Alessandro Pelizzola 2005 J. Phys. A: Math. Gen. 38 R309 doi:10.1088/0305-4470/38/33/R01
Alessandro Pelizzola
Show affiliationsThe 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. 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 message-passing algorithms are discussed.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.10.-a Computational methods in statistical physics and nonlinear dynamics
02.50.-r Probability theory, stochastic processes, and statistics
62H30 Classification and discrimination; cluster analysis (See also 68T10)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 33 (19 August 2005)
Received 16 May 2005, in final form 12 July 2005
Published 3 August 2005
Alessandro Pelizzola 2005 J. Phys. A: Math. Gen. 38 R309
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