Consistent Multiple Change-point Estimation with Fused Gaussian Graphical Models

Alex J. Gibberd, Sandipan Roy

Research output: Contribution to journalArticle

2 Downloads (Pure)

Abstract

We consider the consistency properties of a regularised estimator for the simultaneous identification of both changepoints and graphical dependency structure in multivariate time-series. Traditionally, estimation of Gaussian graphical models (GGM) is performed in an i.i.d setting. More recently, such models have been extended to allow for changes in the distribution, but primarily where changepoints are known a priori. In this work, we study the Group-Fused Graphical Lasso (GFGL) which penalises partial correlations with an L1 penalty while simultaneously inducing block-wise smoothness over time to detect multiple changepoints. We present a proof of consistency for the estimator, both in terms of changepoints, and the structure of the graphical models in each segment. We contrast our results, which are based on a global, i.e. graph-wide likelihood, with those previously obtained for performing dynamic graph estimation at a node-wise (or neighbourhood) level.

Original languageEnglish
JournalAnnals of the Institute of Statistical Mathematics
Early online date17 Mar 2020
DOIs
Publication statusE-pub ahead of print - 17 Mar 2020

Keywords

  • Asymptotics
  • Changepoint
  • Graphical model
  • Regularisation

ASJC Scopus subject areas

  • Statistics and Probability

Fingerprint Dive into the research topics of 'Consistent Multiple Change-point Estimation with Fused Gaussian Graphical Models'. Together they form a unique fingerprint.

  • Cite this