# 1 how likely is the ta to take over the world if he

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1. How likely is the TA to take over the world, if he manages to graduate? P ( WD = T | G = T ) = ? 1

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2. P ( WD = T | FF = T ) = ? 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
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.

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1 How likely is the TA to take over the world if he manages...

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