# 3 should we even be worried about him graduating p g

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3. Should we even be worried about him graduating? P ( G = T ) = ? 4. P ( M = T | K = T ) = ? Additionally, report the ordering used and the factors produced after eliminating each vari- able for the first query [ P ( WD = T | G = T )]. Figure 1: World Domination network 2 Triangulation 1. Moralize the Bayes net in figure 2. 2. Supply a perfect elimination ordering ( i.e. , one that yields no fill edges). 3. Supply an elimination ordering that yields a triangulated graph with at least 5 nodes in one or more cliques 4. Draw clique trees for the elimination orderings in parts 2 and 3. 2

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Figure 2: Bayes net for question 2 3 Variable Elimination in Clique Trees Consider a chain graphical model with the structure X 1 - X 2 - · · · - X n , where each X i takes on one of d possible assignments. You can form the following clique tree for this GM: C 1 - C 2 - · · · - C n - 1 , where Scope [ C i ] = { X i , X i + 1 } . You can assume that this clique tree has already been calibrated. Using this clique tree, we can directly obtain P ( X i , X i + 1). As promised in class, your goal in this question is to compute P ( X i , X j ), for any j > i . 1. Briefly, describe how variable elimination can be used to compute P ( X i , X j ), for some j > i , in linear time, given the calibrated clique tree. 2. What is the running time of the algorithm in part 3.1 if you wanted to compute P ( X i , X j ) for all n choose 2 choices of i and j ? 3. Consider a particular chain X 1 - X 2 - X 3 - X 4 . Show that by caching P ( X 1 , X 3 ), you can compute P ( X 1 , X 4 ) more efficiently than directly applying variable elimination as described in part 3.1.
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