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Journal of Statistical Mechanics: Theory and Experiment

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Journal of Statistical Mechanics: Theory and Experiment Volume 2012 August 2012

Federico Ricci-Tersenghi J. Stat. Mech. (2012) P08015 doi:10.1088/1742-5468/2012/08/P08015

The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods

Federico Ricci-Tersenghi

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Abstract References Cited By

Paper

The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-field approximations, but which one performs better in the general case is still not completely clear. In the first part of this work, I summarize the formulas for several mean-field approximations and I derive new analytical expressions for the Bethe approximation, which allow one to solve the inverse Ising problem without running the susceptibility propagation algorithm (thus avoiding the lack of convergence). In the second part, I compare the accuracy of different mean-field approximations on several models (diluted ferromagnets and spin glasses) defined on random graphs and regular lattices, showing which one is in general more effective. A simple improvement over these approximations is proposed. Also a fundamental limitation is found in using methods based on TAP and Bethe approximations in the presence of an external field.


Keywords

statistical inference

spin glasses (theory)

PACS

75.10.Hk Classical spin models

75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects

75.50.Lk Spin glasses and other random magnets

02.30.Zz Inverse problems

75.10.Nr Spin-glass and other random models

MSC

05C80 Random graphs

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)

82D30 Random media, disordered materials (including liquid crystals and spin glasses)

Subjects

Mathematical physics

Condensed matter: electrical, magnetic and optical

Dates

Issue 08 (August 2012)

Received 30 March 2012, accepted for publication 6 August 2012

Published 24 August 2012

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  1. The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods

    Federico Ricci-Tersenghi J. Stat. Mech. (2012) P08015

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