Change-Point Estimation in High-Dimensional Markov Random Field Models

TL;DR

This paper introduces a new method for detecting change-points in high-dimensional Markov Random Field models, effectively handling large networks with limited data, and demonstrates its application on synthetic and real political data.

Contribution

It proposes a profile penalized pseudo-likelihood approach for change-point estimation in high-dimensional MRFs, with theoretical bounds and practical evaluation.

Findings

Estimator performs well on synthetic data.

Successfully applied to US Senate voting patterns.

Provides tight bounds for estimation accuracy.

Abstract

This paper investigates a change-point estimation problem in the context of high-dimensional Markov Random Field models. Change-points represent a key feature in many dynamically evolving network structures. The change-point estimate is obtained by maximizing a profile penalized pseudo-likelihood function under a sparsity assumption. We also derive a tight bound for the estimate, up to a logarithmic factor, even in settings where the number of possible edges in the network far exceeds the sample size. The performance of the proposed estimator is evaluated on synthetic data sets and is also used to explore voting patterns in the US Senate in the 1979-2012 period.