\begin{frame}
	\myheading{Module 17.8: Independencies encoded by a Bayesian network (Case 3: Node and its descendants)}
\end{frame}

\begin{frame}
	\begin{columns}
		\column{0.5\textwidth}
		\begin{overlayarea}{\textwidth}{\textheight}
%			\vspace{0.8in}
%			\includegraphics[scale=0.45]{images/module8/mod8_1.jpg}
			\input{modules/Module8/tikz_images/deep_wide_net.tex}
		\end{overlayarea}
		\column{0.5\textwidth}
		\begin{overlayarea}{\textwidth}{\textheight}
			\vspace{0.2in}
			\begin{itemize}\justifying
		  	\onslide<1->{\item $(G\not\perp D)$ $(G\not\perp I)$ $(S\not\perp I)$ $(L\not\perp G)$\\ A node is not independent of its parents}
				%\vspace{0.1in}
				\onslide<2->{\item $(G\not\perp D, I)|S,L$\\$(S\not\perp I)|D,G,L$\\ $(L\not\perp G)|D,I,S$\\ A node is not independent of its parents even when other variables are given}
				%\vspace{0.1in}
				\onslide<3->{\item $(S\perp G)|I$?\\ $(L\perp D,I,S)|G$?\\ $(G\perp L)|D,I$?\\ A node \textbf{seems to be} independent of other variables given its parents}
			\end{itemize}
		\end{overlayarea}
	\end{columns}
\end{frame}
\begin{frame}
        \begin{columns}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        \input{modules/Module8/tikz_images/deep_wide_net.tex}

                \end{overlayarea}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        \vspace{0.2in}
                        \begin{itemize}\justifying
                                \onslide<1->{\item Let us inspect this last rule}
                                \vspace{0.1in}
                                \onslide<2->{\item Is $(G\perp L)|D,I$?}
                                \vspace{0.1in}
                                \onslide<3->{\item If you know that $d=0$ and $i=1$ then you would expect the student to get a good grade}
				\vspace{0.1in}
                                \onslide<4->{\item But now if someone tells you that the student got a poor letter, your belief will change}
                                \vspace{0.1in}
                                \onslide<5->{\item So $(G\not\perp L)|D,I$}
				\vspace{0.1in}
                                \onslide<6->{\item The effect (letter) actually gives us information about the cause (grade)}
                        \end{itemize}
                \end{overlayarea}
        \end{columns}
\end{frame}
\begin{frame}
        \begin{columns}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
%                        \vspace{0.2in}
%                        \includegraphics[scale=0.45]{images/module8/mod8_1.jpg}
			 			 \input{modules/Module8/tikz_images/deep_wide_net.tex}
                \end{overlayarea}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        %\vspace{0.2in}
                        \begin{itemize}\justifying
                        	\onslide<1->{\item $(G\not\perp D)$ $(G\not\perp I)$ $(S\not\perp I)$ $(L\not\perp G)$\\ A node is not independent of its parents}
                        	%\vspace{0.1in}
                        	\onslide<2->{\item $(G\not\perp D, I)|S,L$\\$(S\not\perp I)|D,G,L$\\ $(L\not\perp G)|D,I,S$\\ A node is not independent of its parents even when other variables are given}
                            \onslide<3->{\item $(S\perp G)|I$\\ $(L\perp D,I,S)|G$\\ $(G\not\perp L)|D,I$\\ Given its parents, a node is independent of all variables \underline{except its descendants}}
                        \end{itemize}
                \end{overlayarea}
        \end{columns}
\end{frame}

