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

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Title: Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso
Author(s): Gibberd, AJ
Nelson, JDB
Item Type: Journal Article
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 are 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 a genetic time-course dataset. Supplementary material for this article is available online.
Publication Date: 7-Mar-2017
Date of Acceptance: 7-Mar-2017
URI: http://hdl.handle.net/10044/1/52580
DOI: https://dx.doi.org/10.1080/10618600.2017.1302340
ISSN: 1061-8600
Publisher: Taylor & Francis
Start Page: 623
End Page: 634
Journal / Book Title: Journal of Computational and Graphical Statistics
Volume: 26
Issue: 3
Copyright Statement: This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Computational and Graphical Statistics on 7 Mar 2017, available online at: http://www.tandfonline.com/10.1080/10618600.2017.1302340
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Changepoint
High-dimensional
M-estimator
Sparsity
Time-series
INVERSE COVARIANCE ESTIMATION
SPARSE-GROUP LASSO
DROSOPHILA-MELANOGASTER
SELECTION
REGRESSION
NETWORKS
stat.ME
stat.ME
stat.CO
stat.ML
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Changepoint
High-dimensional
M-estimator
Sparsity
Time-series
INVERSE COVARIANCE ESTIMATION
SPARSE-GROUP LASSO
DROSOPHILA-MELANOGASTER
SELECTION
REGRESSION
NETWORKS
0104 Statistics
Statistics & Probability
Publication Status: Published
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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