Graph polynomials and approximation of partition functions with Loopy Belief Propagation

Details Graph polynomials and approximation of partition functions with Loopy Belief Propagation Graph polynomials and approximation of partition functions with Loopy Belief Propagation

2009-03-26

arxiv.org/abs/0903.4527v2

Computer Science

Discrete Mathematics

7 pages. The 9th conference of Japanese Society for Artificial Intelligence, Special Interest Group on Data Mining and Statist

Scientific paper

The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. 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 labeled by subgraphs called generalized loops. In our recent paper, we derive the loop series expansion in form of a polynomial with coefficients positive integers, and extend the result to the expansion of marginals. In this paper, we give more clear derivation for the results and discuss the properties of the polynomial which is introduced in the paper.

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