Learning and inference in a nonequilibrium Ising model with hidden nodes

TL;DR

This paper develops a path integral approach and dynamical mean-field theory to improve inference and learning of couplings in a partially observed kinetic Ising model with hidden nodes, addressing instability issues.

Contribution

It introduces a novel path integral representation and Gaussian correction methods for inference in nonequilibrium Ising models with hidden nodes, enhancing learning accuracy.

Findings

Gaussian corrections stabilize learning rules

Improved coupling inference with hidden nodes

Enhanced learning of observed node couplings

Abstract

We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.