4_ScikitLearn_Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table of Contents\n",
    "\n",
    "- **Data Representation**\n",
    "- **Supervised Learning**\n",
    "    - Example: Classification with KNearestNeighbors\n",
    "- **Unsupervised Learning**\n",
    "    - Example: Dimensionality Reduction with PCA\n",
    "- **Scikit-learn's estimator interface**\n",
    "- **Evaluation Metrics for classification problems**\n",
    "- **Model Evaluation**\n",
    "- **Cross-Validation**\n",
    "- **`sklearn` Pipelines: Chaining estimators**\n",
    "- **Feature Selection**\n",
    "    - K-Best selection\n",
    "- **Classifiers comparison**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the [sklearn tutorial](https://ogrisel.github.io/scikit-learn.org/sklearn-tutorial/tutorial/astronomy/general_concepts.html) \"Machine Learning 101: General Concepts\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[**scikit-learn**](http://scikit-learn.org) is a Python package designed to give access to well-known **machine learning algorithms within Python** code, through a clean, well-thought-out API. It has been built by hundreds of contributors from around the world, and is used across industry and academia.\n",
    "\n",
    "scikit-learn is built upon Python's [NumPy](http://www.numpy.org/) (Numerical Python) and [SciPy](http://www.scipy.org/) (Scientific Python) libraries, which enable efficient in-core numerical and scientific computation within Python. As such, scikit-learn is not specifically designed for extremely large datasets, though there is some work in this area."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Representation\n",
    "\n",
    "Most machine learning algorithms implemented in scikit-learn expect a **two-dimensional array or matrix** `X`, usually represented as a NumPy ndarray. The expected shape of `X` is `(n_samples, n_features)`.\n",
    "\n",
    "* `n_samples`: The number of samples, where each sample is an item to process (e.g., classify). A sample can be a document, a picture, a sound, a video, a row in database or CSV file, or whatever you can describe with a fixed set of quantitative traits.\n",
    "* `n_features`:\tThe number of features or distinct traits that can be used to describe each item in a quantitative manner. Features are generally real-valued, but may be boolean or discrete-valued in some cases.\n",
    "\n",
    "The number of features must be fixed in advance. However it can be very high dimensional (e.g. millions of features) with most of them being zeros for a given sample. In this case we may use `scipy.sparse` matrices instead of NumPy arrays so as to make the data fit in memory.\n",
    "\n",
    "The *supervised* machine learning algorithms implemented in scikit-learn also expect a **one-dimensional array** `y` with shape `(n_samples,)`. This array associated a target class to every sample in the input `X`.\n",
    "\n",
    "![data-layout.png](images/data-layout.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, we will explore the **Iris dataset**. The machine learning community often uses a simple flowers database where each row in the database (or CSV file) is a set of measurements of an individual iris flower. Each sample in this dataset is described by 4 features and can belong to one of three target classes:\n",
    "\n",
    "**Features in the Iris dataset:**\n",
    " \t\n",
    "* sepal length in cm\n",
    "* sepal width in cm\n",
    "* petal length in cm\n",
    "* petal width in cm\n",
    "\n",
    "**Target classes to predict:**\n",
    " \t\n",
    "* Iris Setosa\n",
    "* Iris Versicolour\n",
    "* Iris Virginica\n",
    "\n",
    "Scikit-Learn embeds a copy of the Iris CSV file along with a helper function to load it into NumPy arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:17.025725Z",
     "start_time": "2020-06-29T13:20:16.933133Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "iris = load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sklearn.utils.Bunch"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(iris)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['DESCR',\n",
       " 'data',\n",
       " 'data_module',\n",
       " 'feature_names',\n",
       " 'filename',\n",
       " 'frame',\n",
       " 'target',\n",
       " 'target_names']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(iris)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The features of each sample flower are stored in the `data` attribute of the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:17.044284Z",
     "start_time": "2020-06-29T13:20:17.029214Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "150\n",
      "4\n",
      "[5.1 3.5 1.4 0.2]\n"
     ]
    }
   ],
   "source": [
    "n_samples, n_features = iris.data.shape\n",
    "\n",
    "print(n_samples)\n",
    "print(n_features)\n",
    "print(iris.data[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The information about the class of each sample is stored in the `target` attribute of the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150,)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.data.shape\n",
    "iris.target.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:17.057979Z",
     "start_time": "2020-06-29T13:20:17.049112Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
      " 2 2]\n"
     ]
    }
   ],
   "source": [
    "print(iris.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 50, 1: 50, 2: 50}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique, counts = np.unique(iris.target, return_counts = True)\n",
    "dict(zip(unique,counts))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data is four dimensional, but we can visualize two of the dimensions at a time using a simple scatter-plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:17.410008Z",
     "start_time": "2020-06-29T13:20:17.070793Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_index = 0\n",
    "y_index = 1\n",
    "\n",
    "# this formatter will label the colorbar with the correct target names\n",
    "formatter = plt.FuncFormatter(lambda i, *args: iris.target_names[int(i)])\n",
    "\n",
    "plt.scatter(iris.data[:, x_index], iris.data[:, y_index], c=iris.target, cmap=plt.cm.get_cmap('Paired', 3))\n",
    "plt.colorbar(ticks=[0, 1, 2], format=formatter)\n",
    "plt.clim(-0.5, 2.5)\n",
    "plt.xlabel(iris.feature_names[x_index])\n",
    "plt.ylabel(iris.feature_names[y_index])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data exploration using pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
       "0                  5.1               3.5                1.4               0.2   \n",
       "1                  4.9               3.0                1.4               0.2   \n",
       "2                  4.7               3.2                1.3               0.2   \n",
       "3                  4.6               3.1                1.5               0.2   \n",
       "4                  5.0               3.6                1.4               0.2   \n",
       "..                 ...               ...                ...               ...   \n",
       "145                6.7               3.0                5.2               2.3   \n",
       "146                6.3               2.5                5.0               1.9   \n",
       "147                6.5               3.0                5.2               2.0   \n",
       "148                6.2               3.4                5.4               2.3   \n",
       "149                5.9               3.0                5.1               1.8   \n",
       "\n",
       "     target  \n",
       "0         0  \n",
       "1         0  \n",
       "2         0  \n",
       "3         0  \n",
       "4         0  \n",
       "..      ...  \n",
       "145       2  \n",
       "146       2  \n",
       "147       2  \n",
       "148       2  \n",
       "149       2  \n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_iris = pd.DataFrame(iris.data,columns = iris.feature_names)\n",
    "df_iris['target'] = iris.target\n",
    "df_iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    50\n",
       "1    50\n",
       "2    50\n",
       "Name: target, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_iris.target.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.843333</td>\n",
       "      <td>3.057333</td>\n",
       "      <td>3.758000</td>\n",
       "      <td>1.199333</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.828066</td>\n",
       "      <td>0.435866</td>\n",
       "      <td>1.765298</td>\n",
       "      <td>0.762238</td>\n",
       "      <td>0.819232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>4.300000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.100000</td>\n",
       "      <td>2.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>5.800000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.350000</td>\n",
       "      <td>1.300000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.400000</td>\n",
       "      <td>3.300000</td>\n",
       "      <td>5.100000</td>\n",
       "      <td>1.800000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>7.900000</td>\n",
       "      <td>4.400000</td>\n",
       "      <td>6.900000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       sepal length (cm)  sepal width (cm)  petal length (cm)  \\\n",
       "count         150.000000        150.000000         150.000000   \n",
       "mean            5.843333          3.057333           3.758000   \n",
       "std             0.828066          0.435866           1.765298   \n",
       "min             4.300000          2.000000           1.000000   \n",
       "25%             5.100000          2.800000           1.600000   \n",
       "50%             5.800000          3.000000           4.350000   \n",
       "75%             6.400000          3.300000           5.100000   \n",
       "max             7.900000          4.400000           6.900000   \n",
       "\n",
       "       petal width (cm)      target  \n",
       "count        150.000000  150.000000  \n",
       "mean           1.199333    1.000000  \n",
       "std            0.762238    0.819232  \n",
       "min            0.100000    0.000000  \n",
       "25%            0.300000    0.000000  \n",
       "50%            1.300000    1.000000  \n",
       "75%            1.800000    2.000000  \n",
       "max            2.500000    2.000000  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_iris.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sepal length (cm)    0\n",
       "sepal width (cm)     0\n",
       "petal length (cm)    0\n",
       "petal width (cm)     0\n",
       "target               0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_iris.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_iris.iloc[:,:-1].hist(figsize = (10,7))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supervised Learning\n",
    "\n",
    "![supervised machine learning overview](images/plot_ML_flow_chart_12.png)\n",
    "\n",
    "A supervised learning algorithm makes the distinction between the raw observed data `X` with shape `(n_samples, n_features)` and some label given to the model while training by some teacher. \n",
    "In scikit-learn this array is often noted `y` and has generally the shape `(n_samples,)`.\n",
    "\n",
    "After training, the fitted model does no longer expect the `y` as an input: it will try to predict the most likely labels `y_new` for a new set of samples `X_new`.\n",
    "\n",
    "Depending on the nature of the target `y`, supervised learning can be given different names:\n",
    "\n",
    "* If `y` has values in a fixed set of **categorical outcomes** (represented by integers) the task to predict `y` is called **classification**.\n",
    "* If `y` has **floating point values** (e.g. to represent a price, a temperature, a size...), the task to predict `y` is called **regression**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classification Example\n",
    "\n",
    "K nearest neighbors (kNN) is one of the simplest learning strategies: given a new, unknown observation, look up in your reference database which ones have the closest features and assign the predominant class.\n",
    "\n",
    "Let's try it out on our iris classification problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:17.447694Z",
     "start_time": "2020-06-29T13:20:17.416027Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['versicolor']\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X, y = iris.data, iris.target\n",
    "\n",
    "# create the model\n",
    "knn = KNeighborsClassifier(n_neighbors=5)\n",
    "\n",
    "# fit the model\n",
    "knn.fit(X, y)\n",
    "\n",
    "# What kind of iris has 3cm x 5cm sepal and 4cm x 2cm petal?\n",
    "# call the \"predict\" method:\n",
    "result = knn.predict([[3, 5, 4, 2],])\n",
    "\n",
    "print(iris.target_names[result])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unsupervised Learning\n",
    "\n",
    "![unsupervised machine learning overview](images/plot_ML_flow_chart_32.png)\n",
    "\n",
    "Unsupervised learning addresses a different sort of problem. Here the data has no labels, and we are interested in finding similarities between the objects in question. \n",
    "An unsupervised learning algorithm only uses a single set of observations `X` with shape `(n_samples, n_features)` and does not use any kind of labels.\n",
    "\n",
    "Unsupervised learning comprises tasks such as *dimensionality reduction* and *clustering*. For example, in the Iris data discussed above, we can use unsupervised methods to determine combinations of the measurements which best display the structure of the data. \n",
    "\n",
    "Sometimes the two may even be combined: e.g. Unsupervised learning can be used to find useful features in heterogeneous data, and then these features can be used within a supervised framework."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimensionality Reduction: PCA\n",
    "\n",
    "Principle Component Analysis (PCA) is a dimensionality reduction technique that can find the combinations of variables that explain the most variance.\n",
    "\n",
    "Consider the Iris dataset. It cannot be visualized in a single 2D plot, as it has 4 features. We are going to extract 2 combinations of sepal and petal dimensions to visualize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Object `PCA` not found.\n"
     ]
    }
   ],
   "source": [
    "PCA?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:18.366686Z",
     "start_time": "2020-06-29T13:20:18.170838Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reduced dataset shape: (150, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = iris.data, iris.target\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=0.95)\n",
    "pca.fit(X)\n",
    "X_reduced = pca.transform(X)\n",
    "print(\"Reduced dataset shape:\", X_reduced.shape)\n",
    "plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap='Paired')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scikit-learn's estimator interface\n",
    "\n",
    "Scikit-learn strives to have a uniform interface across all methods, and we have seen examples of these above. Every algorithm is exposed in scikit-learn via an **estimator** object. Given a scikit-learn estimator object named model, the following methods are available:\n",
    "\n",
    "* Available in **all estimators**:\n",
    "    - `model.fit()`: fit training data. \n",
    "        - For supervised learning applications, this accepts two arguments: the data `X` and the labels `y` (e.g. `model.fit(X, y)`). \n",
    "        - For unsupervised learning applications, this accepts only a single argument, the data `X` (e.g. `model.fit(X)`).\n",
    "\n",
    "* Available in **supervised estimators**:\n",
    "\n",
    "    - `model.predict()`: given a trained model, predict the label of a new set of data. This method accepts one argument, the new data `X_new` (e.g. `model.predict(X_new)`), and returns the learned label for each object in the array.\n",
    "    - `model.predict_proba()`: For classification problems, some estimators also provide this method, which returns the probability that a new observation has each categorical label. In this case, the label with the highest probability is returned by `model.predict()`.\n",
    "    - `model.score()`: for classification or regression problems, most estimators implement a score method. Scores are between 0 and 1, with a larger score indicating a better fit.\n",
    "\n",
    "* Available in **unsupervised estimators**:\n",
    "\n",
    "    - `model.predict()`: predict labels in clustering algorithms.\n",
    "    - `model.transform()`: given an unsupervised model, transform new data into the new basis. This also accepts one argument X_new, and returns the new representation of the data based on the unsupervised model.\n",
    "    - `model.fit_transform()`: some estimators implement this method, which more efficiently performs a fit and a transform on the same input data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation Metrics for classification problems\n",
    "\n",
    "Machine learning models are often used to predict the outcomes of a classification problem. Predictive models rarely predict everything perfectly, so there are many performance metrics that can be used to analyze our models.\n",
    "\n",
    "When you run a prediction on your data to distinguish among two classes (*positive* and *negative* classes, for simplicity), your results can be broken down into 4 parts:\n",
    "\n",
    "<img src=\"images/classification_report.png\" alt=\"drawing\" width=\"450\"/>\n",
    "\n",
    "* **True Positives**: data in class *positive* that the model predicts will be in class *positive*;\n",
    "* **True Negatives**: data in class *negative* that the model predicts will be in class *negative*;\n",
    "* **False Positives**: data in class *negative* that the model predicts will be in class *positive*;\n",
    "* **False Negatives**: data in class *positive* that the model predicts will be in class *negative*.\n",
    "\n",
    "The most common performance metrics in this binary classification scenario are the following:\n",
    "\n",
    "* **accuracy**: the fraction of observations (both positive and negative) predicted correctly:\n",
    "\n",
    "$$ Accuracy = \\frac{(TP+TN)}{(TP+FP+TN+FN)} $$\n",
    "* **recall**: the fraction of positive observations that are predicted correctly:\n",
    "\n",
    "$$ Recall = \\frac{TP}{(TP+FN)} $$\n",
    "\n",
    "* **precision**: the fraction of of predicted positive observations that are actually positive:\n",
    "\n",
    "$$ Precision = \\frac{TP}{(TP+FP)} $$\n",
    "\n",
    "* **f1-score**: a composite measure that combines both precision and recall:\n",
    "\n",
    "$$ F_1 = \\frac{2 \\cdot P \\cdot R}{(P+R)}$$\n",
    "\n",
    "The **confusion matrix** is useful for quickly calculating precision and recall given the predicted labels from a model. A confusion matrix for binary classification shows the four different outcomes: true positive, false positive, true negative, and false negative. The actual values form the columns, and the predicted values (labels) form the rows. The intersection of the rows and columns show one of the four outcomes. \n",
    "\n",
    "![confusion-matrix.png](images/confusion-matrix.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the **digits** dataset example (8x8 images of handwritten digits)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Syntax      | Description |\n",
    "| ----------- | ----------- |\n",
    "| Number of Instances | 1797       |\n",
    "| Number of Attributes | 64        |\n",
    "| Number of Classes | 10        |\n",
    "| Attributes Information | 8x8 image of integer pixels in the range 0..16 |\n",
    "| Missing Attribute Values | None |\n",
    "| Date | July; 1998 |\n",
    "| Info | [digits-dataset](https://scikit-learn.org/stable/datasets/toy_dataset.html#digits-dataset) |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:18.822242Z",
     "start_time": "2020-06-29T13:20:18.586749Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "digits = load_digits()\n",
    "X = digits.data\n",
    "y = digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1797, 64), (1797,))"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 178,\n",
       " 1: 182,\n",
       " 2: 177,\n",
       " 3: 183,\n",
       " 4: 181,\n",
       " 5: 182,\n",
       " 6: 181,\n",
       " 7: 179,\n",
       " 8: 174,\n",
       " 9: 180}"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique, counts = np.unique(y, return_counts = True)\n",
    "dict(zip(unique,counts))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " **How might we check the performance of our model?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "A simple way to test a model is to **use a hold-out set which doesn't participate in the training**, using scikit-learn's `train_test_split` utility, defined in the `sklearn.model_selection` module."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font color='blue'>TODO:</font> \n",
    "- #### <font color='blue'>Split the dataset in training and test set</font>\n",
    "- #### <font color='blue'>Train a KNN model with default parameters</font>\n",
    "- #### <font color='blue'>Predict the label of samples in the test set and evaluate the performance of the classifier</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Single hold-out validation may provide a coarse estimate of the generalization capability of the model.\n",
    "Random sampling of examples for training and testing may result in an accurate estimate and the single output value may not be sufficient, for example, to compare the performance of several classifiers.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another option is to use **$K$-fold cross-validation**, where we partition the data into $K$ subsets, called **folds**. Then, we iteratively train the algorithm on $k-1$ folds while using the remaining fold as the test set (called the “**holdout fold**”):\n",
    "\n",
    "![Cross-Validation-Diagram.jpg](images/Cross-Validation-Diagram.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "-------------------------------------------fold 0\n",
      "\n",
      "TRAIN: [ 335  347  349 ... 1794 1795 1796] (1437,)\n",
      "TEST: [  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17\n",
      "  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35\n",
      "  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53\n",
      "  54  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71\n",
      "  72  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89\n",
      "  90  91  92  93  94  95  96  97  98  99 100 101 102 103 104 105 106 107\n",
      " 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125\n",
      " 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143\n",
      " 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161\n",
      " 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179\n",
      " 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197\n",
      " 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215\n",
      " 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233\n",
      " 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251\n",
      " 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269\n",
      " 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287\n",
      " 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305\n",
      " 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323\n",
      " 324 325 326 327 328 329 330 331 332 333 334 336 337 338 339 340 341 342\n",
      " 343 344 345 346 348 350 351 352 353 356 358 361 364 366 367 370 375 377] (360,)\n",
      "-------------------------------------------end fold 0\n",
      "\n",
      "-------------------------------------------fold 1\n",
      "\n",
      "TRAIN: [   0    1    2 ... 1794 1795 1796] (1437,)\n",
      "TEST: [335 347 349 354 355 357 359 360 362 363 365 368 369 371 372 373 374 376\n",
      " 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395\n",
      " 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413\n",
      " 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431\n",
      " 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449\n",
      " 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467\n",
      " 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485\n",
      " 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503\n",
      " 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521\n",
      " 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539\n",
      " 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557\n",
      " 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575\n",
      " 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593\n",
      " 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611\n",
      " 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629\n",
      " 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647\n",
      " 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665\n",
      " 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683\n",
      " 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 702\n",
      " 703 704 705 706 707 710 711 712 713 714 715 716 717 719 727 733 743 746] (360,)\n",
      "-------------------------------------------end fold 1\n",
      "\n",
      "-------------------------------------------fold 2\n",
      "\n",
      "TRAIN: [   0    1    2 ... 1794 1795 1796] (1438,)\n",
      "TEST: [ 701  708  709  718  720  721  722  723  724  725  726  728  729  730\n",
      "  731  732  734  735  736  737  738  739  740  741  742  744  745  747\n",
      "  748  749  750  751  752  753  754  755  756  757  758  759  760  761\n",
      "  762  763  764  765  766  767  768  769  770  771  772  773  774  775\n",
      "  776  777  778  779  780  781  782  783  784  785  786  787  788  789\n",
      "  790  791  792  793  794  795  796  797  798  799  800  801  802  803\n",
      "  804  805  806  807  808  809  810  811  812  813  814  815  816  817\n",
      "  818  819  820  821  822  823  824  825  826  827  828  829  830  831\n",
      "  832  833  834  835  836  837  838  839  840  841  842  843  844  845\n",
      "  846  847  848  849  850  851  852  853  854  855  856  857  858  859\n",
      "  860  861  862  863  864  865  866  867  868  869  870  871  872  873\n",
      "  874  875  876  877  878  879  880  881  882  883  884  885  886  887\n",
      "  888  889  890  891  892  893  894  895  896  897  898  899  900  901\n",
      "  902  903  904  905  906  907  908  909  910  911  912  913  914  915\n",
      "  916  917  918  919  920  921  922  923  924  925  926  927  928  929\n",
      "  930  931  932  933  934  935  936  937  938  939  940  941  942  943\n",
      "  944  945  946  947  948  949  950  951  952  953  954  955  956  957\n",
      "  958  959  960  961  962  963  964  965  966  967  968  969  970  971\n",
      "  972  973  974  975  976  977  978  979  980  981  982  983  984  985\n",
      "  986  987  988  989  990  991  992  993  994  995  996  997  998  999\n",
      " 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013\n",
      " 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027\n",
      " 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041\n",
      " 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055\n",
      " 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1070 1071 1072\n",
      " 1073 1074 1077 1078 1079 1081 1085 1091 1095] (359,)\n",
      "-------------------------------------------end fold 2\n",
      "\n",
      "-------------------------------------------fold 3\n",
      "\n",
      "TRAIN: [   0    1    2 ... 1794 1795 1796] (1438,)\n",
      "TEST: [1067 1068 1069 1075 1076 1080 1082 1083 1084 1086 1087 1088 1089 1090\n",
      " 1092 1093 1094 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106\n",
      " 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120\n",
      " 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134\n",
      " 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148\n",
      " 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162\n",
      " 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176\n",
      " 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190\n",
      " 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204\n",
      " 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218\n",
      " 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232\n",
      " 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246\n",
      " 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260\n",
      " 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274\n",
      " 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288\n",
      " 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302\n",
      " 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316\n",
      " 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330\n",
      " 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344\n",
      " 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358\n",
      " 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372\n",
      " 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386\n",
      " 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400\n",
      " 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414\n",
      " 1415 1416 1417 1418 1419 1420 1421 1422 1424 1425 1426 1427 1428 1429\n",
      " 1430 1431 1432 1434 1435 1439 1440 1441 1444] (359,)\n",
      "-------------------------------------------end fold 3\n",
      "\n",
      "-------------------------------------------fold 4\n",
      "\n",
      "TRAIN: [   0    1    2 ... 1440 1441 1444] (1438,)\n",
      "TEST: [1423 1433 1436 1437 1438 1442 1443 1445 1446 1447 1448 1449 1450 1451\n",
      " 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465\n",
      " 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479\n",
      " 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493\n",
      " 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507\n",
      " 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521\n",
      " 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535\n",
      " 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549\n",
      " 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563\n",
      " 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577\n",
      " 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591\n",
      " 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605\n",
      " 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619\n",
      " 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633\n",
      " 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647\n",
      " 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661\n",
      " 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675\n",
      " 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689\n",
      " 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703\n",
      " 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717\n",
      " 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731\n",
      " 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745\n",
      " 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759\n",
      " 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773\n",
      " 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787\n",
      " 1788 1789 1790 1791 1792 1793 1794 1795 1796] (359,)\n",
      "-------------------------------------------end fold 4\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import StratifiedKFold\n",
    "skf = StratifiedKFold(5)\n",
    "\n",
    "for enu,(train_index, test_index) in enumerate(skf.split(X, y)):\n",
    "    print()\n",
    "    print(f'-------------------------------------------fold {enu}')\n",
    "    print(f'')\n",
    "    print(\"TRAIN:\", train_index, train_index.shape)\n",
    "    print(\"TEST:\", test_index, test_index.shape)\n",
    "\n",
    "    # train model on the current training set\n",
    "    # test model on the current test set\n",
    "    \n",
    "    print(f'-------------------------------------------end fold {enu}')\n",
    "\n",
    "# compute average metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:20:19.541198Z",
     "start_time": "2020-06-29T13:20:19.190171Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.92777778 0.98333333 0.97777778 0.95555556 0.97222222 0.97222222\n",
      " 0.98888889 0.98324022 0.98324022 0.96648045]\n",
      "0.9710738671632526\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "cv = cross_val_score(KNeighborsClassifier(5), X, y, cv=10)\n",
    "\n",
    "print(cv)\n",
    "print(cv.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that you want to perform dimensionality reduction before. How can we combine the two steps?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `sklearn` Pipelines: Chaining estimators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pipeline can be used to **chain multiple estimators into one**. This is useful as there is often a fixed sequence of steps in processing the data, for example feature selection, normalization and classification. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that:\n",
    "- All estimators in a pipeline, except the last one, must be transformers (i.e., must have a `transform` method). \n",
    "- The last estimator may be any type (transformer, classifier, etc.)\n",
    "\n",
    "Indeed you can include in your pipeline pretty any function for:\n",
    "- [preprocessing](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.preprocessing)\n",
    "- [feature extraction](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.feature_extraction)\n",
    "- [feature selection](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.feature_selection)\n",
    "- classification / clustering\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building and using a `pipeline`\n",
    "The Pipeline is built using a list of **(key, value) pairs**, where \n",
    "- the key is a string containing the name you want to give this step \n",
    "- the value is an estimator object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('reduce_dim', PCA(n_components=0.95)),\n",
       "                ('clf', KNeighborsClassifier())])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.svm import LinearSVC\n",
    "from sklearn.decomposition import PCA\n",
    "estimators = [('reduce_dim', PCA(n_components=0.95)), ('clf', KNeighborsClassifier())]\n",
    "pipe = Pipeline(estimators)\n",
    "pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calling `fit` on the pipeline is the same as \n",
    "- sequentially calling fit on each estimator\n",
    "- transform the input and pass it on to the next step. \n",
    "\n",
    "Furthermore, the pipeline has **all the methods that the last estimator in the pipeline has**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xtr, Xte, ytr, yte = train_test_split(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1347, 64), (450, 64), (1347,), (450,))"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xtr.shape, Xte.shape, ytr.shape, yte.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('reduce_dim', PCA(n_components=0.95)),\n",
       "                ('clf', KNeighborsClassifier())])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe.fit(Xtr,ytr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = pipe.predict(Xte)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9777777777777777"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_pred,yte)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accessing the steps of a `pipeline`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access the steps of a `pipeline` in three ways:\n",
    "- throught the `steps` attribute\n",
    "- by index\n",
    "- by name\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(('reduce_dim', PCA(n_components=0.95)),\n",
       " PCA(n_components=0.95),\n",
       " PCA(n_components=0.95))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe.steps[0], pipe[0], pipe['reduce_dim']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.46330361e-20, -1.96967902e-02, -2.35037440e-01, ...,\n",
       "        -6.98556732e-02, -4.86125992e-02, -1.48170879e-02],\n",
       "       [ 4.29544993e-18,  5.43529284e-03, -2.67263291e-03, ...,\n",
       "        -1.96854529e-01, -2.80680053e-02,  2.17197051e-03],\n",
       "       [ 3.14666276e-18,  1.53832073e-02,  1.05701836e-01, ...,\n",
       "         2.26292780e-01,  1.58245126e-01,  3.34202413e-02],\n",
       "       ...,\n",
       "       [-1.22327459e-17, -5.28315335e-03, -6.55937300e-02, ...,\n",
       "        -2.21287841e-01,  3.20979044e-02, -5.09163990e-02],\n",
       "       [-7.64461913e-18,  7.72978163e-04,  1.20912495e-01, ...,\n",
       "        -1.00912795e-01,  3.62962475e-01,  1.41090600e-01],\n",
       "       [ 4.75717805e-18,  1.63204524e-02,  6.29688075e-02, ...,\n",
       "         1.64723662e-01, -1.65797552e-02,  1.50082220e-02]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe[0].components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 64)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe[0].components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1257, 28)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe[0].transform(X_train).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why do we use pipelines?\n",
    "Pipeline serves multiple purposes here:\n",
    "\n",
    "- Convenience and encapsulation: you only have to call **fit and predict once on your data** to fit a whole sequence of estimators.\n",
    "\n",
    "- Joint parameter selection: you can **grid search over parameters of all estimators** in the pipeline at once.\n",
    "\n",
    "- Safety: pipelines help **avoid leaking statistics from your test data into the trained model in cross-validation**, by ensuring that the same samples are used to train the transformers and predictors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.92777778, 0.99444444, 0.98333333, 0.95      , 0.97222222,\n",
       "       0.98333333, 0.98888889, 0.98882682, 0.97765363, 0.96648045])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_val_score(pipe,X,y,cv = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imbalance classification and cross-validation\n",
    "\n",
    "`scikit-learn` does not natively handle methods for *imbalanced learning*.\n",
    "\n",
    "[`Imbalanced-learn`](https://imbalanced-learn.org/stable/) (imported as `imblearn`) is an open source, MIT-licensed library relying on scikit-learn and provides tools when dealing with classification with imbalanced classes.\n",
    "\n",
    "We can use the pipelines of imblearn in exactly the same way as those of scikit-learn, so that we can correctly perdorm rebalancing when working in cross-validation.\n",
    "\n",
    "```python\n",
    "from imblearn.pipeline import Pipeline\n",
    "pipe = Pipeline([\n",
    "        ('sampling', SMOTE()),\n",
    "        ... ,\n",
    "        ('classification', LogisticRegression())\n",
    "    ])\n",
    "\n",
    "results = cross_val_score(pipe, data, target, ...)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Selection\n",
    "\n",
    "The dataset we want to feed into our machine learning model could include a vast amount of features. Among them, there can be *redundant* as well as *irrelevant* features. **Redundant features** convey the same information contained in other features, while **irrelevant features** regard information useless for the learning process.\n",
    "\n",
    "While a domain expert could recognize such features, the process will be long or almost impossible to be carried out by hand. The **feature selection** methods aim at reducing automatically the number of features in a dataset without negatively impacting the predictive power of the learned model.\n",
    "\n",
    "Three benefits of performing feature selection before modeling your data may be:\n",
    "\n",
    "* **Reducing overfitting**: less redundant data means less opportunity to make decisions based on noise.\n",
    "* **Improving accuracy**: less misleading data means modeling accuracy improves.\n",
    "* **Reducing training time**: less data means that algorithms train faster.\n",
    "\n",
    "The classes in the `sklearn.feature_selection` module can be used for feature selection/dimensionality reduction on sample sets.\n",
    "\n",
    "The simplest baseline approach to feature selection is `VarianceThreshold`. It removes all features whose variance doesn’t meet some threshold. By default, it removes all zero-variance features, i.e. features that have the same value in all samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:21:32.916227Z",
     "start_time": "2020-06-29T13:21:32.905612Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 1]\n",
      " [0 1 0]\n",
      " [1 0 0]\n",
      " [0 1 1]\n",
      " [0 1 0]\n",
      " [0 1 1]]\n",
      "[0.13888889 0.22222222 0.25      ]\n",
      "[[0 1]\n",
      " [1 0]\n",
      " [0 0]\n",
      " [1 1]\n",
      " [1 0]\n",
      " [1 1]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.feature_selection import VarianceThreshold\n",
    "\n",
    "X_synth = np.array([[0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 1, 1], [0, 1, 0], [0, 1, 1]])\n",
    "print(X_synth)\n",
    "\n",
    "feat_selector = VarianceThreshold(threshold=0.2)\n",
    "X_sel = feat_selector.fit_transform(X_synth)\n",
    "print(X_sel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K-Best selection\n",
    "\n",
    "`SelectKBest` removes all but the $k$ highest scoring features, in terms of $\\chi^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-29T13:23:38.304042Z",
     "start_time": "2020-06-29T13:23:38.292245Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import SelectKBest, chi2\n",
    "feat_selector = SelectKBest(chi2,k=10) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `SelectKBest` object takes as input a scoring function that returns univariate scores. As scoring function, you may use:\n",
    "- For regression: `f_regression`, `mutual_info_regression`\n",
    "- For classification: `chi2`, `f_classif`, `mutual_info_classif`\n",
    "\n",
    "The methods based on **F-test** estimate the degree of linear dependency between two random variables. On the other hand, **mutual information** methods can capture any kind of statistical dependency, but being nonparametric, they require more samples for accurate estimation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font color='blue'>TODO:</font> \n",
    "- #### <font color='blue'>Chain the feature-selection and the classification step in a pipeline</font>\n",
    "- #### <font color='blue'>Evaluate the model using 10-fold stratified cross-validation</font>\n",
    "- #### <font color='blue'>Can you tell whether using feature-selection is beneficial or not? </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classifiers comparison\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>KNN</th>\n",
       "      <th>Fsel-KNN</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.927778</td>\n",
       "      <td>0.866667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.983333</td>\n",
       "      <td>0.944444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.977778</td>\n",
       "      <td>0.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.955556</td>\n",
       "      <td>0.855556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.972222</td>\n",
       "      <td>0.938889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.972222</td>\n",
       "      <td>0.966667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.988889</td>\n",
       "      <td>0.944444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.983240</td>\n",
       "      <td>0.955307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.983240</td>\n",
       "      <td>0.893855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.966480</td>\n",
       "      <td>0.927374</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        KNN  Fsel-KNN\n",
       "0  0.927778  0.866667\n",
       "1  0.983333  0.944444\n",
       "2  0.977778  0.900000\n",
       "3  0.955556  0.855556\n",
       "4  0.972222  0.938889\n",
       "5  0.972222  0.966667\n",
       "6  0.988889  0.944444\n",
       "7  0.983240  0.955307\n",
       "8  0.983240  0.893855\n",
       "9  0.966480  0.927374"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let \"results\" and \"results_fsel\" the output of cross-validate from the previous exercise\n",
    "metrics = pd.DataFrame({'KNN':results['test_score'],'Fsel-KNN': results_fsel['test_score']})\n",
    "metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:title={'center':'KNN'}>,\n",
       "        <AxesSubplot:title={'center':'Fsel-KNN'}>, <AxesSubplot:>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "metrics.hist(layout = (1,3),figsize = (10,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "metrics.boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Statistical tests\n",
    "- [t-test for paired samples](https://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples) ([scipy ref](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_rel.html))\n",
    "- [Wilcoxon signed-rank test](https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test) ([scipy ref](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wilcoxon.html))\n",
    "    - serves the same purpose of student *t*-test for matched samples, but does not assume that the data is normally distributed\n",
    "    - tests the **null hypothesis** that **two related paired samples come from the same distribution**.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=0.0, pvalue=0.001953125)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import wilcoxon\n",
    "wilcoxon(metrics.KNN,metrics['Fsel-KNN'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***p*-value** is the probability of obtaining a value of the W statistic equal to or lower than the one actually observed, under the assumption that the null hypothesis is correct.\n",
    "\n",
    "A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.\n",
    "\n",
    "In other words, given a confidence level $\\alpha$ (typically 0.05), we can conclude that:\n",
    "\n",
    "- if ***p*-value $ \\leq \\alpha$**, I reject the null hypothesis (with a confidence level of $\\alpha$): result is said to be statistically significant. \n",
    "- if ***p*-value $ > \\alpha$**, I cannot reject the null hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reject the null hypothesis at a confidence level of 5%, concluding that there is a difference in accuracy between the classifiers"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}