Convergent message-passing algorithms for inference over general graphs with convex free energies

Tamir Hazan, Amnon Shashua
Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, PMLR R6:264-273, 2008.

Abstract

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixed-points of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases of interest. Moreover, the Bethe free energy is non-convex for graphical models with cycles thus introducing great difficulty in deriving efficient algorithms for finding local minima of the free energy for general graphs. In this paper we introduce two efficient BP-like algorithms, one sequential and the other parallel, that are guaranteed to converge to the global minimum, for any graph, over the class of energies known as "convex free energies". In addition, we propose an efficient heuristic for setting the parameters of the convex free energy based on the structure of the graph.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR6-hazan08a, title = {Convergent message-passing algorithms for inference over general graphs with convex free energies}, author = {Hazan, Tamir and Shashua, Amnon}, booktitle = {Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence}, pages = {264--273}, year = {2008}, editor = {McAllester, David A. and Myllymäki, Petri}, volume = {R6}, series = {Proceedings of Machine Learning Research}, month = {09--12 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r6/main/assets/hazan08a/hazan08a.pdf}, url = {https://proceedings.mlr.press/r6/hazan08a.html}, abstract = {Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixed-points of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases of interest. Moreover, the Bethe free energy is non-convex for graphical models with cycles thus introducing great difficulty in deriving efficient algorithms for finding local minima of the free energy for general graphs. In this paper we introduce two efficient BP-like algorithms, one sequential and the other parallel, that are guaranteed to converge to the global minimum, for any graph, over the class of energies known as "convex free energies". In addition, we propose an efficient heuristic for setting the parameters of the convex free energy based on the structure of the graph.}, note = {Reissued by PMLR on 09 October 2024.} }
Endnote
%0 Conference Paper %T Convergent message-passing algorithms for inference over general graphs with convex free energies %A Tamir Hazan %A Amnon Shashua %B Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2008 %E David A. McAllester %E Petri Myllymäki %F pmlr-vR6-hazan08a %I PMLR %P 264--273 %U https://proceedings.mlr.press/r6/hazan08a.html %V R6 %X Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixed-points of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases of interest. Moreover, the Bethe free energy is non-convex for graphical models with cycles thus introducing great difficulty in deriving efficient algorithms for finding local minima of the free energy for general graphs. In this paper we introduce two efficient BP-like algorithms, one sequential and the other parallel, that are guaranteed to converge to the global minimum, for any graph, over the class of energies known as "convex free energies". In addition, we propose an efficient heuristic for setting the parameters of the convex free energy based on the structure of the graph. %Z Reissued by PMLR on 09 October 2024.
APA
Hazan, T. & Shashua, A.. (2008). Convergent message-passing algorithms for inference over general graphs with convex free energies. Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R6:264-273 Available from https://proceedings.mlr.press/r6/hazan08a.html. Reissued by PMLR on 09 October 2024.

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