Bethe and Related Pairwise Entropy Approximations

Adrian Weller
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:9-18, 2015.

Abstract

For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Focusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation may be generalized to a broad family of related pairwise free energy approximations with arbitrary counting numbers. We explore comparisons to the true (Gibbs) free energy and shed light on the empirical success of the Bethe approximation.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-weller15a, title = {{B}ethe and Related Pairwise Entropy Approximations}, author = {Weller, Adrian}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {9--18}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/weller15a/weller15a.pdf}, url = {https://proceedings.mlr.press/r13/weller15a.html}, abstract = {For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Focusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation may be generalized to a broad family of related pairwise free energy approximations with arbitrary counting numbers. We explore comparisons to the true (Gibbs) free energy and shed light on the empirical success of the Bethe approximation.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Bethe and Related Pairwise Entropy Approximations %A Adrian Weller %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-weller15a %I PMLR %P 9--18 %U https://proceedings.mlr.press/r13/weller15a.html %V R13 %X For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Focusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation may be generalized to a broad family of related pairwise free energy approximations with arbitrary counting numbers. We explore comparisons to the true (Gibbs) free energy and shed light on the empirical success of the Bethe approximation. %Z Reissued by PMLR on 04 October 2026.
APA
Weller, A.. (2015). Bethe and Related Pairwise Entropy Approximations. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:9-18 Available from https://proceedings.mlr.press/r13/weller15a.html. Reissued by PMLR on 04 October 2026.

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