Adaptive cluster expansion for the inverse Ising problem: convergence, algorithm and tests

TL;DR

This paper introduces an adaptive cluster expansion method to solve the inverse Ising problem, efficiently inferring interactions from correlation data by selecting relevant variable clusters to improve accuracy and computational feasibility.

Contribution

The paper proposes a novel adaptive cluster expansion algorithm with convergence analysis, pseudo-code implementation, and validation on synthetic data for the inverse Ising problem.

Findings

Effective in reconstructing interactions from synthetic data

Reduces overfitting by discarding small contributions

Provides a practical algorithm with convergence guarantees

Abstract

We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific clusters of variables, based on their contributions to the cross-entropy of the Ising model. Small contributions are discarded to avoid overfitting and to make the computation tractable. The properties of the cluster expansion and its performances on synthetic data are studied. To make the implementation easier we give the pseudo-code of the algorithm.