Resummed mean-field inference for strongly coupled data

Hugo Jacquin and A. Rançon
Phys. Rev. E 94, 042118 – Published 17 October 2016

Abstract

We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for N auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.

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  • Received 21 October 2015
  • Revised 21 July 2016

DOI:https://doi.org/10.1103/PhysRevE.94.042118

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Techniques
Statistical Physics & Thermodynamics

Authors & Affiliations

Hugo Jacquin

  • Laboratoire de Physique Statistique, École Normale Supérieure, UMR CNRS 8550, 24 rue Lhomond, 75005 Paris, France

A. Rançon

  • Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France

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Issue

Vol. 94, Iss. 4 — October 2016

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