TOPICAL REVIEW: Cluster variation method in statistical physics and probabilistic graphical models
Abstract
The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Isinglike) models in equilibrium statistical mechanics, improving on the meanfield approximation and the BethePeierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models. The foundations of the CVM are briefly reviewed, and the relations with similar techniques are discussed. The main properties of the method are considered, with emphasis on its exactness for particular models and on its asymptotic properties. The problem of the minimization of the variational free energy, which arises in the CVM, is also addressed, and recent results about both provably convergent and messagepassing algorithms are discussed.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 2005
 DOI:
 10.1088/03054470/38/33/R01
 arXiv:
 arXiv:condmat/0508216
 Bibcode:
 2005JPhA...38R.309P
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Computer Science  Information Theory
 EPrint:
 36 pages, 17 figures