Inverse Ising inference from high-temperature re-weighting of observations

TL;DR

This paper introduces a new data-driven method for inferring system models, specifically Boltzmann machines, by re-weighting observed configurations to approximate a flat distribution, avoiding complex partition function calculations.

Contribution

It proposes a novel, computationally transparent approach to system inference that relies solely on observed data, bypassing the need for intractable partition function computations.

Findings

Accurately infers models using only observed configurations.

Effective for systems with many degrees of freedom.

Avoids complex partition function calculations.

Abstract

Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of partition functions summing over all configurations, both observed and unobserved. We present here a conceptually and computationally transparent data-driven approach to system inference that is based on the simple question: How should the Boltzmann weights of observed configurations be modified to make the probability distribution of observed configurations close to a flat distribution? This algorithm gives accurate inference by using only observed configurations for systems with a large number of degrees of freedom where other approaches are intractable.