Maximum likelihood reconstruction for Ising models with asynchronous updates

TL;DR

This paper presents methods for inferring couplings in asynchronous kinetic Ising models using maximum likelihood, considering cases with known and unknown update times, validated through numerical experiments.

Contribution

It introduces a novel learning rule for asynchronous Ising models that depends solely on spin correlations, derived from equations of motion and approximations.

Findings

Effective inference of couplings demonstrated in numerical simulations

Good convergence observed aligning with theoretical predictions

Methods applicable to various data lengths, system sizes, and conditions

Abstract

We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases, one in which we know both the spin history and the update times and one in which we only know the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.