Loop Calculus and Belief Propagation for q-ary Alphabet: Loop Tower

2007/01/12 by Vladimir Chernyak, Vladimir Y. Chernyak, Michael Chertkov +2
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Modeling and Causal Inference #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.cs/0701086

5 pages, 2 figures, proceedings of ISIT '07, misprints corrected

openalex publication_date 2007/01/12 · arxiv created 2008/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Loop Calculus introduced in [Chertkov, Chernyak '06] constitutes a new theoretical tool that explicitly expresses the symbol Maximum-A-Posteriori (MAP) solution of a general statistical inference problem via a solution of the Belief Propagation (BP) equations. This finding brought a new significance to the BP concept, which in the past was thought of as just a loop-free approximation. In this paper we continue a discussion of the Loop Calculus. We introduce an invariant formulation which allows to generalize the Loop Calculus approach to a q-are alphabet.

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