# 1 supply an elimination ordering that yields a

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1. Supply an elimination ordering that yields a triangulated graph with no more than 3 nodes per clique. 2. Supply an elimination ordering that yields a triangulated graph with four nodes in one or more cliques. 3. Draw junction trees based on both the triangulated graphs above. 3.2 [3 pts] Consider a circular graph with 8 nodes. 1. Draw the triangulation that results from eliminating the nodes in a sequence around the circle. 2. Draw the triangulation that results from eliminating every other node in a sequence around the circle (i . e . , with the nodes numbered in the natural order, use the elimina- tion ordering 1,3,5,7,2,4,6,8) 3. Consider an arbitrary circular graph. Using variable elimination, is it ever possible to obtain a clique with more than 3 nodes? Why or why not? 4 [14 pts] Clique sizes in Clique Trees Assume that we have constructed a clique tree T for a given Bayesian network graph G , and that each of the cliques in T contains at most k nodes. Now, the user decides to add a single edge to the Bayesian network, resulting in a network G prime . (The edge can be added between any pair of nodes in the network, so long as it maintains acyclicity.) What is the tightest bound you can provide on the maximum clique size in a clique tree T prime for G prime ? Justify 2

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your response by explaining how to construct such a clique tree.(Note: You do not need to provide the optimal clique tree T prime . The question asks for the tightest clique tree that you
• Fall '07
• CarlosGustin
• Maximum likelihood, Likelihood function, Belief propagation, Chordal graph, tree decomposition

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