Tightening fractional covering upper bounds on the partition function for high-order region graphs

Tamir Hazan, Jian Peng, Amnon Shashua

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationUncertainty in Artificial Intelligence - Proceedings of the 28th Conference, UAI 2012
Pages356-366
Number of pages11
StatePublished - Dec 1 2012
Externally publishedYes
Event28th Conference on Uncertainty in Artificial Intelligence, UAI 2012 - Catalina Island, CA, United States
Duration: Aug 15 2012Aug 17 2012

Publication series

NameUncertainty in Artificial Intelligence - Proceedings of the 28th Conference, UAI 2012

Other

Other28th Conference on Uncertainty in Artificial Intelligence, UAI 2012
CountryUnited States
CityCatalina Island, CA
Period8/15/128/17/12

ASJC Scopus subject areas

  • Artificial Intelligence

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    Hazan, T., Peng, J., & Shashua, A. (2012). Tightening fractional covering upper bounds on the partition function for high-order region graphs. In Uncertainty in Artificial Intelligence - Proceedings of the 28th Conference, UAI 2012 (pp. 356-366). (Uncertainty in Artificial Intelligence - Proceedings of the 28th Conference, UAI 2012).