major pdf changes to fix slides_all compilation

slides/advriskmin/chapter-order-slides-all.tex

@@ -0,0 +1,72 @@
+%% needs to be filled!!
+% slides-advriskmin-risk-minimizer
+% slides-advriskmin-pseudo-residuals
+% slides-advriskmin-regression-l2
+% slides-advriskmin-regression-l1
+% slides-advriskmin-regression-further-losses
+% slides-advriskmin-classification-01
+% slides-advriskmin-classification-bernoulli
+% slides-advriskmin-logreg-deepdive
+% slides-advriskmin-classification-brier
+% slides-advriskmin-classification-furtherlosses
+% slides-advriskmin-classification-deepdive
+% slides-advriskmin-max-likelihood-l2
+% slides-advriskmin-max-likelihood-other
+% slides-advriskmin-losses-properties
+% slides-advriskmin-bias-variance-decomposition
+
+%- slides-evaluation-intro
+
+\subsection{Risk Minimizers}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-risk-minimizer.pdf}
+
+\subsection{Pseudo-Residuals}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-pseudo-residuals.pdf}
+
+\subsection{L2- and L1-loss}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-regression-l2-l1.pdf}
+
+\subsection{L1 Risk Minimizer (Deep-Dive)}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-regression-l1-deepdive.pdf}
+
+\subsection{Advanced Regression Losses}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-regression-further-losses.pdf}
+
+\subsection{0-1-loss}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-classification-01.pdf}
+
+\subsection{Bernoulli Loss}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-classification-bernoulli.pdf}
+
+\subsection{Logistic Regression (Deep-Dive)}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-logreg-deepdive.pdf}
+
+%\subsection{Proper Scoring Rules}
+%\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-proper-scoring-rules.pdf}
+
+\subsection{Brier Score}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-classification-brier.pdf}
+
+%\subsection{Tree Splitting and Loss Functions}
+%\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-tree-splitting.pdf}
+
+\subsection{Advanced Classification Losses}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-classification-furtherlosses.pdf}
+
+\subsection{Optimal constant model for the empirical log loss risk}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-classification-deepdive.pdf}
+
+\subsection{Maximum Likelihood Estimization vs. Empirical Risk Minimization I}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-max-likelihood-l2.pdf}
+
+\subsection{Maximum Likelihood Estimization vs. Empirical Risk Minimization II}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-max-likelihood-other.pdf}
+
+\subsection{Loss Properties}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-losses-properties.pdf}
+
+\subsection{Bias Variance Decomposition}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-bias-variance-decomposition.pdf}
+
+\subsection{Bias Variance Decomposition (Deep-Dive)}
+\includepdf[pages=-]{../../slides-pdf/slides-advriskmin-bias-variance-decomposition-deepdive.pdf}

slides/advriskmin/slides-advriskmin-logreg-deepdive.tex

@@ -62,24 +62,25 @@
 
 \vspace*{-0.5cm}
 
+{\small
 \begin{align*}
-  \frac{\partial}{\partial\thetab}\riske  & = & 
+  \frac{\partial}{\partial\thetab}\riske  & =  
  -\sumin \frac{\partial}{\partial\pixit }\yi\log(\pixit)\frac{\partial\pixit}{\partial \thetab} +  \\
- &&  \frac{\partial}{\partial\pixit} (1-\yi)\log(1-\pixit)\frac{\partial\pixit}{\partial \thetab}\\
- & = & 
+ & \qquad \frac{\partial}{\partial\pixit} (1-\yi)\log(1-\pixit)\frac{\partial\pixit}{\partial \thetab}\\
+ & =  
  -\sumin \frac{\yi}{\pixit}\frac{\partial\pixit}{\partial \thetab} -  \frac{1-\yi}{1-\pixit}\frac{\partial\pixit}{\partial \thetab}\\
- &=&  
+ &=  
   -\sumin \left(\frac{\yi}{\pixit} -  \frac{1-\yi}{1-\pixit}\right)\frac{\partial s(\fxit)}{\partial  \fxit}\frac{\partial  \fxit}{\partial\thetab}\\
-  &=&  
+  &=  
   -\sum^n_{i=1} \left(\yi(1-\pixit)  -  (1-\yi)\pixit \right)\left(\xi\right)^\top.\\
 \end{align*}
-
+}
 
 
 \framebreak
 \begin{align*}
   \quad &=& 
-  \sumin \left(\pixit - \yi\right)\left(\xi\right)^\top.\\
+  \sumin \left(\pixit - \yi\right)\left(\xi\right)^\top\\
     \quad &=& 
   \left(\pi(\mathbf{X}\vert\;\thetab) - \mathbf{y}\right)^\top\mathbf{X}\\
 \end{align*}
@@ -96,7 +97,7 @@
 
 \vspace*{1cm}
 
-$\Rightarrow$ The gradient $\nabla_{\thetab}\riske = \left(\frac{\partial}{\partial\thetab}\riske\right)^\top =  \mathbf{X}^\top\left(\pi(\mathbf{X}\vert\;\thetab) - \mathbf{y}\right)$ 
+$\implies$ The gradient $\nabla_{\thetab}\riske = \left(\frac{\partial}{\partial\thetab}\riske\right)^\top =  \mathbf{X}^\top\left(\pi(\mathbf{X}\vert\;\thetab) - \mathbf{y}\right)$ 
 
 \vspace*{1cm}
 
@@ -109,17 +110,19 @@
 
 We find the Hessian via differentiation, s.t.,
 
+{\small
 \begin{align*}
-  \nabla^2_{\thetab}\riske  = \frac{\partial^2}{\partial{\thetab^\top}\partial\thetab}\riske  & = & 
+  \nabla^2_{\thetab}\riske  = \frac{\partial^2}{\partial{\thetab^\top}\partial\thetab}\riske  & =  
  \frac{\partial}{\partial{\thetab^\top}} \sumin \left(\pixit - \yi\right)\left(\xi\right)^\top\\
- & = & 
+ & =  
   \sum^n_{i=1}\xi \left(\pixit\left(1-\pixit\right)\right)\left(\xi\right)^\top\\
-  & = & 
+  & =  
 \mathbf{X}^\top \mathbf{D} \mathbf{X}\\
 \end{align*}
 
 where $\mathbf{D} \in \mathbb{R}^{n\times n}$ is a diagonal matrix with diagonal 
 $$\left(\pixit[1](1-\pixit[1], \dots, \pixit[n](1-\pixit[n]\right).$$
+}
 
 Can now be used in Newton-Raphson and other 2nd order optimizers.
 

slides/all/slides_sl.tex

@@ -75,7 +75,7 @@
 
 % Include tuning lecture slides
 \section{Advanced Risk Minimization}
-\input{../advriskmin/chapter-order.tex}
+\input{../advriskmin/chapter-order-slides-all.tex}
 
 \section{Multiclass Classification}
 \input{../multiclass/chapter-order.tex}

slides/regularization/slides-regu-l1vsl2.tex

@@ -185,7 +185,7 @@
     \item $L1$ penalty is not \textit{strictly} convex. Hence, no unique solution exists if $x_4=x_5$, and sum of coefficients can be arbitrarily allocated to both features while remaining minimizers (no grouping property!):\\
     For any solution $\thetah_{4,lasso},\thetah_{5,lasso}$, equivalent minimizers are given by 
     \vspace{-0.1cm}
-    {\small $$\Tilde{\theta}_{4,lasso}=s\cdot(\thetah_{4,lasso}+\thetah_{5,lasso}) \,\,\text{and}\,\,\Tilde{\theta}_{5,lasso}=(1-s)\cdot(\thetah_{4,lasso}+\thetah_{5,lasso})\,\forall s\in[0,1]$$}
+    {\footnotesize $$\Tilde{\theta}_{4,lasso}=s\cdot(\thetah_{4,lasso}+\thetah_{5,lasso}) \,\,\text{and}\,\,\Tilde{\theta}_{5,lasso}=(1-s)\cdot(\thetah_{4,lasso}+\thetah_{5,lasso})\,\forall s\in[0,1]$$}
 \end{itemize}
 
 \framebreak