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	\myheading{Independencies encoded by a Bayesian network (Case 3: Node and its descendants)}
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			\input{modules/Module8/tikz_images/deep_wide_net.tex}
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			\begin{itemize}
		  	\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}
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				\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}
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				\onslide<3->{\item $S\perp (G|I)$ $L\perp(D,I,S|G)$ $G\perp(L|D,I)$? A node seems to be independent of other variables given its parents}
			\end{itemize}
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                        \vspace{0.2in}

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                        \begin{itemize}
                                \onslide<1->{\item Let us inspect this last question}
                                \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.}
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                                \onslide<4->{\item But now if someone tells you that the student got a poor letter, your belief will change}
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                                \onslide<5->{\item So $G\not\perp(L|D),I$}
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                                \onslide<6->{\item The effect (letter) actually gives us information about the cause (grade)}
                        \end{itemize}
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\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}
                        \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 $S\perp (G|I)$ $L\perp(D,I,S|G)$ $G\perp(L|D,I)$? Given its parents, a node is independent of all variables \underline{except its descendants}}
                        \end{itemize}
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        \end{columns}
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