Departmental Papers (CIS)

Document Type

Conference Paper

Date of this Version

July 2004

Comments

Postprint version. Copyright ACM, 2004. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 20th Conference on Uncertainty in Artifical Intelligence 2004, pages 382-391.
Publisher URL: http://portal.acm.org/dl.cfm

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 concise for circuits of bounded tree width (unlike BDDs) and can concisely represent the set of parse trees over a given string under a given context free grammar (also 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 mininum cost variable assignment. Both algorithms run in time proportional to the size of the CFD.

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Date Posted: 10 September 2005