High dimensional changepoint detection with a dynamic graphical lasso

Abstract

The use of sparsity to encourage parsimony in graphical models continues to attract much attention at the interface between multivariate Signal Processing and Statistics. We propose and investigate two approaches for the detection of changepoints in the correlation structure of evolving Gaussian graphical models. Both approaches employ two-stages; first estimating the dynamic graphical structure through regularising the precision matrix, before changepoints are selected via a group fused lasso. Experiments on simulated data illustrate the efficacy of the two approaches. Furthermore, results on real internet traffic flow data containing a Denial Of Service attack demonstrate that the proposed approaches have potential utility in information forensics and security.