On mean-field approximations for estimating correlations and solving the inverse Ising problem

Details On mean-field approximations for estimating correlations and solving the inverse Ising problem On mean-field approximations for estimating correlations and solving the inverse Ising problem

2011-12-20

arxiv.org/abs/1112.4814v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

18 pages, 6 figures

Scientific paper

I consider mean-field approximations for solving two fundamental problems in Ising models, namely estimating 2-point correlations given the couplings (direct problem) and estimating the couplings given the correlations and the magnetizations (inverse problem). I derive analytical expressions for the Bethe approximation, which allow to solve the problems without running the Susceptibility Propagation algorithm. I compare the accuracy of 5 different mean field approximations on several models (diluted ferromagnets and spin glasses) on random graphs and regular lattices. A simple improvement over these approximations is proposed.

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