Title: Multiple change-point estimation in Gaussian graphical models
Authors: Alex Gibberd - Lancaster University (United Kingdom)
Sandipan Roy - University of Bath (United Kingdom) [presenting]
Abstract: Consistency properties are considered for a regularised estimator for the simultaneous identification of both change points and dependency structure in multivariate time-series. Traditionally, the 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 change points are known a-priori. 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 change points. We present a proof of change-point consistency for the estimator. In particular, we demonstrate that both the change-point and graphical structure of the process can be consistently recovered and provide finite sample bounds.