Mean-field theory for the inverse Ising problem at low temperatures

Abstract

The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of spin configurations sampled from the Boltzmann measure. To invert the relationship between model parameters and observables (magnetisations and correlations) mean-field approximations are often used, allowing to determine model parameters from data. However, all known mean-field methods fail at low temperatures with the emergence of multiple thermodynamic states. Here we show how clustering spin configurations can approximate these thermodynamic states, and how mean-field methods applied to thermodynamic states allow an efficient reconstruction of Ising models also at low temperatures.

References in corpus (4)

• Identification of direct residue contacts in protein-protein interaction by message passing
• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• High-dimensional Ising model selection using ${\ell }_1$-regularized logistic regression
• Small-correlation expansions for the inverse Ising problem

Cited by in corpus (2)

• Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models
• Pairwise MRF Calibration by Perturbation of the Bethe Reference Point