Counting Belief Propagation
Kristian Kersting, Babak Ahmadi, Sriraam Natarajan
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.
PDF Link: /papers/09/p277-kersting.pdf
AUTHOR = "Kristian Kersting
and Babak Ahmadi and Sriraam Natarajan",
TITLE = "Counting Belief Propagation",
BOOKTITLE = "Proceedings of the Twenty-Fifth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-09)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2009",
PAGES = "277--284"