Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics

TL;DR

This paper demonstrates that learning the structure of Ising models from correlated samples generated by a dynamical process can require exponentially fewer samples than from independent samples, especially when the process is far from equilibrium.

Contribution

It introduces an analysis of sample complexity for learning Ising models from correlated dynamical samples, revealing exponential reductions compared to i.i.d. sampling.

Findings

Sample complexity reduces exponentially for samples from far-from-equilibrium dynamics.

Two estimators based on interaction screening and conditional likelihood are analyzed.

Learning from correlated samples can be more efficient than from independent samples.

Abstract

The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probability distribution. However, for many models the mixing time of the respective Markov chain can be very large and i.i.d. samples may not be obtained. We study the problem of reconstructing binary graphical models from correlated samples produced by a dynamical process, which is natural in many applications. We analyze the sample complexity of two estimators that are based on the interaction screening objective and the conditional likelihood loss. We observe that for samples coming from a dynamical process far from equilibrium, the sample complexity reduces exponentially compared to a dynamical process that mixes quickly.