
     score_threshold = 0.3
@@ -145,7 +147,8 @@ def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str],
     network = network % score_threshold
 
     # define different subsets and IoUs that are used for evaluation
-    subsets = [[], ['cx', 'cy'], ['w', 'h'], ['cx', 'cy', 'w', 'h']]
+    # subsets = [[], ['cx', 'cy'], ['w', 'h'], ['cx', 'cy', 'w', 'h']]
+    subsets = [[], ['cx', 'cy', 'w', 'h']]
     ious = [0.5, 0.75]
 
     print("Load dataset")
@@ -157,4 +160,4 @@ def calibrate(frames: List[Dict], dataset: str, network: str, subset: List[str],
 
     # perform confidence calibration for each subset
     for subset in subsets:
-        calibrate(frames, dataset, network, subset, ious, train_ids)
+        calibrate(frames, dataset, network, subset, ious, train_ids, bayesian)
diff --git a/examples/detection/Evaluation.py b/examples/detection/Evaluation.py
index 9242dd6..6a7ff43 100644
--- a/examples/detection/Evaluation.py
+++ b/examples/detection/Evaluation.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
@@ -18,7 +18,7 @@
 from netcal.binning import HistogramBinning
 from netcal.scaling import LogisticCalibration, BetaCalibration
 from netcal.scaling import LogisticCalibrationDependent, BetaCalibrationDependent
-from netcal.metrics import ECE
+from netcal.metrics import ECE, PICP, QCE
 from netcal.presentation import ReliabilityDiagram
 from examples.detection.Helper import read_json, read_image_ids, match_frames_with_groundtruth
 from examples.detection.Features import get_features
@@ -29,7 +29,16 @@
     raise ImportError("Need detectron2 to evaluate object detection calibration. You can get the latest version at https://github.com/facebookresearch/detectron2")
 
 
-def transform(frames: List[Dict], dataset: str, network: str, subset: List, ious: List, test_ids: List[int]):
+def transform(
+        frames: List[Dict],
+        dataset: str,
+        network: str,
+        subset: List,
+        ious: List,
+        test_ids: List[int],
+        common_thing_classes: List[str],
+        bayesian: bool
+):
     """
     After calibration training, evaluate the trained models by several miscalibration metrics. These metrics are:
     D-ECE, Brier, NLL. Also capture area under precision-recall curve (AUPRC).
@@ -55,19 +64,29 @@ def transform(frames: List[Dict], dataset: str, network: str, subset: List, ious
         List of data frame ids used for calibration testing.
     """
 
+    n_stochastic = 1000
+    random_seed = 0
+    quantiles = np.linspace(0.05, 0.95, 21)
+
     # get meta information and specify all relevant paths
     meta = MetadataCatalog.get(dataset)
-    model_dir = os.path.join("calibration", network, "models")
-    output_dir = os.path.join("output", network)
+    model_dir = os.path.join("calibration" if not bayesian else "bayesian_calibration", network, "models")
+    output_dir = os.path.join("output" if not bayesian else "bayesian_output", network, dataset)
     diagram_path = os.path.join(output_dir, "diagrams", ''.join(subset) if len(subset) > 0 else "confidence")
 
     os.makedirs(output_dir, exist_ok=True)
     os.makedirs(diagram_path, exist_ok=True)
 
     # calibration methods that have also been used for calibration training
-    methods = [("histogram", HistogramBinning), ("lr", LogisticCalibration),
-               ("lr_dependent", LogisticCalibrationDependent), ("betacal", BetaCalibration),
-               ("betacal_dependent", BetaCalibrationDependent)]
+    methods = [
+        ("lr", LogisticCalibration),
+        ("lr_dependent", LogisticCalibrationDependent),
+        ("betacal", BetaCalibration),
+        ("betacal_dependent", BetaCalibrationDependent)
+    ]
+
+    if not bayesian:
+        methods.append(("histogram", HistogramBinning))
 
     # reverse mapping of category ids to network class ids (e.g. for COCO dataset)
     if hasattr(meta, "thing_dataset_id_to_contiguous_id"):
@@ -75,14 +94,28 @@ def transform(frames: List[Dict], dataset: str, network: str, subset: List, ious
     else:
         reverse_dictionary = None
 
+    if common_thing_classes is not None:
+        eval_classes = list(filter(lambda x: x[1] in common_thing_classes, enumerate(meta.thing_classes)))
+    else:
+        eval_classes = enumerate(meta.thing_classes)
+
+    n_classes_in_dataset = len(meta.thing_classes)
+
     # lists and placeholders for evaluation metrics
     n_samples_total = 0
-    n_samples_per_class = []
-    dece_per_class = [[[] for _ in ious] for _ in range(len(methods)+1)]
+    n_samples_per_class = np.zeros(n_classes_in_dataset, dtype=np.int64)
+
+    # fill anything by NaN so that e.g. empty classes are not considered for the final computation
+    dece_per_class = np.full((len(methods)+1, len(ious), n_classes_in_dataset), fill_value=np.nan, dtype=np.float32)
+
+    brier_per_class = np.full((len(methods)+1, len(ious), n_classes_in_dataset), fill_value=np.nan, dtype=np.float32)
+    nll_per_class = np.full((len(methods)+1, len(ious), n_classes_in_dataset), fill_value=np.nan, dtype=np.float32)
+    average_precision = np.full((len(methods)+1, len(ious), n_classes_in_dataset), fill_value=np.nan, dtype=np.float32)
 
-    brier_per_class = [[[] for _ in ious] for _ in range(len(methods) + 1)]
-    nll_per_class = [[[] for _ in ious] for _ in range(len(methods) + 1)]
-    average_precision = [[[] for _ in ious] for _ in range(len(methods) + 1)]
+    # uncertainty metrics
+    picp_per_class = np.full((len(methods)+1, len(ious), n_classes_in_dataset), fill_value=np.nan, dtype=np.float32)
+    mpiw_per_class = np.full((len(methods)+1, len(ious), n_classes_in_dataset), fill_value=np.nan, dtype=np.float32)
+    qce_per_class = np.full((len(methods)+1, len(ious), n_classes_in_dataset), fill_value=np.nan, dtype=np.float32)
 
     # -----------------------------------------------------
     # visualization routine
@@ -94,17 +127,38 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
         # Define function for diagram output
 
         # plot baseline miscalibration
-        figures = [diagram0d.plot(f[:, :1], m, tikz=False, title_suffix=title, filename=formatter % "0d")]
+        figures = [diagram0d.plot(
+            f[..., :1], m,
+            tikz=False,
+            title_suffix=title,
+            filename=formatter % "0d",
+            uncertainty="mean" if bayesian else None
+        )]
 
         # plot all additional features in 1D miscalibration plots
         for i, fname in enumerate(['cx', 'cy', 'w', 'h']):
-            figures.append(diagram1d.plot(f[:, (0, i + 1)], m, tikz=False, feature_names=[fname], title_suffix=title,
-                                          filename=formatter % ("1d_%s" % fname)))
+            figures.append(
+                diagram1d.plot(
+                    f[..., (0, i + 1)], m,
+                    tikz=False,
+                    feature_names=[fname],
+                    title_suffix=title,
+                    filename=formatter % ("1d_%s" % fname),
+                    uncertainty="mean" if bayesian else None
+                )
+            )
 
         # finally, plot all feature combinations of size 2
         for (i, fname1), (j, fname2) in itertools.combinations(enumerate(['cx', 'cy', 'w', 'h']), 2):
-            figures.append(diagram2d.plot(f[:, (0, i + 1, j + 1)], m, tikz=False, feature_names=[fname1, fname2],
-                                          title_suffix=title, filename=formatter % ("2d_%s_%s" % (fname1, fname2))))
+            figures.append(
+                diagram2d.plot(
+                    f[..., (0, i + 1, j + 1)], m,
+                    tikz=False,
+                    feature_names=[fname1, fname2],
+                    title_suffix=title,
+                    filename=formatter % ("2d_%s_%s" % (fname1, fname2)),
+                    uncertainty="mean" if bayesian else None)
+            )
 
         # free memory space
         for fig in figures:
@@ -113,7 +167,7 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
     # -----------------------------------------------------
 
     # iterate over all classes that are present in the current dataset
-    for i, classname in enumerate(meta.thing_classes):
+    for i, classname in eval_classes:
 
         # get calibration features for selected class
         category_id = reverse_dictionary[i] if reverse_dictionary is not None else i
@@ -124,6 +178,8 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
             print("No samples for category %s found" % classname)
             continue
 
+        n_samples, n_features = features.shape
+
         # different binning schemes for different feature dimensions
         if features.shape[1] == 1:
             bins = 20
@@ -136,7 +192,10 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
 
         # define D-ECE metric
         dece = ECE(bins=bins, detection=True, sample_threshold=8)
-        n_samples_per_class.append(features.shape[0])
+        picp = PICP(bins=bins, detection=True, sample_threshold=8)
+        qce = QCE(bins=bins, detection=True, marginal=True, sample_threshold=8)
+
+        n_samples_per_class[i] = features.shape[0]
         n_samples_total += features.shape[0]
 
         # failed flag is required to optionally blank failed or non-present classes during evaluation
@@ -144,25 +203,26 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
         failed = False
 
         # perform evaluation for each category separately
-        print("Inference: category %d: %d samples" % (category_id, features.shape[0]))
+        print("Inference: category %d (%s): %d samples" % (category_id, classname, features.shape[0]))
         for j, (iou, m) in enumerate(zip(ious, matched)):
 
             score = average_precision_score(m, features[:, 0])
             if not np.isfinite(score) or np.isnan(score):
-                brier_per_class[0][j].append(0.)
-                nll_per_class[0][j].append(0.)
-                dece_per_class[0][j].append(0.)
-                average_precision[0][j].append(0.)
                 failed = True
 
             # compute average precision, Brier, NLL and ECE
             else:
-                brier_per_class[0][j].append(np.mean(np.square(features[:, 0] - m)))
-                nll_per_class[0][j].append(-np.mean(m * np.log(features[:, 0]) + (1. - m) * np.log(1. - features[:, 0])))
-                dece_per_class[0][j].append(dece.measure(features, m))
-                average_precision[0][j].append(score)
+                brier_per_class[0, j, i] = np.mean(np.square(features[:, 0] - m))
+                nll_per_class[0, j, i] = -np.mean(m * np.log(features[:, 0]) + (1. - m) * np.log(1. - features[:, 0]))
+                dece_per_class[0, j, i] = dece.measure(features, m)
+                average_precision[0, j, i] = score
+
+            # uncertainty metrics are not defined for uncalibrated baseline
+            picp_per_class[0, j, i] = np.nan
+            mpiw_per_class[0, j, i] = np.nan
+            qce_per_class[0, j, i] = np.nan
 
-            diagramname = os.path.join(diagram_path, "default_cls-%02d_iou%.2f" % (i, iou) + "_%s.tex")
+            diagramname = os.path.join(diagram_path, "default_cls-%02d_iou%.2f" % (i, iou) + "_%s.png")
             plot(all_features, m, title="default", formatter=diagramname)
 
             # start calibration evaluation for each method separately
@@ -170,59 +230,96 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
                 instance = method()
 
                 try:
-                    print("Load %s and transform" % name)
-                    instance.load_model(os.path.join(model_dir, "%s_%s_iou%.2f_cls-%02d.pkl" % (name, ''.join(subset), iou, i)))
-                    calibrated = instance.transform(features)
+                    model_path = os.path.join(model_dir, "%s_%s_iou%.2f_cls-%02d.pkl" % (name, ''.join(subset), iou, i))
+                    print("Load %s at path: \'%s\'" % (name, model_path))
+                    instance.load_model(model_path)
+
+                    if bayesian:
+                        calibrated = instance.transform(features, num_samples=n_stochastic, random_state=random_seed)
+                        calibrated_mean = np.mean(calibrated, axis=0)
+                    else:
+                        calibrated = instance.transform(features)
+                        calibrated_mean = calibrated
 
                     # perform clipping
-                    np.clip(calibrated, np.finfo(np.float32).eps, 1.-np.finfo(np.float32).eps, out=calibrated)
-                    score = average_precision_score(m, calibrated)
+                    np.clip(calibrated, np.finfo(np.float32).eps, 1. - np.finfo(np.float32).eps, out=calibrated)
+                    np.clip(calibrated_mean, np.finfo(np.float32).eps, 1. - np.finfo(np.float32).eps, out=calibrated_mean)
+
+                    score = average_precision_score(m, calibrated_mean)
                     if not np.isfinite(score) or np.isnan(score):
                         raise ValueError("Couldn't compute AUPRC score")
 
-                    average_precision[k][j].append(score)
-
-                    brier_per_class[k][j].append(np.mean(np.square(calibrated - m)))
-                    nll_per_class[k][j].append(-np.mean(m * np.log(calibrated) + (1. - m) * np.log(1. - calibrated)))
-
-                    input = np.concatenate((np.reshape(calibrated, (-1, 1)), features[:, 1:]), axis=1)
-                    dece_per_class[k][j].append(dece.measure(input, m))
-
-                    diagramname = os.path.join(diagram_path, "%s_cls-%02d_iou%.2f" % (name, i, iou) + "_%s.tex")
-                    input = np.concatenate((np.reshape(calibrated, (-1, 1)), all_features[:, 1:]), axis=1)
+                    average_precision[k, j, i] = score
+
+                    brier_per_class[k, j, i] = np.mean(np.square(calibrated_mean - m))
+                    nll_per_class[k, j, i] = -np.mean(m * np.log(calibrated_mean) + (1. - m) * np.log(1. - calibrated_mean))
+
+                    input = np.concatenate(
+                        (
+                            np.expand_dims(calibrated, axis=-1),  # ([t,] n, 1)
+                            features[:, 1:] if not bayesian else np.broadcast_to(features[None, :, 1:], (n_stochastic, n_samples, n_features-1))  # ([t,] n, d-1)
+                        ),
+                        axis=-1
+                    )  # ([t,] n, d)
+                    dece_per_class[k, j, i] = dece.measure(input, m, uncertainty="mean" if bayesian else None)
+
+                    # now measure quality of bayesian output distributions
+                    if bayesian:
+                        picp_score, mpiw_score = picp.measure(input, m, uncertainty="mean")
+                        picp_per_class[k, j, i] = picp_score
+                        mpiw_per_class[k, j, i] = mpiw_score
+                        qce_per_class[k, j, i] = qce.measure(input, m, quantiles, kind="confidence", reduction="mean")
+
+                    diagramname = os.path.join(diagram_path, "%s_cls-%02d_iou%.2f" % (name, i, iou) + "_%s.png")
+                    input = np.concatenate(
+                        (
+                            np.expand_dims(calibrated, axis=-1),  # ([t,] n, 1)
+                            all_features[:, 1:] if not bayesian else np.broadcast_to(all_features[None, :, 1:], (n_stochastic, n_samples, 4))  # ([t,] n, d-1)
+                        ),
+                        axis=-1
+                    )
                     plot(input, m, title=name, formatter=diagramname)
 
-                except (FileNotFoundError, ValueError):
+                except (FileNotFoundError, ValueError) as e:
+                    print(e)
                     print("Could not find weight file ", os.path.join(model_dir, "%s_%s_iou%.2f_cls-%02d.pkl" % (name, ''.join(subset), iou, i)))
                     print("Disable evaluation for class %d" % i)
 
-                    brier_per_class[k][j].append(0.)
-                    nll_per_class[k][j].append(0.)
-                    dece_per_class[k][j].append(0.)
-                    average_precision[k][j].append(0.)
+                    brier_per_class[k, j, i] = np.nan
+                    nll_per_class[k, j, i] = np.nan
+                    dece_per_class[k, j, i] = np.nan
+                    average_precision[k, j, i] = np.nan
+
+                    picp_per_class[k, j, i] = np.nan
+                    mpiw_per_class[k, j, i] = np.nan
+                    qce_per_class[k, j, i] = np.nan
 
                     failed = True
 
         if failed:
-            n_samples_total -= n_samples_per_class[-1]
-            n_samples_per_class[-1] = 0
+            n_samples_total -= n_samples_per_class[i]
+            n_samples_per_class[i] = 0
 
     # convert all lists to NumPy arrays
-    weights = np.array(n_samples_per_class) / n_samples_total
-    brier_per_class = np.array(brier_per_class)
-    nll_per_class = np.array(nll_per_class)
-    dece_per_class = np.array(dece_per_class)
-    average_precision = np.array(average_precision)
-
-    # compute a feed-forward average and and a weighted counter-part
-    brier_global = np.mean(brier_per_class, axis=2)
-    weighted_brier_global = np.average(brier_per_class, weights=weights, axis=2)
-    nll_global = np.mean(nll_per_class, axis=2)
-    weighted_nll_global = np.average(nll_per_class, weights=weights, axis=2)
-    dece_global = np.mean(dece_per_class, axis=2)
-    weighted_dece_global = np.average(dece_per_class, weights=weights, axis=2)
-    average_precision_macro = np.mean(average_precision, axis=2)
-    average_precision_weighted = np.average(average_precision, weights=weights, axis=2)
+    weights = n_samples_per_class / n_samples_total  # (classes,)
+
+    def get_average_unweighted_weighted(array: np.ndarray):
+        # compute a feed-forward average and and a weighted counter-part
+
+        unweighted = np.nanmean(array, axis=2)
+        current_weights = (~np.isnan(array)) * weights  # (methods, iou, classes)
+        current_weights = current_weights / np.sum(current_weights, axis=2, keepdims=True)  # rescale so that the weights sum up to 1
+        weighted = np.nansum(array * current_weights, axis=2)
+
+        return unweighted, weighted
+
+    brier_global, weighted_brier_global = get_average_unweighted_weighted(brier_per_class)
+    nll_global, weighted_nll_global = get_average_unweighted_weighted(nll_per_class)
+    dece_global, weighted_dece_global = get_average_unweighted_weighted(dece_per_class)
+    average_precision_macro, average_precision_weighted = get_average_unweighted_weighted(average_precision)
+    picp_global, weighted_picp_global = get_average_unweighted_weighted(picp_per_class)
+    mpiw_global, weighted_mpiw_global = get_average_unweighted_weighted(mpiw_per_class)
+    qce_global, weighted_qce_global = get_average_unweighted_weighted(qce_per_class)
 
     # use tabulate library to visualize the evaluation results
     header = []
@@ -230,10 +327,55 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
     body.extend([[name] for name, method in methods])
     for i, iou in enumerate(ious):
 
-        header.extend(['D-ECE(w) @ IoU %.2f' % iou, 'D-ECE @ IoU %.2f' % iou, 'Brier(w) @ IoU %.2f' % iou, 'Brier @ IoU %.2f' % iou, 'NLL(w) @ IoU %.2f' % iou, 'NLL @ IoU %.2f' % iou, 'AP(w) @ IoU %.2f' % iou, 'AP @ IoU %.2f'])
-        body[0].extend([weighted_dece_global[0][i], dece_global[0][i], weighted_brier_global[0][i], brier_global[0][i], weighted_nll_global[0][i], nll_global[0][i], average_precision_weighted[0][i], average_precision_macro[0][i]])
+        header.extend([
+            'D-ECE(w) @ IoU %.2f' % iou,
+            'D-ECE @ IoU %.2f' % iou,
+            'Brier(w) @ IoU %.2f' % iou,
+            'Brier @ IoU %.2f' % iou,
+            'NLL(w) @ IoU %.2f' % iou,
+            'NLL @ IoU %.2f' % iou,
+            'AP(w) @ IoU %.2f' % iou,
+            'AP @ IoU %.2f' % iou,
+            'PICP(w) @ IoU %.2f' % iou,
+            'PICP @ IoU %.2f' % iou,
+            'MPIW(w) @ IoU %.2f' % iou,
+            'MPIW @ IoU %.2f' % iou,
+            'QCE(w) @ IoU %.2f' % iou,
+            'QCE @ IoU %.2f' % iou,
+        ])
+        body[0].extend([
+            weighted_dece_global[0, i],
+            dece_global[0, i],
+            weighted_brier_global[0, i],
+            brier_global[0, i],
+            weighted_nll_global[0, i],
+            nll_global[0, i],
+            average_precision_weighted[0, i],
+            average_precision_macro[0, i],
+            weighted_picp_global[0, i],
+            picp_global[0, i],
+            weighted_mpiw_global[0, i],
+            mpiw_global[0, i],
+            weighted_qce_global[0, i],
+            qce_global[0, i]
+        ])
         for k, (name, method) in enumerate(methods):
-            body[k+1].extend([weighted_dece_global[k+1][i], dece_global[k+1][i], weighted_brier_global[k+1][i], brier_global[k+1][i], weighted_nll_global[k+1][i], nll_global[k+1][i], average_precision_weighted[k+1][i], average_precision_macro[k+1][i]])
+            body[k+1].extend([
+                weighted_dece_global[k+1, i],
+                dece_global[k+1, i],
+                weighted_brier_global[k+1, i],
+                brier_global[k+1, i],
+                weighted_nll_global[k+1, i],
+                nll_global[k+1, i],
+                average_precision_weighted[k+1, i],
+                average_precision_macro[k+1, i],
+                weighted_picp_global[k+1, i],
+                picp_global[k+1, i],
+                weighted_mpiw_global[k+1, i],
+                mpiw_global[k+1, i],
+                weighted_qce_global[k+1, i],
+                qce_global[k+1, i]
+            ])
 
     results = [header, *body]
 
@@ -251,27 +393,42 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
     # to use this script, perform inference of neural network using Detectron2 first. The predictions are stored as
     # a JSON file in COCO annotations format. This JSON file is understood by the methods in this script.
 
+    # set 'bayesian' to true if you want to use stochastic variational inference for calibration training
+    bayesian = False
+
+    # classes that are common within Cityscapes and COCO. Is everything in Cityscapes except class "rider"
+    # only required when performing cross-evaluation
+    common_thing_classes = ['person', 'car', 'truck', 'bus', 'train', 'motorcycle', 'bicycle']
+    # common_thing_classes = None
+
     # COCO data - Faster RCNN
-    filename = "./data/faster-rcnn-coco/inference/coco_instances_results.json"
-    network = "COCO-faster-rcnn-threshold-%.f"
+    # filename = "./data/faster-rcnn-coco/inference/coco_instances_results.json"
+    # filename = "./data/faster-rcnn-coco-eval-on-cityscapes/converted_coco_instances_results.json"
+    # network = "COCO-faster-rcnn-threshold-%.2f"
 
     # COCO data - RetinaNet
     # filename = "./data/retinanet-coco/inference/coco_instances_results.json"
-    # network = "COCO-retinanet-threshold-%.f"
-
-    dataset = "coco_2017_val"
-    train_ids, val_ids = read_image_ids("image_ids_coco.json")
+    filename = "./data/retinanet-coco-eval-on-cityscapes/converted_coco_instances_results.json"
+    network = "COCO-retinanet-threshold-%.2f"
 
     # Cityscapes data
     # filename = "./data/mask-rcnn-cityscapes/inference/coco_instances_results.json"
-    # dataset = "cityscapes_fine_instance_seg_val"
-    # network = "Cityscapes-mask-rcnn-threshold-%.f"
-    # train_ids, val_ids = read_image_ids("image_ids_cityscapes.json")
+    # filename = "./data/mask-rcnn-cityscapes-eval-on-coco/converted_coco_instances_results.json"
+    # network = "Cityscapes-mask-rcnn-threshold-%.2f"
+
+    # dataset = "coco_2017_val"
+    # train_ids, val_ids = read_image_ids("image_ids_coco.json")
+
+    dataset = "cityscapes_fine_instance_seg_val"
+    train_ids, val_ids = read_image_ids("image_ids_cityscapes.json")
 
     score_threshold = 0.3
     # score_threshold = 0.05
 
-    subsets = [[], ['cx', 'cy'], ['w', 'h'], ['cx', 'cy', 'w', 'h']]
+    network = network % score_threshold
+
+    # subsets = [[], ['cx', 'cy'], ['w', 'h'], ['cx', 'cy', 'w', 'h']]
+    subsets = [[], ['cx', 'cy', 'w', 'h']]
     ious = [0.5, 0.75]
 
     # read frames and match the frames with the according ground-truth boxes. This is mandatory to assess the precision
@@ -281,4 +438,4 @@ def plot(f: np.ndarray, m: np.ndarray, title: str, formatter: str):
 
     # perform confidence calibration evaluation for each subset
     for subset in subsets:
-        transform(frames, dataset, network, subset, ious, val_ids)
+        transform(frames, dataset, network, subset, ious, val_ids, common_thing_classes, bayesian)
diff --git a/examples/detection/Features.py b/examples/detection/Features.py
index 00d31f8..6baaa72 100644
--- a/examples/detection/Features.py
+++ b/examples/detection/Features.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/examples/detection/Helper.py b/examples/detection/Helper.py
index 69d1582..fd8b045 100644
--- a/examples/detection/Helper.py
+++ b/examples/detection/Helper.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/examples/detection/__init__.py b/examples/detection/__init__.py
index e1e1791..3ae410e 100644
--- a/examples/detection/__init__.py
+++ b/examples/detection/__init__.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2019-2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this

From c90899fe0cb2a6cdf05073b9ef4dd51c42197f25 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 10:20:00 +0200
Subject: [PATCH 15/21] Add new example package for regression calibration.

---
 examples/__init__.py                          |     4 +-
 examples/regression/README.rst                |     1 +
 examples/regression/__init__.py               |     9 +
 examples/regression/artificial/README.rst     |    44 +
 examples/regression/artificial/__init__.py    |    10 +
 examples/regression/artificial/data.py        |    47 +
 examples/regression/artificial/img/data.svg   | 18969 +++++++++
 .../regression/artificial/img/methods.svg     | 33931 ++++++++++++++++
 .../regression/artificial/img/reliability.svg |  2337 ++
 examples/regression/artificial/main.py        |   164 +
 examples/regression/artificial/visualize.py   |   134 +
 examples/regression/multivariate/README.rst   |    36 +
 examples/regression/multivariate/__init__.py  |    12 +
 examples/regression/multivariate/data.py      |    40 +
 examples/regression/multivariate/main.py      |   299 +
 examples/regression/multivariate/visualize.py |    82 +
 16 files changed, 56117 insertions(+), 2 deletions(-)
 create mode 100644 examples/regression/README.rst
 create mode 100644 examples/regression/__init__.py
 create mode 100644 examples/regression/artificial/README.rst
 create mode 100644 examples/regression/artificial/__init__.py
 create mode 100644 examples/regression/artificial/data.py
 create mode 100644 examples/regression/artificial/img/data.svg
 create mode 100644 examples/regression/artificial/img/methods.svg
 create mode 100644 examples/regression/artificial/img/reliability.svg
 create mode 100644 examples/regression/artificial/main.py
 create mode 100644 examples/regression/artificial/visualize.py
 create mode 100644 examples/regression/multivariate/README.rst
 create mode 100644 examples/regression/multivariate/__init__.py
 create mode 100644 examples/regression/multivariate/data.py
 create mode 100644 examples/regression/multivariate/main.py
 create mode 100644 examples/regression/multivariate/visualize.py

diff --git a/examples/__init__.py b/examples/__init__.py
index 53a5dfe..ddc809b 100644
--- a/examples/__init__.py
+++ b/examples/__init__.py
@@ -1,5 +1,5 @@
-# Copyright (C) 2021 Ruhr West University of Applied Sciences, Bottrop, Germany
-# AND Elektronische Fahrwerkssysteme, Gaimersheim, Germany
+# Copyright (C) 2021-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
 #
 # This Source Code Form is subject to the terms of the Apache License 2.0
 # If a copy of the APL2 was not distributed with this
diff --git a/examples/regression/README.rst b/examples/regression/README.rst
new file mode 100644
index 0000000..7d6817f
--- /dev/null
+++ b/examples/regression/README.rst
@@ -0,0 +1 @@
+TODO: write readme on regression examples
\ No newline at end of file
diff --git a/examples/regression/__init__.py b/examples/regression/__init__.py
new file mode 100644
index 0000000..1e0b1ac
--- /dev/null
+++ b/examples/regression/__init__.py
@@ -0,0 +1,9 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+# TODO: update docstring to include into sphinx
+# TODO: write and include all readmes of the sub-packages
diff --git a/examples/regression/artificial/README.rst b/examples/regression/artificial/README.rst
new file mode 100644
index 0000000..ecdec71
--- /dev/null
+++ b/examples/regression/artificial/README.rst
@@ -0,0 +1,44 @@
+Artificial Regression Calibration Example
+=========================================
+
+In this package, we demonstrate the usage of the regression calibration methods provided by the *netcal* library.
+The file *main.py* holds an artificial example that samples data around a cosine function with a certain mean and a variance.
+The sampled variance can be set to depend on the mean (cosine value).
+This is demonstrated in the following figure:
+
+.. image:: img/data.svg
+    :align: center
+
+Each sample within the array *ymean* and *ystd* reflects a mean and stddev prediction by an artificial estimator.
+The calibration methods are fit to the ground truth *y* using these estimates as inputs.
+The following methods apply a recalibration on the cumulative (CDF) and thus output points on the CDF:
+
+- Isotonic Regression
+- GP-Beta
+
+Using the function *cumulative_moments()*, it is possible to get a mean/stddev estimate by the provided CDF function.
+The following methods apply a parametric recalibration (e.g., Gaussian, Cauchy):
+
+- Variance Scaling
+- GP-Normal
+- GP-Cauchy
+
+If we visualize the recalibrated distribution functions of the first sample, we get the following image:
+
+.. image:: img/methods.svg
+    :align: center
+
+You can use Scipy's *norm* or *cauchy* module to get a density (PDF) or a CDF function.
+Finally, we demonstrate how to use the metrics provided by the *netcal.metrics* package to measure regression calibration.
+The following metrics are implemented:
+
+- NLL
+- Expected Normalized Calibration Error (ENCE)
+- Uncertainty Calibration Error (UCE)
+- Quantile Calibration Error (QCE)
+- Pinball Loss
+
+Furthermore, you can also visualize the miscalibration using the *ReliabilityRegression* class within the *netcal.presentation* package:
+
+.. image:: img/reliability.svg
+    :align: center
diff --git a/examples/regression/artificial/__init__.py b/examples/regression/artificial/__init__.py
new file mode 100644
index 0000000..15889d9
--- /dev/null
+++ b/examples/regression/artificial/__init__.py
@@ -0,0 +1,10 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from .data import generate_mean_dependent
+from .data import generate_variance_dependent
+from .visualize import draw_distributions
diff --git a/examples/regression/artificial/data.py b/examples/regression/artificial/data.py
new file mode 100644
index 0000000..19cbbce
--- /dev/null
+++ b/examples/regression/artificial/data.py
@@ -0,0 +1,47 @@
+import numpy as np
+from scipy.stats import norm
+from scipy.special import expit
+
+
+def generate_mean_dependent(n_samples):
+    """
+    Generate samples of an artificial base estimator that are consistently overconfident.
+    Introduce a dependency on the mean.
+    """
+
+    # step 1: generate some y ground-truth and add a hypothetical regressor that fits its mean predictions
+    # to the ground-truth
+    x = np.linspace(-5, 5, n_samples)
+    y = np.cos(x)
+    ymean = np.array(y)
+
+    # step 2: corrupt the ground-truth with gaussian noise based on the mean estimate
+    y = norm.rvs(loc=y, scale=np.ones_like(y) * expit(y*1.5) * 1.5 + .125)
+
+    # step 3: sample the stddev that is also predicted by a hypothetical regressor that however consistently
+    # underestimates the true variance
+    ystd = np.random.uniform(low=0.25, high=0.5, size=(n_samples,))
+
+    return x, y, ymean, ystd
+
+
+def generate_variance_dependent(n_samples):
+    """
+    Generate samples of an artificial base estimator that are consistently overconfident.
+    Introduce a dependency on the variance.
+    """
+
+    # step 1: generate some y ground-truth and add a hypothetical regressor that fits its mean predictions
+    # to the ground-truth
+    x = np.linspace(-5, 5, n_samples)
+    y = np.cos(x)
+    ymean = np.array(y)
+
+    # step 2: sample the stddev that is predicted by a hypothetical regressor that however consistently
+    # underestimates the true variance
+    ystd = np.random.uniform(low=0.1, high=0.25, size=(n_samples,))
+
+    # step 3: corrupt the ground-truth with gaussian noise that bases on the predicted variance
+    y = norm.rvs(loc=y, scale=np.ones_like(y) * expit((ystd-0.175) * 2.) * .5 + .25)
+
+    return x, y, ymean, ystd
diff --git a/examples/regression/artificial/img/data.svg b/examples/regression/artificial/img/data.svg
new file mode 100644
index 0000000..258a8bb
--- /dev/null
+++ b/examples/regression/artificial/img/data.svg
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diff --git a/examples/regression/artificial/main.py b/examples/regression/artificial/main.py
new file mode 100644
index 0000000..9cfe265
--- /dev/null
+++ b/examples/regression/artificial/main.py
@@ -0,0 +1,164 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+from matplotlib import pyplot as plt
+
+from netcal import manual_seed, cumulative_moments
+from netcal.regression import IsotonicRegression, VarianceScaling, GPBeta, GPNormal, GPCauchy
+from netcal.metrics import NLL, ENCE, UCE, QCE, PinballLoss
+from netcal.presentation import ReliabilityRegression
+
+from examples.regression.artificial import generate_variance_dependent, generate_mean_dependent, draw_distributions
+
+
+if __name__ == '__main__':
+
+    # parameter for regression calibration
+    mean_dependent = True  # set to true to sample data with mean dependency
+    n_samples = 2000  # number of training/evaluation samples
+    seed = 0
+    bins = 20  # used for evaluation metrics
+    quantiles = np.linspace(0.05, 0.95, 19)  # quantile levels, used for evaluation metrics
+
+    # the following parameters are used during Gaussian process optimization
+    n_inducing_points = 12  # number of inducing points used within the GP
+    n_random_samples = 256  # number of random samples used for GP training/inference
+    n_epochs = 200  # optimization epochs
+    use_cuda = False  # or: "cuda:0", "cuda:1", etc.
+
+    # number of samples to describe a cumulative distribution
+    t = 256
+
+    # initialize tensorboard logging
+    tensorboard = SummaryWriter("logs/netcal/regression/artificial")
+    reliability = ReliabilityRegression(quantiles=bins+1)
+    figures = []
+
+    # use fixed random seed
+    with manual_seed(seed):
+
+        # sample from artificial distributions
+        if mean_dependent:
+            x, y, ymean, ystd = generate_mean_dependent(n_samples=n_samples)
+        else:
+            x, y, ymean, ystd = generate_variance_dependent(n_samples=n_samples)
+
+        # -------------------------------------------------
+        # fit isotonic regression model
+        isotonic = IsotonicRegression()
+        isotonic.fit((ymean, ystd), y, tensorboard=tensorboard)
+        t_iso, s_iso, q_iso = isotonic.transform((ymean, ystd), t=t)
+
+        # squeeze t, pdf and cdf and get distribution moments
+        t_iso, s_iso, q_iso = t_iso[..., 0], s_iso[..., 0], q_iso[..., 0]
+        ymean_iso, yvar_iso = cumulative_moments(t_iso, q_iso)
+        ystd_iso = np.sqrt(yvar_iso)
+
+        # -------------------------------------------------
+        # fit VarianceScaling model
+        varscaling = VarianceScaling()
+        varscaling.fit((ymean, ystd), y, tensorboard=tensorboard)
+        ystd_varscaling = varscaling.transform((ymean, ystd))
+
+        # squeeze calibrated stddev
+        ymean_varscaling = ymean
+        ystd_varscaling = ystd_varscaling[..., 0]
+
+        # # -------------------------------------------------
+        # fit GPBeta model
+        gpbeta = GPBeta(n_inducing_points=n_inducing_points, n_random_samples=n_random_samples, n_epochs=n_epochs, use_cuda=use_cuda)
+        gpbeta.fit((ymean, ystd), y, tensorboard=tensorboard)
+        t_gpbeta, s_gpbeta, q_gpbeta = gpbeta.transform((ymean, ystd), t=t)
+
+        # squeeze t, pdf and cdf and get distribution moments
+        t_gpbeta, s_gpbeta, q_gpbeta = t_gpbeta[..., 0], s_gpbeta[..., 0], q_gpbeta[..., 0]
+        ymean_gpbeta, yvar_gpbeta = cumulative_moments(t_gpbeta, q_gpbeta)
+        ystd_gpbeta = np.sqrt(yvar_gpbeta)
+
+        # -------------------------------------------------
+        # fit GPNormal model
+        gpnormal = GPNormal(n_inducing_points=n_inducing_points, n_random_samples=n_random_samples, n_epochs=n_epochs, use_cuda=use_cuda)
+        gpnormal.fit((ymean, ystd), y, tensorboard=tensorboard)
+        ystd_gpnormal = gpnormal.transform((ymean, ystd))
+
+        # squeeze calibrated stddev
+        ymean_gpnormal = ymean
+        ystd_gpnormal = ystd_gpnormal[..., 0]
+
+        # -------------------------------------------------
+        # fit GPCauchy model
+        gpcauchy = GPCauchy(n_inducing_points=n_inducing_points, n_random_samples=n_random_samples, n_epochs=n_epochs, use_cuda=use_cuda)
+        gpcauchy.fit((ymean, ystd), y, tensorboard=tensorboard)
+        ysscale_gpcauchy = gpcauchy.transform((ymean, ystd))
+
+        ymode_gpcauchy = ymean
+        yscale_gpcauchy = ysscale_gpcauchy[..., 0]
+
+    # store all methods in a single dict
+    methods = {
+        "Uncalibrated": {"mean": ymean, "std": ystd},
+        "Isotonic Regression": {"t": t_iso, "cdf": q_iso, "mean": ymean_iso, "std": ystd_iso},
+        "VarianceScaling": {"mean": ymean_varscaling, "std": ystd_varscaling},
+        "GPBeta": {"t": t_gpbeta, "cdf": q_gpbeta, "mean": ymean_gpbeta, "std": ystd_gpbeta},
+        "GPNormal": {"mean": ymean_gpnormal, "std": ystd_gpnormal},
+        "GPCauchy": {"mode": ymode_gpcauchy, "scale": yscale_gpcauchy},
+    }
+
+    # draw data distribution and log to tensorboard
+    dist_fig = draw_distributions(x, y, methods, 0.9, bins=bins, quantiles=quantiles)
+
+    nll = NLL()
+    pinball = PinballLoss()
+    uce = UCE(bins=bins)
+    ence = ENCE(bins=bins)
+    qce = QCE(bins=bins, marginal=False)
+
+    print("{method: <25}NLL            Pinball        UCE            ENCE           QCE".format(method="Method"))
+
+    # iterate over methods and measure miscalibration/visualize reliability plots
+    for method, values in methods.items():
+
+        if "t" in values and "cdf" in values:
+            univariate = (values["t"], values["cdf"])
+            kind = "cumulative"
+        elif "mode" in values and "scale" in values:
+            univariate = (values["mode"], values["scale"])
+            kind = "cauchy"
+        else:
+            univariate = (values["mean"], values["std"])
+            kind = "meanstd"
+
+        nll_loss = nll.measure(univariate, y, kind=kind)
+        pinball_loss = pinball.measure(univariate, y, q=quantiles, kind=kind)
+        uce_loss = uce.measure(univariate, y, kind=kind)
+        ence_loss = ence.measure(univariate, y, kind=kind)
+        qce_loss = qce.measure(univariate, y, q=quantiles, kind=kind)
+
+        fig = reliability.plot(univariate, y, kind=kind, title_suffix=method)
+
+        hparam_dict = {"method": method, "bins": bins}
+        metric_dict = {"nll": nll_loss, "pinball": pinball_loss, "uce": uce_loss, "ence": ence_loss, "qce": qce_loss}
+
+        # save figure in tensorboard
+        tensorboard.add_figure("artificial/reliability/%s" % method, fig, close=False)
+        tensorboard.add_hparams(hparam_dict=hparam_dict, metric_dict=metric_dict, run_name=method)
+        figures.append(fig)
+
+        print(
+            "{method: <25}{nll:10.4f}     {pinball:10.4f}     {uce:10.4f}     {ence:10.4f}     {qce:10.4f}".format(
+                method=method,
+                nll=float(nll_loss),
+                pinball=float(pinball_loss),
+                uce=float(uce_loss),
+                ence=float(ence_loss),
+                qce=float(qce_loss)
+            )
+        )
+
+    plt.show()
diff --git a/examples/regression/artificial/visualize.py b/examples/regression/artificial/visualize.py
new file mode 100644
index 0000000..c61cc2b
--- /dev/null
+++ b/examples/regression/artificial/visualize.py
@@ -0,0 +1,134 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Dict, List
+import numpy as np
+from scipy.stats import norm
+from matplotlib import pyplot as plt
+
+from netcal.metrics import PinballLoss, ENCE, UCE, QCE, NLL
+
+
+def draw_distributions(
+        x: np.ndarray,
+        y: np.ndarray,
+        methods: Dict,
+        quantile: float = 0.9,
+        bins: int = 20,
+        quantiles: np.ndarray = np.linspace(0.05, 0.95, 19),
+) -> plt.Figure:
+    """
+    Draw the training/evaluation data distributions based on their estimated moments.
+
+    Parameters
+    ----------
+    x : np.ndarray, shape: (n, [d])
+        Input scores on the base x-axis.
+    y : np.ndarray, shape: (n, [d])
+        Ground-truth target scores on the y-axis.
+    methods : dict
+        Distributional estimates of y for several calibration methods.
+    quantile : float, default: 0.9
+        Width of the quantile boundaries used to visualize the base estimators.
+    bins : int, default: 20
+        Number of quantiles/bins used to estimate the ENCE, UCE and P-NEES metrics.
+    quantiles : np.ndarray, shape: (q,)
+        Quantile levels used for the evaluation of Pinball loss and Quantile Calibration Error (QCE).
+
+    Returns
+    -------
+    matplotlib.pyplot.Figure
+    """
+
+    # visualize dataset
+    axes = []
+    fig = plt.figure(figsize=(4 * len(methods), 10))
+
+    gs = fig.add_gridspec(2, 3)
+    axes.append(fig.add_subplot(gs[:, 0]))
+    axes.append(fig.add_subplot(gs[0, 1]))
+    axes.append(fig.add_subplot(gs[0, 2]))
+    axes.append(fig.add_subplot(gs[1, 1]))
+    axes.append(fig.add_subplot(gs[1, 2]))
+
+    zscore = norm.ppf(1 - ((1-quantile) / 2))
+    bbox_probs = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
+
+    # initialize miscalibration metrics
+    nll = NLL()
+    pinball = PinballLoss()
+    uce = UCE(bins=bins)
+    ence = ENCE(bins=bins)
+    qce = QCE(bins=bins, marginal=False)
+
+    # iterate over data / calibration methods
+    for ax, (method, values), letter in zip(axes, methods.items(), ["a", "b", "c", "d", "e"]):
+
+        # get mean and stddev estimates
+        mean = values["mean"]
+        std = values["std"]
+
+        # plot ground truth and mean estimate of the base estimator
+        ax.plot(x, y, "x", color="green", alpha=0.5)
+        ax.plot(x, mean, "-", color="blue")
+
+        # prefer 'raw' cumulative over mean/stddev moments if cumulative is given
+        if "t" in values and "cdf" in values:
+
+            t = values["t"]
+            cdf = values["cdf"]
+
+            # get bounds idx of cumulative
+            lb_idx = np.argmax(cdf > (1. - quantile) / 2, axis=0)
+            ub_idx = np.argmax(cdf > 1 - ((1. - quantile) / 2), axis=0)
+
+            idx = np.arange(cdf.shape[1])
+            lb = t[lb_idx, idx]
+            ub = t[ub_idx, idx]
+
+            ax.fill_between(x, lb, ub, alpha=0.9)
+
+            # use cumulative to calculate the metrics
+            nll_loss = nll.measure((values["t"], values["cdf"]), y, kind="cumulative")
+            pinball_loss = pinball.measure((values["t"], values["cdf"]), y, q=quantiles, kind="cumulative")
+            uce_loss = uce.measure((values["t"], values["cdf"]), y, kind="cumulative")
+            ence_loss = ence.measure((values["t"], values["cdf"]), y, kind="cumulative")
+            qce_loss = qce.measure((values["t"], values["cdf"]), y, q=quantiles, kind="cumulative")
+
+        # otherwise, assert normal distribution
+        else:
+
+            # use prediction interval obtained by a normal distribution
+            ax.fill_between(x, mean - zscore * std, mean + zscore * std, alpha=0.9)
+
+            # use mean/stddev to calculate the metrics
+            nll_loss = nll.measure((values["mean"], values["std"]), y, kind="meanstd")
+            pinball_loss = pinball.measure((values["mean"], values["std"]), y, q=quantiles, kind="meanstd")
+            uce_loss = uce.measure((values["mean"], values["std"]), y, kind="meanstd")
+            ence_loss = ence.measure((values["mean"], values["std"]), y, kind="meanstd")
+            qce_loss = qce.measure((values["mean"], values["std"]), y, q=quantiles, kind="meanstd")
+
+        # display metrics in plot
+        ax.text(
+           0.05, 0.95,
+           'NLL: %.4f\nQCE: %.4f\nPinnball: %.4f\nENCE: %.4f\nUCE: %.4f' % (nll_loss, qce_loss, pinball_loss, ence_loss, uce_loss),
+           transform=ax.transAxes, fontsize=14, verticalalignment='top', bbox=bbox_probs
+        )
+
+        ax.set_title("%s) %s" % (letter, method))
+        ax.grid(True)
+        ax.set_xlim([-5., 5.])
+        ax.set_ylim([-3.5, 4.5])
+
+        ax.xaxis.set_ticks([])
+        ax.yaxis.set_ticks([])
+        ax.xaxis.set_ticklabels([])
+        ax.yaxis.set_ticklabels([])
+
+        fig.tight_layout()
+
+    return fig
diff --git a/examples/regression/multivariate/README.rst b/examples/regression/multivariate/README.rst
new file mode 100644
index 0000000..03abf1a
--- /dev/null
+++ b/examples/regression/multivariate/README.rst
@@ -0,0 +1,36 @@
+Multivariate Regression Calibration Example
+===========================================
+
+In this package, we demonstrate the usage of the regression calibration methods with additional correlation estimation and recalibration.
+The file *main.py* holds an artificial example that samples 2D data around a sine and cosine function with a certain mean and a variance.
+Furthermore, the variance on the data is correlated to a certain degree.
+The calibration methods can be used to identify and capture the correlations within the input data.
+Thus, it is possible to model parametric multivariate distributions based on independently learned/provided distributions for each dimension,
+
+Basically, each calibration method can be used to recalibrate multiple (independent) dimensions.
+However, only the *GPNormal* is able to model a joint multivariate Gaussian with correlations as calibration output.
+See the code example below:
+
+.. code-block:: python
+
+    mean          # NumPy n-D array holding the estimated mean of shape (n, d) with n samples and d dimensions
+    stddev        # NumPy n-D array holding the estimated stddev (independent) of shape (n, d) with n samples and d dimensions
+    ground_truth  # NumPy n-D array holding the ground-truth scores of shape (n, d) with n samples and d dimensions
+
+    from netcal.regression import GPNormal
+
+    gpnormal = GPNormal(
+        n_inducing_points=12,    # number of inducing points
+        n_random_samples=256,    # random samples used for likelihood
+        n_epochs=256,            # optimization epochs
+        use_cuda=False,          # can also use CUDA for computations
+        correlations=True,       # enable correlation capturing
+        name_prefix="gpnormal",  # internal name prefix required for Pyro
+    )
+
+    # fit GP-Normal
+    gpnormal.fit((mean, stddev), ground_truth)
+
+    # transform distributions to obtain covariance matrices
+    cov = gpnormal.transform((mean, stddev))  # NumPy array with covariances - has shape (n, d, d)
+
diff --git a/examples/regression/multivariate/__init__.py b/examples/regression/multivariate/__init__.py
new file mode 100644
index 0000000..70ca697
--- /dev/null
+++ b/examples/regression/multivariate/__init__.py
@@ -0,0 +1,12 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+# TODO: update docstring to include into sphinx
+# TODO: include README.rst
+
+from .data import generate
+from .visualize import draw_single_distribution
diff --git a/examples/regression/multivariate/data.py b/examples/regression/multivariate/data.py
new file mode 100644
index 0000000..f58293a
--- /dev/null
+++ b/examples/regression/multivariate/data.py
@@ -0,0 +1,40 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Tuple
+import numpy as np
+from scipy.special import expit as sigmoid
+import torch
+import torch.distributions as dist
+
+
+def generate(n_samples: int) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
+    """
+    Generate samples of an artificial base estimator that are not miscalibrated.
+    """
+
+    x1, x2 = np.linspace(-5, 5, n_samples, dtype=np.float32), np.linspace(-5, 5, n_samples, dtype=np.float32)
+    x = np.stack((x1, x2), axis=-1)
+
+    y1_mean = np.sin(x1)
+    y2_mean = np.cos(x2)
+    ymean = np.stack((y1_mean, y2_mean), axis=-1)
+
+    corr = np.tanh(x1) * np.tanh(x2)
+
+    y1_var = sigmoid(x1 * 0.5)
+    y2_var = 1. - sigmoid(x1 * 0.25)
+    ycovar = corr * np.sqrt(y1_var * y2_var)
+    yvar = np.stack((y1_var, y2_var), axis=-1)
+
+    ycov = torch.diag_embed(torch.from_numpy(yvar))
+    ycov[..., 0, 1] = ycov[..., 1, 0] = torch.from_numpy(ycovar)
+
+    mvn = dist.MultivariateNormal(loc=torch.from_numpy(ymean), covariance_matrix=ycov)
+    y = mvn.sample()
+
+    return x, y.numpy(), ymean, ycov.numpy()
diff --git a/examples/regression/multivariate/main.py b/examples/regression/multivariate/main.py
new file mode 100644
index 0000000..f8c450d
--- /dev/null
+++ b/examples/regression/multivariate/main.py
@@ -0,0 +1,299 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Tuple
+import numpy as np
+import torch
+from torch.utils.tensorboard import SummaryWriter
+from matplotlib import pyplot as plt
+
+from netcal import manual_seed
+from netcal.regression import GPNormal, GPBeta, GPCauchy, IsotonicRegression, VarianceScaling
+from netcal.presentation import ReliabilityRegression, ReliabilityQCE
+from netcal.metrics import NLL, QCE, PinballLoss, ENCE, UCE
+
+from examples.regression.multivariate import generate, draw_single_distribution
+
+
+def get_meanstd_from_cdf(t: np.ndarray, cdf: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
+    """ Calculate mean and stddev from given cumulative distribution. """
+
+    delta_cdf_iso = np.diff(cdf, axis=0)  # (t-1, n, d)
+    t_mid = (t[:-1, ...] + t[1:, ...]) / 2  # (t-1, n, d)
+    mean = np.sum(t_mid * delta_cdf_iso, axis=0)  # (n, d)
+    std = np.sqrt(np.sum(np.square(t_mid) * delta_cdf_iso, axis=0) - np.square(mean))  # (n, d)
+
+    return mean, std
+
+
+def fit_isotonic() -> Tuple[np.ndarray, np.ndarray]:
+    """ Fit isotonic regression model """
+
+    isotonic = IsotonicRegression()
+    isotonic.fit((ymean, ystd), y, tensorboard=tensorboard)
+    t_iso, s_iso, q_iso = isotonic.transform((ymean, ystd), t=t)
+
+    return t_iso, q_iso
+
+
+def fit_varscaling() -> Tuple[np.ndarray, np.ndarray]:
+    """ Fit VarianceScaling recalibration model """
+
+    varscaling = VarianceScaling()
+    varscaling.fit((ymean, ystd), y, tensorboard=tensorboard)
+    ystd_varscaling = varscaling.transform((ymean, ystd))
+
+    # convert stddev to covariance matrix
+    ymean_varscaling = ymean
+    ycov_varscaling = torch.diag_embed(torch.from_numpy(ystd_varscaling) ** 2).numpy()
+
+    return ymean_varscaling, ycov_varscaling
+
+
+def fit_gpbeta() -> Tuple[np.ndarray, np.ndarray]:
+    """ Fit GPBeta recalibration model """
+
+    gpbeta = GPBeta(
+        n_inducing_points=n_inducing_points,
+        n_random_samples=n_random_samples,
+        n_epochs=n_epochs_independent,
+        use_cuda=use_cuda
+    )
+    gpbeta.fit((ymean, ystd), y, tensorboard=tensorboard)
+    t_gpbeta, s_gpbeta, q_gpbeta = gpbeta.transform((ymean, ystd), t=t)
+
+    return t_gpbeta, q_gpbeta
+
+
+def fit_gpnormal_variance_only() -> Tuple[np.ndarray, np.ndarray]:
+    """ Fit GPNormal model - variant 1: no input correlations, no output correlations """
+
+    gpnormal = GPNormal(
+        n_inducing_points=n_inducing_points,
+        n_random_samples=n_random_samples,
+        n_epochs=n_epochs_independent,
+        use_cuda=use_cuda,
+        correlations=False,
+        name_prefix="gpnormal_fully_independent"
+    )
+    gpnormal.fit((ymean, ystd), y, tensorboard=tensorboard)
+    ystd_gpnormal = gpnormal.transform((ymean, ystd))
+
+    # convert stddev to covariance matrix
+    ymean_gpnormal = ymean
+    ycov_gpnormal = torch.diag_embed(torch.from_numpy(ystd_gpnormal) ** 2).numpy()
+
+    return ymean_gpnormal, ycov_gpnormal
+
+
+def fit_gpnormal_correlations(use_input_cov: bool) -> Tuple[np.ndarray, np.ndarray]:
+    """
+    Fit GPNormal model.
+    If use_input_cov is False: variant 2: no input correlations, model output correlations
+    If use_input_cov is True:  variant 3: provide input correlations, model output correlations
+    """
+
+    var_in = ystd if not use_input_cov else ycov
+    name_prefix = "gpnormal_without_input_cov" if not use_input_cov else "gpnormal_with_input_cov"
+
+    gpnormal = GPNormal(
+        n_inducing_points=n_inducing_points,
+        n_random_samples=n_random_samples,
+        n_epochs=n_epochs_multivariate,
+        use_cuda=use_cuda,
+        correlations=True,
+        name_prefix=name_prefix
+    )
+    gpnormal.fit((ymean, var_in), y, tensorboard=tensorboard)
+    ycov_gpnormal = gpnormal.transform((ymean, var_in))
+    ymean_gpnormal = ymean
+
+    return ymean_gpnormal, ycov_gpnormal
+
+
+def fit_gpcauchy() -> Tuple[np.ndarray, np.ndarray]:
+    """ Fit GPCauchy model - no input correlations, no output correlations """
+
+    gpcauchy = GPCauchy(
+        n_inducing_points=n_inducing_points,
+        n_random_samples=n_random_samples,
+        n_epochs=n_epochs_independent,
+        use_cuda=use_cuda,
+        name_prefix="gpcauchy_fully_independent"
+    )
+    gpcauchy.fit((ymean, ystd), y, tensorboard=tensorboard)
+    ysscale_gpcauchy = gpcauchy.transform((ymean, ystd))
+
+    # convert stddev to covariance matrix
+    ymode_gpcauchy = ymean
+
+    return ymode_gpcauchy, ysscale_gpcauchy
+
+
+if __name__ == '__main__':
+
+    # parameter for regression calibration
+    n_samples = 1000  # number of training/evaluation samples
+    seed = 0
+    bins = 20  # used for evaluation metrics
+
+    # the following parameters are used during Gaussian process optimization
+    n_inducing_points = 12  # number of inducing points used within the GP
+    n_random_samples = 128  # number of random samples used for GP training/inference
+    n_epochs_independent = 256  # number of epochs for the univariate (uncorrelated) GP methods
+    n_epochs_multivariate = 256  # number of epochs for the multivariate (correlated) GP methods
+    use_cuda = False  # or: "cuda:0", "cuda:1", etc.
+
+    # number of samples to describe a cumulative distribution
+    t = 256
+
+    # quantile levels used for evaluation
+    q = np.linspace(0.05, 0.95, 19)
+
+    # initialize tensorboard logging
+    tensorboard = SummaryWriter(log_dir="logs/netcal/regression/multivariate")
+    hparam_dict = {
+        'n_samples': n_samples,
+        'seed': seed,
+        'bins': bins,
+        'n_inducing_points': n_inducing_points,
+        'n_random_samples': n_random_samples,
+        'n_epochs_independent': n_epochs_independent,
+        'n_epochs_multivariate': n_epochs_multivariate,
+        't': t,
+        'q': torch.from_numpy(q),
+    }
+
+    # initialize metrics
+    pinball = PinballLoss()
+    ence = ENCE(bins=bins)
+    uce = UCE(bins=bins)
+    nll = NLL()
+    qce = QCE(bins=bins, marginal=False)
+
+    # initialize visualization tools
+    reliability = ReliabilityRegression(quantiles=bins + 1)
+    reliability_qce = ReliabilityQCE(bins=bins)
+    figures = []
+
+    # use fixed random seed
+    with manual_seed(seed):
+
+        # generate training/evaluation samples
+        x, y, ymean, ycov = generate(n_samples)
+        yvar = np.diagonal(ycov, axis1=-2, axis2=-1)
+        ystd = np.sqrt(yvar)
+
+        # run recalibration methods
+        t_iso, q_iso = fit_isotonic()
+
+        ymean_varscaling, ycov_varscaling = fit_varscaling()
+        t_gpbeta, q_gpbeta = fit_gpbeta()
+        ymean_gpnormal_independent, ycov_gpnormal_independent = fit_gpnormal_variance_only()
+        ymean_gpnormal_without_cov, ycov_gpnormal_without_cov = fit_gpnormal_correlations(use_input_cov=False)
+        ymean_gpnormal_with_cov, ycov_gpnormal_with_cov = fit_gpnormal_correlations(use_input_cov=True)
+        ymode_cauchy, yscale_cauchy = fit_gpcauchy()
+
+    # store all methods in a single dict
+    methods = {
+        "Uncalibrated": {"mean": ymean, "cov": ycov},
+        "IsotonicRegression": {"t": t_iso, "cdf": q_iso},
+        "VarianceScaling": {"mean": ymean_varscaling, "cov": ycov_varscaling},
+        "GPBeta": {"t": t_gpbeta, "cdf": q_gpbeta},
+        "GPNormal (independent)": {"mean": ymean_gpnormal_independent, "cov": ycov_gpnormal_independent},
+        "GPNormal (without cov)": {"mean": ymean_gpnormal_without_cov, "cov": ycov_gpnormal_without_cov},
+        "GPNormal (with cov)": {"mean": ymean_gpnormal_with_cov, "cov": ycov_gpnormal_with_cov},
+        "GPCauchy (independent)": {"mode": ymode_cauchy, "scale": yscale_cauchy},
+    }
+
+    # draw a single distribution and store the result in tensorboard
+    dist_fig = draw_single_distribution(methods)
+
+    # iterate over methods and visualize reliability plots
+    for method, values in methods.items():
+
+        # use mean and stddev (normal distributions)
+        # extract the stddev from the covariance matrices
+        if "mean" in values:
+            std = np.sqrt(np.diagonal(values["cov"], axis1=-2, axis2=-1))
+            univariate = (values["mean"], std)
+            multivariate = (values["mean"], values["cov"])
+            kind = "meanstd"
+        elif "t" in values:
+            univariate = (values["t"], values["cdf"])
+            multivariate = univariate
+            kind = "cumulative"
+        elif "scale" in values:
+            univariate = (values["mode"], values["scale"])
+            multivariate = univariate
+            kind = "cauchy"
+        else:
+            cov = values["cov"]
+            scale = np.diagonal(values["cov"], axis1=-2, axis2=-1)
+            univariate = (values["mode"], scale)
+            multivariate = (values["mode"], cov)
+            kind = "cauchy"
+
+        # -------------------------------------------------
+        # metrics
+        pinball_loss = np.mean(
+            pinball.measure(univariate, y, q, kind=kind, reduction="none"),  # (q, n, d)
+            axis=(0, 1)
+        )  # (d,)
+
+        uce_loss = uce.measure(univariate, y, kind=kind)  # (d,)
+        ence_loss = ence.measure(univariate, y, kind=kind)  # (d,)
+
+        nll_loss_independent = nll.measure(univariate, y, kind=kind, reduction="batchmean")  # (d,)
+        qce_loss_independent = qce.measure(univariate, y, q, kind=kind, reduction="batchmean")  # (d,)
+        nll_loss_joint = nll.measure(multivariate, y, kind=kind, reduction="batchmean")  # scalar or (d,)
+
+        if not kind == "cauchy":
+            qce_loss_joint = qce.measure(multivariate, y, q, kind=kind, reduction="batchmean")
+        else:
+            qce_loss_joint = np.nan
+
+        if nll_loss_joint.size > 1:
+            nll_loss_joint = np.sum(nll_loss_joint)
+
+        if isinstance(qce_loss_joint, np.ndarray) and qce_loss_joint.size > 1:
+            qce_loss_joint = np.mean(qce_loss_joint)
+
+        metric_dict = {'nll_joint': nll_loss_joint, 'qce_joint': qce_loss_joint}
+        metric_dict.update({'pinball_%02d' % dim: loss for dim, loss in enumerate(pinball_loss)})
+        metric_dict.update({'uce_%02d' % dim: loss for dim, loss in enumerate(pinball_loss)})
+        metric_dict.update({'ence_%02d' % dim: loss for dim, loss in enumerate(pinball_loss)})
+        metric_dict.update({'nll_dim_%02d' % dim: loss for dim, loss in enumerate(pinball_loss)})
+        metric_dict.update({'qce_dim_%02d' % dim: loss for dim, loss in enumerate(pinball_loss)})
+
+        tensorboard.add_hparams(hparam_dict=hparam_dict, metric_dict=metric_dict, run_name=method)
+
+        # -------------------------------------------------
+        # visualization
+
+        fig_reliability_independent = reliability.plot(univariate, y, kind=kind, title_suffix=method)
+        fig_qce_independent = reliability_qce.plot(univariate, y, q, kind=kind, title_suffix=method)
+
+        # save figure in tensorboard
+        tensorboard.add_figure("multivariate/reliability/%s_independent" % method, fig_reliability_independent, close=False)
+        tensorboard.add_figure("multivariate/reliability_qce/%s_independent" % method, fig_qce_independent, close=False)
+
+        figures.append(fig_reliability_independent)
+        figures.append(fig_qce_independent)
+
+        if kind == "meanstd":
+            # plot diagrams with full covariance matrices
+            fig_reliability_joint = reliability.plot(multivariate, y, kind=kind, title_suffix=method)
+            fig_qce_joint = reliability_qce.plot(multivariate, y, q, kind=kind, title_suffix=method)
+
+            tensorboard.add_figure("multivariate/reliability/%s_joint" % method, fig_reliability_joint, close=False)
+            tensorboard.add_figure("multivariate/reliability_qce/%s_joint" % method, fig_qce_joint, close=False)
+
+            figures.append(fig_reliability_joint)
+            figures.append(fig_qce_joint)
+
+    plt.show()
diff --git a/examples/regression/multivariate/visualize.py b/examples/regression/multivariate/visualize.py
new file mode 100644
index 0000000..d1395cf
--- /dev/null
+++ b/examples/regression/multivariate/visualize.py
@@ -0,0 +1,82 @@
+# Copyright (C) 2019-2022 Ruhr West University of Applied Sciences, Bottrop, Germany
+# AND e:fs TechHub GmbH, Gaimersheim, Germany
+#
+# This Source Code Form is subject to the terms of the Apache License 2.0
+# If a copy of the APL2 was not distributed with this
+# file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
+
+from typing import Dict
+import numpy as np
+from scipy.interpolate import interp1d
+from matplotlib import pyplot as plt
+
+import torch
+import torch.distributions as dist
+
+from netcal import mv_cauchy_log_density, density_from_cumulative
+
+
+def draw_single_distribution(methods: Dict):
+
+    x, y = np.linspace(-3, 1, 1000, dtype=np.float32), np.linspace(-3, 2, 1000, dtype=np.float32)
+    xx, yy = np.meshgrid(x, y)
+    xy = torch.from_numpy(np.stack((xx, yy), axis=2)).to(dtype=torch.float32)
+
+    # try to display sample number 256
+    idx = 256 % len(x)
+
+    fig, axes = plt.subplots(nrows=len(methods), ncols=2, figsize=(10, 5 * len(methods)))
+    for (ax1, ax2), (method, values) in zip(axes, methods.items()):
+
+        # if "t" is in values, we have a cumulative function
+        if "t" in values:
+            t = values["t"][:, idx]  # (t, 2)
+            cdf = values["cdf"][:, idx]  # (t, 2)
+
+            # get pdf from cdf
+            pdf = density_from_cumulative(t[:, None], cdf[:, None])  # (t, 1, 2)
+
+            # interpolate pdf to image grid
+            independent_density_x = interp1d(t[:, 0], pdf[:, 0, 0], kind="cubic", bounds_error=False, fill_value=0.)(x)  # (x,)
+            independent_density_y = interp1d(t[:, 1], pdf[:, 0, 1], kind="cubic", bounds_error=False, fill_value=0.)(y)  # (y,)
+
+            independent_density = np.stack(np.meshgrid(independent_density_x, independent_density_y, indexing="ij"), axis=2)  # (x, y, 2)
+            independent_density = np.prod(independent_density, axis=2)  # (x, y)
+
+            multivariate_density = independent_density
+
+        # if "mode" is in values, we have Cauchy
+        elif "mode" in values:
+            mode = torch.from_numpy(values["mode"][idx])
+
+            # univariate case without correlations
+            if "scale" in values:
+                scale = torch.from_numpy(values["scale"][idx])
+                independent_density = dist.Independent(dist.Cauchy(loc=mode, scale=scale), 1).log_prob(xy).exp().numpy()
+                multivariate_density = independent_density
+
+            # multivariate case
+            else:
+                cov = torch.from_numpy(values["cov"][idx])
+                scale = torch.diagonal(cov, offset=0, dim1=-2, dim2=-1)
+
+                multivariate_density = mv_cauchy_log_density(xy, loc=mode, cov=cov).exp().numpy()
+                independent_density = dist.Independent(dist.Cauchy(loc=mode, scale=scale), 1).log_prob(xy).exp().numpy()
+
+        # otherwise, treat input as normal
+        else:
+
+            ymean = torch.from_numpy(values["mean"])[idx]
+            ycov = torch.from_numpy(values["cov"])[idx]
+            ycov_independent = torch.diag_embed(torch.diagonal(ycov, dim1=-2, dim2=-1))
+
+            independent_density = dist.MultivariateNormal(loc=ymean, covariance_matrix=ycov_independent).log_prob(xy).exp().numpy()
+            multivariate_density = dist.MultivariateNormal(loc=ymean, covariance_matrix=ycov).log_prob(xy).exp().numpy()
+
+        ax1.contourf(xx, yy, independent_density)
+        ax2.contourf(xx, yy, multivariate_density)
+
+        ax1.set_title("%s - independent" % method)
+        ax2.set_title("%s - multivariate" % method)
+
+    return fig

From 4a669de59207d5619daabc004311a4ed7ec4ce2f Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 10:32:21 +0200
Subject: [PATCH 16/21] fixes #22

---
 netcal/binning/HistogramBinning.py | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/netcal/binning/HistogramBinning.py b/netcal/binning/HistogramBinning.py
index 4293d12..4c85951 100644
--- a/netcal/binning/HistogramBinning.py
+++ b/netcal/binning/HistogramBinning.py
@@ -95,6 +95,7 @@ class are treated as independent of each other (sigmoid).
         self._multiclass_instances = []
 
         # holds the multi-dimensional bin map with calibrated confidence estimates
+        self._bins_internal = None
         self._bin_map = None
         self._bin_bounds = None
 
@@ -106,6 +107,7 @@ def clear(self):
         """
 
         super().clear()
+        self._bins_internal = None
         self._bin_map = None
         self._bin_bounds = None
 
@@ -183,12 +185,14 @@ def fit(self, X: np.ndarray, y: np.ndarray, random_state: int = None,
             # check bins parameter
             # is int? distribute to all dimensions
             if isinstance(self.bins, int):
-                self.bins = [self.bins, ] * num_features
+                self._bins_internal = [self.bins, ] * num_features
 
             # is iterable? check for compatibility with all properties found
             elif isinstance(self.bins, (tuple, list)):
                 if len(self.bins) != num_features:
                     raise AttributeError("Length of \'bins\' parameter must match number of features.")
+                else:
+                    self._bins_internal = self.bins
             else:
                 raise AttributeError("Unknown type of parameter \'bins\'.")
         else:
@@ -196,11 +200,11 @@ def fit(self, X: np.ndarray, y: np.ndarray, random_state: int = None,
             if not isinstance(self.bins, int):
                 raise AttributeError("Parameter \'bins\' must be int for classification mode.")
 
-            self.bins = [self.bins]
+            self._bins_internal = [self.bins]
 
         # ---------------------------------------
         # get bin bounds
-        self._bin_bounds = [np.linspace(0.0, 1.0, bin + 1) for bin in self.bins]
+        self._bin_bounds = [np.linspace(0.0, 1.0, bin + 1) for bin in self._bins_internal]
 
         # on equal_intervals=True, simply use linspace
         # if the goal is to equalize the amount of samples in each bin, use np.quantile
@@ -298,7 +302,7 @@ def transform(self, X: np.ndarray, num_samples: int = 1, random_state: int = Non
 
                     # if an index is out of bounds (e.g. 0), sort into first bin
                     indices[indices == -1] = 0
-                    indices[indices == self.bins[i]] = self.bins[i] - 1
+                    indices[indices == self._bins_internal[i]] = self._bins_internal[i] - 1
                     bin_indices.append(indices)
             else:
                 # TODO: implement equal intervals
@@ -319,7 +323,7 @@ def get_degrees_of_freedom(self) -> int:
             Integer with degree of freedom.
         """
 
-        return int(np.prod(self.bins))
+        return int(np.prod(self._bins_internal))
 
     @property
     def ndim(self):

From 597ed60fc13f780fca1f7ae06f9eb8e0d145610e Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 15:42:43 +0200
Subject: [PATCH 17/21] Fixed clone path and indentation in README.

---
 README.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/README.md b/README.md
index dc92c79..0870bd7 100644
--- a/README.md
+++ b/README.md
@@ -248,13 +248,13 @@ The installation of the calibration suite is quite easy as it registered
 in the Python Package Index (PyPI). You can either install this
 framework using PIP:
 ```shell
-    $ python3 -m pip install netcal
+$ python3 -m pip install netcal
 ```
 Or simply invoke the following command to install the calibration suite when installing from source:
 ```shell
-    $ git clone https://github.com/fabiankueppers/calibration-framework.git
-    $ cd calibration-framework
-    $ python3 -m pip install .
+$ git clone https://github.com/EFS-OpenSource/calibration-framework
+$ cd calibration-framework
+$ python3 -m pip install .
 ```
 
 Note: with update 1.3, we switched from *setup.py* to *pyproject.toml*

From f93c8d4d99dabab0bae07fba6ea0a5efe6bb502c Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 16:22:06 +0200
Subject: [PATCH 18/21] Set mode in pyproject.toml to autodiscover

---
 pyproject.toml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index 53f99e2..ace66b8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -66,8 +66,8 @@ documentation = "https://fabiankueppers.github.io/calibration-framework"
 [project.license]
 file = "LICENSE.txt"
 
-[tool.setuptools]
-packages = ["netcal"]
+[tool.setuptools.packages.find]
+exclude = ["img"]
 
 [tool.setuptools.dynamic]
 version = {attr = "netcal.__version__"}

From b05c008fbff79ab11c9001e3c49c4e0faa7bc323 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 17:23:37 +0200
Subject: [PATCH 19/21] Bugfix: optimization could have returned float64
 weights regardless of passed input

---
 netcal/scaling/AbstractLogisticRegression.py | 43 ++++++++++++++++----
 netcal/scaling/LogisticCalibration.py        |  4 +-
 2 files changed, 38 insertions(+), 9 deletions(-)

diff --git a/netcal/scaling/AbstractLogisticRegression.py b/netcal/scaling/AbstractLogisticRegression.py
index f07b936..4dcb042 100644
--- a/netcal/scaling/AbstractLogisticRegression.py
+++ b/netcal/scaling/AbstractLogisticRegression.py
@@ -104,6 +104,16 @@ class are treated as independent of each other (sigmoid).
        "An introduction to variational methods for graphical models." Machine learning, 37(2): 183–233, 1999.
     """
 
+    dtypes = {
+        torch.float16: np.float16,
+        torch.float32: np.float32,
+        torch.float64: np.float64,
+        torch.int8: np.int8,
+        torch.int16: np.int16,
+        torch.int32: np.int32,
+        torch.int64: np.int64,
+    }
+
     @accepts(str, int, int, int, int, int, bool, bool, (str, bool))
     def __init__(self,
                  method: str = 'mle',
@@ -358,6 +368,10 @@ def fit(self, X: np.ndarray, y: np.ndarray, random_state: int = None, tensorboar
         # prepare data input for algorithm
         data = self.prepare(X).to(self._device)
 
+        # check if input data type is known
+        if data.dtype not in self.dtypes:
+            raise RuntimeError("Unsupported input data type: ", data.dtype)
+
         # if y is given as one-hot, convert back to categorical encoding
         if y.ndim == 2:
             y = np.argmax(y, axis=1)
@@ -537,6 +551,8 @@ def convex(self, data: torch.Tensor, y: torch.Tensor, tensorboard: bool, log_dir
             NumPy array with ground truth labels as 1-D vector (binary).
         """
 
+        dtype = data.dtype
+
         # optimization objective function
         # compute NLL loss - fix weights given of the model for the current iteration step
         def MLE(w, x, y):
@@ -545,14 +561,14 @@ def MLE(w, x, y):
             start = 0
             for name, site in self._sites.items():
                 num_weights = len(site['init']['mean'])
-                data[name] = torch.from_numpy(w[start:start+num_weights]).to(self._device)
+                data[name] = torch.from_numpy(w[start:start+num_weights]).to(
+                    dtype=dtype,
+                    device=self._device,
+                )
                 start += num_weights
 
             return loss_op(torch.squeeze(pyro.condition(self.model, data=data)(x)), y).item()
 
-        # convert input data to double as well as the weights
-        # this might be necessary for the optimizer
-        data = data.double()
         initial_weights = np.concatenate(
             [site['init']['mean'].cpu().numpy() for site in self._sites.values()]
         )
@@ -582,7 +598,7 @@ def loss_op(x, y):
         start = 0
         for name, site in self._sites.items():
             num_weights = len(site['init']['mean'])
-            site['values'] = result.x[start:start + num_weights]
+            site['values'] = result.x[start:start + num_weights].astype(self.dtypes[dtype])
             start += num_weights
 
         # on some methods like Beta calibration, it is necessary to repeat the optimization
@@ -600,7 +616,7 @@ def loss_op(x, y):
         start = 0
         for name, site in self._sites.items():
             num_weights = len(site['init']['mean'])
-            site['values'] = result.x[start:start + num_weights]
+            site['values'] = result.x[start:start + num_weights].astype(self.dtypes[dtype])
             start += num_weights
 
     def momentum(self, data: torch.Tensor, y: torch.Tensor, tensorboard: bool, log_dir: str):
@@ -741,7 +757,11 @@ def process_model(weights: dict) -> torch.Tensor:
 
         # convert input data and weights to torch (and possibly to CUDA)
         data = self.prepare(X).to(self._device)
-        num_data = data.shape[0]
+        dtype = data.dtype
+
+        # check if input data type is known
+        if dtype not in self.dtypes:
+            raise RuntimeError("Unsupported input data type: ", data.dtype)
 
         # if weights is 2-D matrix, we are in sampling mode
         # treat each row as a separate weights vector
@@ -758,11 +778,17 @@ def process_model(weights: dict) -> torch.Tensor:
                     for name, site in self._sites.items():
                         weights[name] = torch.from_numpy(np.mean(self.mcmc_model[name])).to(self._device)
 
+                        if weights[name].dtype != dtype:
+                            raise RuntimeError("Training dtype %s does not match to passed data dtype %s." % (weights[name].dtype, dtype))
+
                 # on variational inference, use mean of the variational distribution for inference
                 elif self.vi_model is not None:
                     for name, site in self._sites.items():
                         weights[name] = torch.from_numpy(self.vi_model['params']['%s_mean' % name]).to(self._device)
 
+                        if weights[name].dtype != dtype:
+                            raise RuntimeError("Training dtype %s does not match to passed data dtype %s." % (weights[name].dtype, dtype))
+
                 else:
                     raise ValueError("Internal error: neither MCMC nor variational model given.")
 
@@ -822,6 +848,9 @@ def process_model(weights: dict) -> torch.Tensor:
             for name, site in self._sites.items():
                 weights[name] = torch.from_numpy(site['values']).to(self._device)
 
+                if weights[name].dtype != dtype:
+                    raise RuntimeError("Training dtype %s does not match to passed data dtype %s." % (weights[name].dtype, dtype))
+
             # on MLE without uncertainty, only return the single model estimate
             calibrated = process_model(weights).cpu().numpy()
             calibrated = squeeze_generic(calibrated, axes_to_keep=0)
diff --git a/netcal/scaling/LogisticCalibration.py b/netcal/scaling/LogisticCalibration.py
index c0e06aa..e379d1b 100644
--- a/netcal/scaling/LogisticCalibration.py
+++ b/netcal/scaling/LogisticCalibration.py
@@ -244,8 +244,8 @@ def prior(self, dtype: torch.dtype):
                 'values': None,
                 'constraint': constraints.real,
                 'init': {
-                    'mean': torch.zeros(num_bias),
-                    'scale': torch.ones(num_bias)
+                    'mean': torch.zeros(num_bias, dtype=dtype),
+                    'scale': torch.ones(num_bias, dtype=dtype)
                 },
                 'prior': dist.Normal(torch.zeros(num_bias, dtype=dtype), 10 * torch.ones(num_bias, dtype=dtype), validate_args=True),
             }

From 2f317f9911d5777cd07b649dd2e869af7c2931d9 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 17:25:18 +0200
Subject: [PATCH 20/21] Set default to CPU optimization. Switched from MAP to
 MLE naming

---
 examples/classification/CIFAR.py      | 24 ++++++++++++------------
 examples/classification/Evaluation.py | 18 +++++++++---------
 examples/classification/utils.py      |  2 ++
 3 files changed, 23 insertions(+), 21 deletions(-)

diff --git a/examples/classification/CIFAR.py b/examples/classification/CIFAR.py
index 923bc37..ca929d4 100644
--- a/examples/classification/CIFAR.py
+++ b/examples/classification/CIFAR.py
@@ -30,10 +30,10 @@ def example_calibration(datafile: str, domain: str = ".") -> int:
 
     # kwargs for uncertainty mode. Those can also be safely set on MLE
     uncertainty_kwargs = {'mcmc_chains': 1,
-                          'mcmc_samples': 300,
-                          'mcmc_warmup_steps': 50,
+                          'mcmc_samples': 100,
+                          'mcmc_warmup_steps': 10,
                           'vi_samples': 300,
-                          'vi_epochs': 3000}
+                          'vi_epochs': 100}
 
     if domain == 'examination-mcmc':
         method = 'mcmc'
@@ -96,10 +96,10 @@ def cross_validation(datafile: str, use_cuda: Union[bool, str] = False, domain:
 
     # kwargs for uncertainty mode. Those can also be safely set on MLE
     uncertainty_kwargs = {'mcmc_chains': 1,
-                          'mcmc_samples': 300,
-                          'mcmc_warmup_steps': 50,
+                          'mcmc_samples': 100,
+                          'mcmc_warmup_steps': 10,
                           'vi_samples': 300,
-                          'vi_epochs': 3000}
+                          'vi_epochs': 100}
 
     hist_bins = 20
     bins = 15
@@ -139,11 +139,11 @@ def cross_validation(datafile: str, use_cuda: Union[bool, str] = False, domain:
 
 if __name__ == '__main__':
 
-    use_cuda = 'cuda:0'
+    use_cuda = False
 
-    # domain = "examination-map"
+    domain = "examination-mle"
     # domain = "examination-mcmc"
-    domain = "examination-variational"
+    # domain = "examination-variational"
 
     # example on CIFAR-10 with LeNet-5 and WideResnet-16-4
     lenet = "records/cifar10/lenet-5-cifar-10.npz"
@@ -153,8 +153,8 @@ def cross_validation(datafile: str, use_cuda: Union[bool, str] = False, domain:
 
     # for each model, perform a single example and a 5x2 cross validation
     for model in cifar10:
-       example_calibration(model)
-       cross_validation(model)
+       example_calibration(model, domain=domain)
+       cross_validation(model, use_cuda=use_cuda, domain=domain)
 
     # example on CIFAR-100 with LeNet-5, DenseNet-BC-100 and WideResnet-16-4
     lenet = "records/cifar100/lenet-5-cifar-100.npz"
@@ -165,5 +165,5 @@ def cross_validation(datafile: str, use_cuda: Union[bool, str] = False, domain:
 
     # for each model, perform a single example and a 5x2 cross validation
     for model in cifar100:
-        example_calibration(model)
+        example_calibration(model, domain=domain)
         cross_validation(model, use_cuda=use_cuda, domain=domain)
diff --git a/examples/classification/Evaluation.py b/examples/classification/Evaluation.py
index ead93bd..886fc81 100644
--- a/examples/classification/Evaluation.py
+++ b/examples/classification/Evaluation.py
@@ -63,7 +63,7 @@ def measure(key: str, ground_truth: List, data: List, uncertainty: str, bins: in
 
 
 def measure_miscalibration(bins: int, methods: List, uncertainty: str,
-                           map_data: List = None, mcmc_data: List = None, vi_data: List = None):
+                           mle_data: List = None, mcmc_data: List = None, vi_data: List = None):
     """
     Measure miscalibration and write to stdout.
 
@@ -79,11 +79,11 @@ def measure_miscalibration(bins: int, methods: List, uncertainty: str,
         Type how to handle uncertainty quantification. Must be either 'mean' or 'flatten'.
     """
 
-    map_gt = [x['test_gt'] for x in map_data]
+    mle_gt = [x['test_gt'] for x in mle_data]
     mcmc_gt = [x['test_gt'] for x in mcmc_data]
     vi_gt = [x['test_gt'] for x in vi_data]
 
-    map_kwargs = {'data': map_data, 'ground_truth': map_gt, 'uncertainty': uncertainty, 'bins': bins}
+    mle_kwargs = {'data': mle_data, 'ground_truth': mle_gt, 'uncertainty': uncertainty, 'bins': bins}
     mcmc_kwargs = {'data': mcmc_data, 'ground_truth': mcmc_gt, 'uncertainty': uncertainty, 'bins': bins}
     vi_kwargs = {'data': vi_data, 'ground_truth': vi_gt, 'uncertainty': uncertainty, 'bins': bins}
 
@@ -92,12 +92,12 @@ def measure_miscalibration(bins: int, methods: List, uncertainty: str,
     column_baseline = []
     columns_methods = [[] for _ in methods]
 
-    if map_data is not None:
+    if mle_data is not None:
         types.append('MLE')
-        column_baseline.append(measure('test_scores', **map_kwargs))
+        column_baseline.append(measure('test_scores', **mle_kwargs))
 
         for i, method in enumerate(methods):
-            columns_methods[i].append(measure(method, **map_kwargs))
+            columns_methods[i].append(measure(method, **mle_kwargs))
 
     if mcmc_data is not None:
         types.append('MCMC')
@@ -130,16 +130,16 @@ def measure_miscalibration(bins: int, methods: List, uncertainty: str,
     # network = "wideresnet-16-4-cifar-100"
     network = "densenet-bc-100-cifar-100"
 
-    base_dir_map = "examination-map/results/"
+    base_dir_mle = "examination-mle/results/"
     base_dir_mcmc = "examination-mcmc/results/"
     base_dir_vi = "examination-variational/results/"
 
-    map_data = read(base_dir_map, network)
+    mle_data = read(base_dir_mle, network)
     mcmc_data = read(base_dir_mcmc, network)
     vi_data = read(base_dir_vi, network)
 
     # mcmc_data = None
     # vi_data = None
 
-    df = measure_miscalibration(bins, methods, uncertainty, map_data, mcmc_data, vi_data)
+    df = measure_miscalibration(bins, methods, uncertainty, mle_data, mcmc_data, vi_data)
     df.to_excel("evaluation-%s-%s.xlsx" % (uncertainty, network))
diff --git a/examples/classification/utils.py b/examples/classification/utils.py
index af11996..e9041e7 100644
--- a/examples/classification/utils.py
+++ b/examples/classification/utils.py
@@ -174,6 +174,8 @@ def cross_validation_5_2(models: list, datafile: str, bins: int, save_models: bo
     else:
         n_classes = 2
 
+    os.makedirs(os.path.join(domain, "results"), exist_ok=True)
+
     # initialize error metrics
     ace = ACE(bins)
     ece = ECE(bins)

From 935faba9a42e92d5ece9fcc6a5bd9863284cad37 Mon Sep 17 00:00:00 2001
From: Fabian Kueppers <fabian.kueppers@efs-auto.com>
Date: Tue, 18 Oct 2022 17:32:47 +0200
Subject: [PATCH 21/21] Switched from RST to MD readme in regression
 calibration examples.

---
 examples/regression/README.rst                |  1 -
 examples/regression/__init__.py               |  2 --
 .../artificial/{README.rst => README.md}      | 12 +++----
 examples/regression/multivariate/README.md    | 34 ++++++++++++++++++
 examples/regression/multivariate/README.rst   | 36 -------------------
 5 files changed, 38 insertions(+), 47 deletions(-)
 delete mode 100644 examples/regression/README.rst
 rename examples/regression/artificial/{README.rst => README.md} (85%)
 create mode 100644 examples/regression/multivariate/README.md
 delete mode 100644 examples/regression/multivariate/README.rst

diff --git a/examples/regression/README.rst b/examples/regression/README.rst
deleted file mode 100644
index 7d6817f..0000000
--- a/examples/regression/README.rst
+++ /dev/null
@@ -1 +0,0 @@
-TODO: write readme on regression examples
\ No newline at end of file
diff --git a/examples/regression/__init__.py b/examples/regression/__init__.py
index 1e0b1ac..6bf2e00 100644
--- a/examples/regression/__init__.py
+++ b/examples/regression/__init__.py
@@ -5,5 +5,3 @@
 # If a copy of the APL2 was not distributed with this
 # file, You can obtain one at https://www.apache.org/licenses/LICENSE-2.0.txt.
 
-# TODO: update docstring to include into sphinx
-# TODO: write and include all readmes of the sub-packages
diff --git a/examples/regression/artificial/README.rst b/examples/regression/artificial/README.md
similarity index 85%
rename from examples/regression/artificial/README.rst
rename to examples/regression/artificial/README.md
index ecdec71..9a4f91c 100644
--- a/examples/regression/artificial/README.rst
+++ b/examples/regression/artificial/README.md
@@ -1,13 +1,11 @@
-Artificial Regression Calibration Example
-=========================================
+# Artificial Regression Calibration Example
 
 In this package, we demonstrate the usage of the regression calibration methods provided by the *netcal* library.
 The file *main.py* holds an artificial example that samples data around a cosine function with a certain mean and a variance.
 The sampled variance can be set to depend on the mean (cosine value).
 This is demonstrated in the following figure:
 
-.. image:: img/data.svg
-    :align: center
+![data](img/data.svg)
 
 Each sample within the array *ymean* and *ystd* reflects a mean and stddev prediction by an artificial estimator.
 The calibration methods are fit to the ground truth *y* using these estimates as inputs.
@@ -25,8 +23,7 @@ The following methods apply a parametric recalibration (e.g., Gaussian, Cauchy):
 
 If we visualize the recalibrated distribution functions of the first sample, we get the following image:
 
-.. image:: img/methods.svg
-    :align: center
+![methods](img/methods.svg)
 
 You can use Scipy's *norm* or *cauchy* module to get a density (PDF) or a CDF function.
 Finally, we demonstrate how to use the metrics provided by the *netcal.metrics* package to measure regression calibration.
@@ -40,5 +37,4 @@ The following metrics are implemented:
 
 Furthermore, you can also visualize the miscalibration using the *ReliabilityRegression* class within the *netcal.presentation* package:
 
-.. image:: img/reliability.svg
-    :align: center
+![reliability](img/reliability.svg)
diff --git a/examples/regression/multivariate/README.md b/examples/regression/multivariate/README.md
new file mode 100644
index 0000000..75ad4d0
--- /dev/null
+++ b/examples/regression/multivariate/README.md
@@ -0,0 +1,34 @@
+# Multivariate Regression Calibration Example
+
+In this package, we demonstrate the usage of the regression calibration methods with additional correlation estimation and recalibration.
+The file *main.py* holds an artificial example that samples 2D data around a sine and cosine function with a certain mean and a variance.
+Furthermore, the variance on the data is correlated to a certain degree.
+The calibration methods can be used to identify and capture the correlations within the input data.
+Thus, it is possible to model parametric multivariate distributions based on independently learned/provided distributions for each dimension,
+
+Basically, each calibration method can be used to recalibrate multiple (independent) dimensions.
+However, only the *GPNormal* is able to model a joint multivariate Gaussian with correlations as calibration output.
+See the code example below:
+
+```python
+mean          # NumPy n-D array holding the estimated mean of shape (n, d) with n samples and d dimensions
+stddev        # NumPy n-D array holding the estimated stddev (independent) of shape (n, d) with n samples and d dimensions
+ground_truth  # NumPy n-D array holding the ground-truth scores of shape (n, d) with n samples and d dimensions
+
+from netcal.regression import GPNormal
+
+gpnormal = GPNormal(
+    n_inducing_points=12,    # number of inducing points
+    n_random_samples=256,    # random samples used for likelihood
+    n_epochs=256,            # optimization epochs
+    use_cuda=False,          # can also use CUDA for computations
+    correlations=True,       # enable correlation capturing
+    name_prefix="gpnormal",  # internal name prefix required for Pyro
+)
+
+# fit GP-Normal
+gpnormal.fit((mean, stddev), ground_truth)
+
+# transform distributions to obtain covariance matrices
+cov = gpnormal.transform((mean, stddev))  # NumPy array with covariances - has shape (n, d, d)
+```
diff --git a/examples/regression/multivariate/README.rst b/examples/regression/multivariate/README.rst
deleted file mode 100644
index 03abf1a..0000000
--- a/examples/regression/multivariate/README.rst
+++ /dev/null
@@ -1,36 +0,0 @@
-Multivariate Regression Calibration Example
-===========================================
-
-In this package, we demonstrate the usage of the regression calibration methods with additional correlation estimation and recalibration.
-The file *main.py* holds an artificial example that samples 2D data around a sine and cosine function with a certain mean and a variance.
-Furthermore, the variance on the data is correlated to a certain degree.
-The calibration methods can be used to identify and capture the correlations within the input data.
-Thus, it is possible to model parametric multivariate distributions based on independently learned/provided distributions for each dimension,
-
-Basically, each calibration method can be used to recalibrate multiple (independent) dimensions.
-However, only the *GPNormal* is able to model a joint multivariate Gaussian with correlations as calibration output.
-See the code example below:
-
-.. code-block:: python
-
-    mean          # NumPy n-D array holding the estimated mean of shape (n, d) with n samples and d dimensions
-    stddev        # NumPy n-D array holding the estimated stddev (independent) of shape (n, d) with n samples and d dimensions
-    ground_truth  # NumPy n-D array holding the ground-truth scores of shape (n, d) with n samples and d dimensions
-
-    from netcal.regression import GPNormal
-
-    gpnormal = GPNormal(
-        n_inducing_points=12,    # number of inducing points
-        n_random_samples=256,    # random samples used for likelihood
-        n_epochs=256,            # optimization epochs
-        use_cuda=False,          # can also use CUDA for computations
-        correlations=True,       # enable correlation capturing
-        name_prefix="gpnormal",  # internal name prefix required for Pyro
-    )
-
-    # fit GP-Normal
-    gpnormal.fit((mean, stddev), ground_truth)
-
-    # transform distributions to obtain covariance matrices
-    cov = gpnormal.transform((mean, stddev))  # NumPy array with covariances - has shape (n, d, d)
-