Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso

TL;DR

This paper introduces a novel regularized M-estimator for jointly estimating sparse, piecewise-constant Gaussian graphical models with changepoint detection, accommodating grouped changepoints and evolving dependency structures.

Contribution

It proposes a new method that relaxes traditional assumptions, enabling simultaneous estimation of graph structure and changepoints, including grouped changepoints, with an efficient algorithm.

Findings

Effective recovery of graph structures demonstrated on synthetic data.

Method successfully detects grouped changepoints in real-world datasets.

Supports both sparse and smoothly evolving graph structures.

Abstract

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data is drawn identically from a generating distribution. Introducing sparsity and sparse-difference inducing priors we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly evolving graph structures, as required. Moreover, our approach extends current methods to allow estimation of changepoints that are grouped across multiple dependencies in a system. An efficient algorithm for estimating structure is proposed. We study the empirical recovery properties in a synthetic setting. The qualitative effect of grouped changepoint estimation is then demonstrated by applying the method on two real-world data-sets.