A mean field method with correlations determined by linear response

Abstract

We introduce a new mean-field approximation based on the reconciliation of maximum entropy and linear response for correlations in the cluster variation method. Within a general formalism that includes previous mean-field methods, we derive formulas improving upon, e.g., the Bethe approximation and the Sessak-Monasson result at high temperature. Applying the method to direct and inverse Ising problems, we find improvements over standard implementations.

15 pages, 8 figures, 9 appendices, significant expansion on versions v1 and v2

References in corpus (4)

• Small-correlation expansions for the inverse Ising problem
• Region graph partition function expansion and approximate free energy landscapes: Theory and some numerical results
• Susceptibility Propagation by Using Diagonal Consistency
• Adaptive Thouless-Anderson-Palmer approach to inverse Ising problems with quenched random fields

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• Regularization and decimation pseudolikelihood approaches to statistical inference in $XY$-spin models
• Resummed mean-field inference for strongly coupled data
• L_1-regularized Boltzmann machine learning using majorizer minimization
• Stochastic gradient method with accelerated stochastic dynamics
• Improving variational methods via pairwise linear response identities
• Data quality for the inverse Ising problem