A Scalable Algorithm for Gaussian Graphical Models with Change-Points

TL;DR

This paper presents a fast, scalable algorithm for detecting change-points in large Gaussian graphical models, significantly improving computational efficiency and providing theoretical convergence guarantees.

Contribution

Introduction of an approximate MM algorithm for change-point detection in large Gaussian graphical models, with high efficiency and proven convergence properties.

Findings

Algorithm is an order of magnitude faster than brute force methods.

High probability convergence within statistical error of true change-point.

Effective application to synthetic data and S&P 500 structural change analysis.

Abstract

Graphical models with change-points are computationally challenging to fit, particularly in cases where the number of observation points and the number of nodes in the graph are large. Focusing on Gaussian graphical models, we introduce an approximate majorize-minimize (MM) algorithm that can be useful for computing change-points in large graphical models. The proposed algorithm is an order of magnitude faster than a brute force search. Under some regularity conditions on the data generating process, we show that with high probability, the algorithm converges to a value that is within statistical error of the true change-point. A fast implementation of the algorithm using Markov Chain Monte Carlo is also introduced. The performances of the proposed algorithms are evaluated on synthetic data sets and the algorithm is also used to analyze structural changes in the S&P 500 over the period 2000-2016.