Inverse Ising inference using all the data

TL;DR

This paper demonstrates that logistic regression utilizing all available data significantly outperforms mean-field methods in solving the inverse Ising problem, especially for strong interactions, and improves topology recovery with regularization.

Contribution

It introduces a logistic regression-based approach for inverse Ising inference that is computationally feasible and more accurate than traditional mean-field methods, especially in low-temperature regimes.

Findings

Logistic regression outperforms mean-field in inverse Ising inference.

Interaction topologies can be accurately recovered from few samples.

L1-regularization enhances inference in low-temperature regimes.

Abstract

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of $l_1$-regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.