Loop Calculus for Non-Binary Alphabets using Concepts from Information Geometry

2013/09/25 by Ryuhei Mori, Mori, Ryuhei · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.1309.6550

18 pages, 4 figures, submitted to IEEE Trans. Inf. Theory

arxiv created 2014/12/19 · arxiv updated 2014/12/22

Abstract

The Bethe approximation is a well-known approximation of the partition function used in statistical physics. Recently, an equality relating the partition function and its Bethe approximation was obtained for graphical models with binary variables by Chertkov and Chernyak. In this equality, the multiplicative error in the Bethe approximation is represented as a weighted sum over all generalized loops in the graphical model. In this paper, the equality is generalized to graphical models with non-binary alphabet using concepts from information geometry.

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