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Counting Belief Propagation

Kristian Kersting; Babak Ahmadi; Sriraam Natarajan
In: Jeff A. Bilmes; Andrew Y. Ng (Hrsg.). UAI 2009, Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence. Conference in Uncertainty in Artificial Intelligence (UAI-2009), June 18-21, Montreal, QC, Canada, Pages 277-284, AUAI Press, 2009.


A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by efficient inference techniques such as belief propagation (BP). In this paper, we present a new and simple BP algorithm, called counting BP, that exploits such additional symmetries. Starting from a given factor graph, counting BP first constructs a compressed factor graph of clusternodes and clusterfactors, corresponding to sets of nodes and factors that are indistinguishable given the evidence. Then it runs a modified BP algorithm on the compressed graph that is equivalent to running BP on the original factor graph. Our experiments show that counting BP is applicable to a variety of important AI tasks such as (dynamic) relational models and boolean model counting, and that significant efficiency gains are obtainable, often by orders of magnitude.

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