Network inference in the non-equilibrium steady state

TL;DR

This paper develops methods to infer parameters of non-equilibrium systems, specifically the asymmetric Ising model, from steady state samples, overcoming the lack of explicit steady state distributions.

Contribution

It introduces both exact and approximate inference algorithms for non-equilibrium steady states, expanding around mean-field theory to handle asymmetric interactions.

Findings

Exact inference algorithm for asymmetric Ising model

Approximate inference method for weak interactions

Observable correlations suffice for parameter inference

Abstract

Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks detailed balance. Such non-equilibrium systems occur naturally in applications like neural networks or gene regulatory networks. Here, we focus on the paradigmatic asymmetric Ising model and show that we can learn its parameters from independent samples of the non-equilibrium steady state. We present both an exact inference algorithm and a computationally more efficient, approximate algorithm for weak interactions based on a systematic expansion around mean-field theory. Obtaining expressions for magnetisations, two- and three-point spin correlations, we establish that these observables are sufficient to infer the model parameters. Further, we discuss the symmetries characterising the different orders of the expansion around the mean field and show how different types of dynamics can be distinguished on the basis of samples from the non-equilibrium steady state.