Let be a polytree, and let be its moral graph. Let denote the factor graph associated with , and let denote the graph associated with . For every node in with no parents, add a factor to that is connected to the node . Prove that and are identical, i.e., the factor graph associated with the moral graph of a polytree is the same as the factor graph associated with the polytree, modulo the single-variable factors. (Hint: Use induction. Work through the nodes in a topological order, building , and .)

Haeusler Stefan 2010-01-26