Convexifying the Bethe Free Energy

Ofer Meshi, Ariel Jaimovich, Amir Globerson, Nir Friedman
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:410-418, 2009.

Abstract

The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-meshi09a, title = {Convexifying the Bethe Free Energy}, author = {Meshi, Ofer and Jaimovich, Ariel and Globerson, Amir and Friedman, Nir}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {410--418}, 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/meshi09a/meshi09a.pdf}, url = {https://proceedings.mlr.press/r7/meshi09a.html}, abstract = {The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Convexifying the Bethe Free Energy %A Ofer Meshi %A Ariel Jaimovich %A Amir Globerson %A Nir Friedman %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-meshi09a %I PMLR %P 410--418 %U https://proceedings.mlr.press/r7/meshi09a.html %V R7 %X The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations. %Z Reissued by PMLR on 04 October 2026.
APA
Meshi, O., Jaimovich, A., Globerson, A. & Friedman, N.. (2009). Convexifying the Bethe Free Energy. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:410-418 Available from https://proceedings.mlr.press/r7/meshi09a.html. Reissued by PMLR on 04 October 2026.

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