Multiple Changepoint Estimation in High-Dimensional Gaussian Graphical Models

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 only 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.

39 pages, 2 figures

References in corpus (5)

• Optimal detection of changepoints with a linear computational cost
• The group fused Lasso for multiple change-point detection
• Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso
• Change-Point Estimation in High-Dimensional Markov Random Field Models
• Computationally efficient change point detection for high-dimensional regression

Cited by in corpus (7)

• Seeded Binary Segmentation: A general methodology for fast and optimal change point detection
• Sequential change-point detection in high-dimensional Gaussian graphical models
• A review on minimax rates in change point detection and localisation
• Univariate Mean Change Point Detection: Penalization, CUSUM and Optimality
• Inference on the Change Point for High Dimensional Dynamic Graphical Models
• Detection and estimation of parameters in high dimensional multiple change point regression models via ${\ell }_1/{\ell }_0$ regularization and discrete optimization
• Online detection of local abrupt changes in high-dimensional Gaussian graphical models