Gibberd, A. and Nelson, J. D. B. (2017) Regularized Estimation of Piecewise Constant Gaussian Graphical Models : The Group-Fused Graphical Lasso. Journal of Computational and Graphical Statistics, 26 (3). pp. 623-634. ISSN 1061-8600
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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.