Consistent multiple changepoint estimation with fused Gaussian graphical models

Gibberd, A. and Roy, S. (2020) Consistent multiple changepoint estimation with fused Gaussian graphical models. Annals of the Institute of Statistical Mathematics. ISSN 0020-3157

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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.

Item Type:
Journal Article
Journal or Publication Title:
Annals of the Institute of Statistical Mathematics
Additional Information:
The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-020-00749-0
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
143324
Deposited By:
Deposited On:
28 Apr 2020 09:30
Refereed?:
Yes
Published?:
Published
Last Modified:
23 Sep 2020 06:05