Gauge-free cluster variational method by maximal messages and moment matching

Physical Review. E
Eduardo DomínguezFederico Ricci-Tersenghi

Abstract

We present an implementation of the cluster variational method (CVM) as a message passing algorithm. The kind of message passing algorithm used for CVM, usually named generalized belief propagation (GBP), is a generalization of the belief propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the partition function. However, the connection between fixed points of GBP and the extremal points of the CVM free energy is usually not a one-to-one correspondence because of the existence of a gauge transformation involving the GBP messages. Our contribution is twofold. First, we propose a way of defining messages (fields) in a generic CVM approximation, such that messages arrive on a given region from all its ancestors, and not only from its direct parents, as in the standard parent-to-child GBP. We call this approach maximal messages. Second, we focus on the case of binary variables, reinterpreting the messages as fields enforcing the consistency between the moments of the local (marginal) probability distributions. We provide a precise rule to enforce all consistencies, avoiding any redundancy, that would otherwise lead to a gauge transformation on the messages. This moment matchi...Continue Reading

References

Aug 1, 1985·Physical Review. B, Condensed Matter·M N BarberJ L Richardson
Aug 1, 1996·Physical Review. B, Condensed Matter·G Parisi, J J Ruiz-Lorenzo
Jun 23, 2005·Neural Computation·Payam Pakzad, Venkat Anantharam
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alejandro Lage-CastellanosTommaso Rizzo
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Muneki YasudaKazuyuki Tanaka

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Citations

Aug 7, 2019·Physical Review Letters·Alfredo BraunsteinLuca Dall'Asta

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