TY - JOUR

T1 - Regularized Estimation of Piecewise Constant Gaussian Graphical Models

T2 - The Group-Fused Graphical Lasso

AU - Gibberd, A.

AU - Nelson, J. D. B.

N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 19/06/2017, available online: https://www.tandfonline.com/doi/full/10.1080/10618600.2017.1302340

PY - 2017/6/19

Y1 - 2017/6/19

N2 - 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.

AB - 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.

KW - Changepoint

KW - High-dimensional

KW - M-estimator

KW - Sparsity

KW - Time-series

U2 - 10.1080/10618600.2017.1302340

DO - 10.1080/10618600.2017.1302340

M3 - Journal article

VL - 26

SP - 623

EP - 634

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

IS - 3

ER -