Estimating a Change-Point in High-Dimensional Markov Random Field Models

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Sandipan Roy*+ and Yves Atchade and George Michailidis
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: change-point ; penalized ; pseudo-likelihood ; consistency

Abstract

We introduce a model for estimating a change-point in a high-dimensional Markov Random Field model. The change point estimate is obtained by maximizing a penalized pseudo-likelihood function that also provides estimates for the structure of the underlying Markov Random Fields before and after the change point. We estimate the change-point by profiling out the pseudo-likelihood over a grid of candidate change-points. The novel key technical result rigorously established is that of consistency of the change point estimate. The performance of the proposed model is evaluated on synthetic data sets and is also used to explore voting patterns in the US Senate.