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The Bethe approximation is a well-known approximation of the partitionfunction used in statistical physics. Recently, an equality relating thepartition function and its Bethe approximation was obtained for graphicalmodels with binary variables by Chertkov and Chernyak. In this equality, themultiplicative error in the Bethe approximation is represented as a weightedsum over all generalized loops in the graphical model. In this paper, theequality is generalized to graphical models with non-binary alphabet usingconcepts from information geometry.

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