Abstract

We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call case-factor diagrams (CFDs). CFDs are similar to binary decision diagrams (BDDs) but are more concise than BDDs for circuits of bounded tree width and can concisely represent the set of parse trees over a given string under a given context free grammar (unlike BDDs). A probabilistic model consists of a CFD defining a feasible set of Boolean assignments and a weight (or cost) for each individual Boolean variable. We give an inside-outside algorithm for simultaneously computing the marginal of each Boolean variable, and a Viterbi algorithm for finding the minimum cost variable assignment. Both algorithms run in time proportional to the size of the CFD. 1 1

Citations