Counting Belief Propagation

Kristian Kersting, Babak Ahmadi, Sriraam Natarajan
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:277-284, 2009.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-kersting09a, title = {Counting Belief Propagation}, author = {Kersting, Kristian and Ahmadi, Babak and Natarajan, Sriraam}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {277--284}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/kersting09a/kersting09a.pdf}, url = {https://proceedings.mlr.press/r7/kersting09a.html}, abstract = {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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Counting Belief Propagation %A Kristian Kersting %A Babak Ahmadi %A Sriraam Natarajan %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-kersting09a %I PMLR %P 277--284 %U https://proceedings.mlr.press/r7/kersting09a.html %V R7 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Kersting, K., Ahmadi, B. & Natarajan, S.. (2009). Counting Belief Propagation. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:277-284 Available from https://proceedings.mlr.press/r7/kersting09a.html. Reissued by PMLR on 04 October 2026.

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