Approximate inference on planar graphs using loop calculus and belief propagation

Vicenç Gómez, Hilbert J. Kappen, Michael Chertkov

Research output: Contribution to conferencePaperpeer-review

1 Citation (Scopus)

Abstract

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006b) allows to express the exact partition function Z of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze in detail both the loop series and the Pfaffian series for models with binary variables and pairwise interactions, and show that the first term of the Pfaffian series can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.

Original languageEnglish
Pages195-202
Number of pages8
Publication statusPublished - 2009
Externally publishedYes
Event25th Conference on Uncertainty in Artificial Intelligence, UAI 2009 - Montreal, QC, Canada
Duration: 18 Jun 200921 Jun 2009

Conference

Conference25th Conference on Uncertainty in Artificial Intelligence, UAI 2009
Country/TerritoryCanada
CityMontreal, QC
Period18/06/0921/06/09

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