Case-Factor Diagrams for Structured Probabilistic Modeling
This work provides a unified framework for structured probabilistic modeling, potentially benefiting researchers in machine learning and natural language processing, though it appears incremental as it builds on existing diagrammatic representations like BDDs.
The paper introduces case-factor diagrams (CFDs), a probabilistic formalism that generalizes Markov random fields of bounded tree width and probabilistic context-free grammars, enabling efficient marginal and Viterbi computations in time proportional to the CFD size.
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 undera given context free grammar (also unlike BDDs). A probabilistic model consists of aCFD defining a feasible set of Boolean assignments and a weight (or cost) for each individual Boolean variable. We give an insideoutside 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.