\begin{frame}
	\myheading{Module 17.7: Independencies encoded by a Bayesian network  (Case 2: Node and its non-parents)}
\end{frame}

\begin{frame}
	\begin{columns}
		\column{0.5\textwidth}
		\begin{overlayarea}{\textwidth}{\textheight}
			\vspace{0.2in}
			\begin{center}
				\input{modules/Module6/tikz_images/deep_thin_net.tex}
			\end{center}
			
		\end{overlayarea}
		\column{0.5\textwidth}
		\begin{overlayarea}{\textwidth}{\textheight}
			\vspace{0.2in}
			\begin{itemize}\justifying
				\onslide<1->{\item Now let's look at the relation between a node and its non-parent nodes}
				%\vspace{0.1in}
				\onslide<2->{\item Is $L \perp S$?}
				%\vspace{0.1in}
				\onslide<3->{\item No, knowing the SAT score tells us about $I$ which in turn tells us something about $G$ and hence $L$}
				\vspace{0.1in}
				\onslide<4->{\item Hence we expect $P(I^1|s^1)>P(I^1|s^0)$}
				%\vspace{0.1in}
				\onslide<5->{\item Similarly we can argue $L\not\perp D$ and $L\not\perp I$}
			\end{itemize}
		\end{overlayarea}
	\end{columns}
\end{frame}

\begin{frame}
	\begin{columns}
		\column{0.5\textwidth}
		\begin{overlayarea}{\textwidth}{\textheight}
			\vspace{0.2in}
			\begin{center}
				\input{modules/Module6/tikz_images/deep_thin_net.tex}
			\end{center}
			
		\end{overlayarea}
		\column{0.5\textwidth}
		\begin{overlayarea}{\textwidth}{\textheight}
			\vspace{0.2in}
			\begin{itemize}\justifying
				\onslide<1->{\item But what if we know the value of $G$?}
				%\vspace{0.1in}
				\onslide<2->{\item Is $(L\perp S)|G$?}
				%\vspace{0.1in}
				\onslide<3->{\item Yes, the grade completely determines the recommendation letter}
				%\vspace{0.1in}
				\onslide<4->{\item Once we know the grade, other variables do not add any information}
				%\vspace{0.1in}
                \onslide<5->{\item Hence $(L \perp S)|G$}
				\vspace{0.1in}
                \onslide<6->{\item Similarly we can argue $(L\perp I)|G$ and $(L\perp D)|G$}
			\end{itemize}
		\end{overlayarea}
	\end{columns}
\end{frame}

\begin{frame}
        \begin{columns}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        \vspace{0.2in}
                        \begin{center}
                        	\input{modules/Module6/tikz_images/deep_thin_net.tex}
                        \end{center}

                \end{overlayarea}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        \vspace{0.2in}
                        \begin{itemize}\justifying
                                \onslide<1->{\item But, wait a minute!}
                                %\vspace{0.1in}
                                \onslide<2->{\item The instructor may also want to look at the SAT score in addition to the grade}
                                %\vspace{0.1in}
                                \onslide<3->{\item Well, we ``assumed" that the instructor only relies on the grade.}
                                %\vspace{0.1in}
                                \onslide<4->{\item That was our ``belief" of how the world works}
                                %\vspace{0.1in}
                                \onslide<5->{\item And hence we drew the network accordingly}
                        \end{itemize}
                \end{overlayarea}
        \end{columns}
\end{frame}
\begin{frame}
        \begin{columns}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        \only<1-3>{\vspace{0.2in}
                        	\input{modules/Module6/tikz_images/deep_thin_net.tex}}
%                        \includegraphics[scale=0.5]{images/module7/mod7_1.jpg}
						 \onslide<4->{\input{modules/Module7/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 Of course we are free to change our assumptions}
                                \vspace{0.1in}
                                \onslide<2->{\item We may want to assume that the instructor also looks at the SAT score}
                                %\vspace{0.1in}
                                \onslide<3->{\item But if that is the case we have to change the network to reflect this dependence}
                                %\vspace{0.1in}
                                \onslide<4->{\item Why just SAT score? The instructor may even consult one of his colleagues and seek his/her opinion}
                        \end{itemize}
                \end{overlayarea}
        \end{columns}
\end{frame}
\begin{frame}
        \begin{columns}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        \input{modules/Module7/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 Remember: The graph is a reflection of our assumptions about how the world works}
                                \vspace{0.1in}
                                \onslide<2->{\item One assumptions about dependencies are encoded in the graph}
                                \vspace{0.1in}
                                \onslide<3->{\item Once we build the graph we freeze it and do all reasoning and analysis (independence) on this graph}
                                \vspace{0.1in}
                                \onslide<4->{\item It is not fair to ask ``what if" questions involving other factors (for example, what if the professor was in a bad mood?)}
                        \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=0.4]{images/module7/mod7_2.jpg}
						 \input{modules/Module7/tikz_images/deep_thin_net.tex}
                \end{overlayarea}
                \column{0.5\textwidth}
                \begin{overlayarea}{\textwidth}{\textheight}
                        \vspace{0.7in}
                        \begin{itemize}
                                \onslide<1->{\item If we believe Graph (a) is how the world works then $ L\perp (S|G)$}
                                \vspace{0.1in}
                                \onslide<2->{\item If we believe Graph(b) is how the world works then $ L\not\perp (S|G)$}
                                \vspace{0.1in}
                                \onslide<3->{\item We will stick to Graph(a) for the discussion}
                        \end{itemize}
                \end{overlayarea}
        \end{columns}
\end{frame}
\begin{frame}
        %\begin{overlayarea}{\textwidth}{\textheight}
                \begin{block}{}
                        \begin{itemize}
                                \onslide<1->{\item Let's return back to our discussion of finding independence relations in the graph}
                                \onslide<2->{\item So far we have seen three cases as summarized in the next module}
                        \end{itemize}
                \end{block}
        %\end{overlayarea}
\end{frame}

