Tightening Fractional Covering Upper Bounds on the Partition Function for High-Order Region Graphs

Tamir Hazan, Jian Peng, Amnon Shashua
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:354-364, 2012.

Abstract

In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general region graphs we utilize the entropy barrier method, thus decomposing the original programs by their dual programs and solve them with dual block optimization scheme. The entropy barrier method provides an elegant framework to generalize the message-passing scheme to high-order region graph, as well as to solve the block dual steps in closed-form. This is a key for computational relevancy for large problems with thousands of regions.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-hazan12a, title = {Tightening Fractional Covering Upper Bounds on the Partition Function for High-Order Region Graphs}, author = {Hazan, Tamir and Peng, Jian and Shashua, Amnon}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {354--364}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/hazan12a/hazan12a.pdf}, url = {https://proceedings.mlr.press/r10/hazan12a.html}, abstract = {In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general region graphs we utilize the entropy barrier method, thus decomposing the original programs by their dual programs and solve them with dual block optimization scheme. The entropy barrier method provides an elegant framework to generalize the message-passing scheme to high-order region graph, as well as to solve the block dual steps in closed-form. This is a key for computational relevancy for large problems with thousands of regions.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Tightening Fractional Covering Upper Bounds on the Partition Function for High-Order Region Graphs %A Tamir Hazan %A Jian Peng %A Amnon Shashua %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-hazan12a %I PMLR %P 354--364 %U https://proceedings.mlr.press/r10/hazan12a.html %V R10 %X In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general region graphs we utilize the entropy barrier method, thus decomposing the original programs by their dual programs and solve them with dual block optimization scheme. The entropy barrier method provides an elegant framework to generalize the message-passing scheme to high-order region graph, as well as to solve the block dual steps in closed-form. This is a key for computational relevancy for large problems with thousands of regions. %Z Reissued by PMLR on 04 October 2026.
APA
Hazan, T., Peng, J. & Shashua, A.. (2012). Tightening Fractional Covering Upper Bounds on the Partition Function for High-Order Region Graphs. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:354-364 Available from https://proceedings.mlr.press/r10/hazan12a.html. Reissued by PMLR on 04 October 2026.

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