post-meeting changes in risk minimization and new latexmath definitio…

…n of \Pxy

latex-math/basic-ml.tex

@@ -5,7 +5,7 @@
 \newcommand{\nset}{\{1, \ldots, n\}} % set from 1 to n
 \newcommand{\pset}{\{1, \ldots, p\}} % set from 1 to p
 \newcommand{\gset}{\{1, \ldots, g\}} % set from 1 to g
-\newcommand{\Pxy}{\mathbb{P}_{xy}} % P_xy
+\newcommand{\Pxy}{P_{xy}} % P_xy
 \newcommand{\Exy}{\mathbb{E}_{xy}} % E_xy: Expectation over random variables xy
 \newcommand{\xv}{\mathbf{x}} % vector x (bold)
 \newcommand{\xtil}{\tilde{\mathbf{x}}} % vector x-tilde (bold)

slides/advriskmin/slides-advriskmin-risk-minimizer.tex

@@ -89,26 +89,26 @@
 \begin{vbframe}{Optimal Constant Model}
 
 \begin{itemize}
+{\footnotesize
 \item We would like a loss optimal, constant baseline predictor
 \item A "featureless" ML model, which always predicts the same value
 \item Can use it as baseline in experiments, if we don't beat this
 with more complex model, that model is useless
 \item Will also be useful as component in algorithms and derivations
+}
 \end{itemize}
 
 %By restricting $\Hspace$ to constant functions $f_c$ independent of $\xv$, the constant model minimizing the theoretical risk 
 
 
 $$f_{c}^{\ast} = \argmin_{c \in \mathbb{R}} \E_{xy} \left[L(y,c)\right] = \argmin_{c \in \mathbb{R}} \E_{y} \left[L(y,c)\right]$$
 
-and 
-
-$\fx = \theta = c$ that optimizes the empirical risk $\risket$ is denoted as as $\hat{f}_c = \argmin_{c \in \mathbb{R}} \risket$.
+{\footnotesize and $\fx = \theta = c$ that optimizes the empirical risk $\risket$ is denoted as as $\hat{f}_c = \argmin_{c \in \mathbb{R}} \risket$.}
 
-\vspace*{-0.5cm}
+\vspace*{-0.2cm}
 
 \begin{center}
-	\includegraphics[width = 0.2\textwidth]{figure/l1_vs_l2.png}
+	\includegraphics[width = 0.38\textwidth]{figure/l1_vs_l2.png}
 \end{center}
 \end{vbframe}