Title: Multiple changepoint estimation in high dimensional Gaussian graphical models
Authors: Alex Gibberd - Lancaster University (United Kingdom) [presenting]
Sandipan Roy - University of Bath (United Kingdom)
Abstract: Many modern datasets exhibit a multivariate dependence structure that can be modelled using networks or graphs. For instance, in financial applications, one may study Markowitz minimum-variance portfolios based on sparse inverse covariance matrices. However, in reality, we expect that the underlying volatility and dependency structure between data-streams may change over time, we thus require a way of tracking these dynamic network structures. We will discuss consistency properties for a regularised M-estimator which simultaneously identifies both change points and graphical dependency structure in multivariate time-series. Specifically, we will study the Group-Fused Graphical Lasso (GFGL), which penalises partial-correlations with an $l_1$ penalty, while simultaneously inducing block-wise smoothness over time to detect multiple change points. Under mild conditions we present a proof of change-point consistency for this estimator. In particular, it is demonstrated that both the changepoint and graphical structure of the process can be consistently recovered, for which finite sample bounds are provided.