Learning graphical models from the Glauber dynamics

TL;DR

This paper introduces a new method for learning binary pairwise graphical models by leveraging data generated from Glauber dynamics, enabling efficient reconstruction with near-optimal sample complexity.

Contribution

It demonstrates that graphical models can be learned efficiently from Glauber dynamics data, deviating from the traditional i.i.d. sample assumption.

Findings

Reconstruction of binary pairwise graphical models is computationally feasible.

The proposed method achieves near information-theoretic minimum sample complexity.

Learning time scales as f(d)p^2 log p, where d is maximum degree and p is number of nodes.

Abstract

In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics. The Glauber dynamics is a Markov chain that sequentially updates individual nodes (variables) in a graphical model and it is frequently used to sample from the stationary distribution (to which it converges given sufficient time). Additionally, the Glauber dynamics is a natural dynamical model in a variety of settings. This work deviates from the standard formulation of graphical model learning in the literature, where one assumes access to i.i.d. samples from the distribution. Much of the research on graphical model learning has been directed towards finding algorithms with low computational cost. As the main result of this work, we establish that the problem of reconstructing binary pairwise graphical models is computationally tractable when we observe the Glauber dynamics. Specifically, we show that a binary pairwise graphical model on $p$ nodes with maximum degree $d$ can be learned in time $f(d)p^2\log p$, for a function $f(d)$, using nearly the information-theoretic minimum number of samples.