2009/03/26 by Yusuke Watanabe, Kenji Fukumizu, Watanabe, Yusuke +1
Computer Science · #Bayesian Modeling and Causal Inference #Constraint Satisfaction and Optimization #Data Management and Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Machine Learning (cs.LG) #cs.DM #cs.LG
paper · pdf · doi:10.48550/arxiv.0903.4527
7 pages. The 9th conference of Japanese Society for Artificial Intelligence, Special Interest Group on Data Mining and Statistical Mathematics (JSAI SIG-DMSM) in Kyoto 2009, March 3,4 Minor typos corrected
openalex publication_date 2009/03/26 · arxiv created 2009/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.