# Cluster Variation Method: from statistical mechanics to message passing algorithms

The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising-like) models in equilibrium statistical mechanics, improving on the mean-field approximation and the Bethe--Peierls approximation, which can be regarded as the lowest level of the CVM. The foundations of the CVM are briefly reviewed, considering different derivations of the method and related techniques, like for instance TAP equations and the cavity method. Issues of realizability and exactness are also addressed.

*Author: Alessandro Pelizzola, Politecnico Di Torino*