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Loop series expansion with propagation diagrams
| Venue: | J. Phy. A: Math. and Theor |
| Citations: | 4 - 2 self |
BibTeX
@ARTICLE{Watanabe_loopseries,
author = {Yusuke Watanabe and Kenji Fukumizu},
title = {Loop series expansion with propagation diagrams},
journal = {J. Phy. A: Math. and Theor},
year = {},
pages = {2009}
}
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Abstract
Abstract. The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called “Loop Series Expansion”, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labelled by subgraphs called generalized loops. In this paper, we derive a loop series expansion of binary pairwise Markov random fields with “propagation diagrams”, which describe rules how “first messages ” and “secondary messages ” propagate. The advantage of our approach is that the loop series expansion formula is given in the form of a polynomial with coefficients positive integers. Using the propagation diagrams, we establish a new formula that shows a relation between the exact marginal probabilities and their Bethe approximations. PACS numbers: 05.50.+q,02.10.Ox
Keyphrases
loop series expansion propagation diagram bethe approximation partition function binary pairwise markov random field successful method secondary message main term exact marginal probability new formula pac number first message probabilistic model loop series expansion formula interesting formula generalized loop coefficient positive integer
