Small-correlation expansions for the inverse Ising problem

TL;DR

This paper introduces a systematic small-correlation expansion method to solve the inverse Ising problem, accurately inferring couplings and fields from correlations and magnetizations, with improved performance on complex models.

Contribution

The authors develop a higher-order expansion technique for the inverse Ising problem, including exact summation of certain diagram classes, outperforming existing algorithms on spin-glass models.

Findings

Couplings calculated up to third order in correlations for generic magnetizations.

Couplings calculated up to seventh order for zero magnetizations.

Outperforms existing algorithms on the Sherrington-Kirkpatrick model.

Abstract

We present a systematic small-correlation expansion to solve the inverse Ising problem: find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations, and to the seventh order in the case of zero magnetizations; in addition we show how to sum some useful classes of diagrams exactly. The resulting expansion outperforms existing algorithms on the Sherrington-Kirkpatrick spin-glass model.