Zoom: https://oregonstate.zoom.us/s/98357211915
Changepoint detection methods for networks and precision matrices, fall into two extremes. At one extreme, global changepoint detection methods identify when matrices differ in terms of overall properties, such as their L-infinity norms. This global approach is very coarse-grained in terms of dimensions and may not identify the locations of the changes if they take place on a subset of the dimensions. On the other extreme, local changepoint detection methods inspect individual pairwise components of a precision or adjacency matrix. These methods can identify changes in individual dimensions, but they are generally computationally expensive in higher dimensions, require careful handling of a large number of hypothesis tests simultaneously, and do not identify subsets in which a change takes place. Our work aims to fill a gap in the middle of these two extremes by efficiently detecting and localizing changepoints caused by changes to a subset of dimensions. Our approach for networks is based on CUSUM statistic for rooted subgraphs. Our approach for precision matrices, which we refer to as LD-CPD (Linear Decomposition Changepoint Detection), uses a linear decomposition of the precision matrix and tests for changes to the components of this decomposition, where these components correspond to a group of dimensions. We benchmark our algorithm on several simulation studies with changes involving groups of dimensions, as well as on real-world sensor networks and stock market data. We show that our approach is effective at identifying changepoints in both regimes in a computationally efficient manner while providing a convenient interpretation of the changes through this linear framework.
Sharmodeep Bhattacharyya is an Associate Professor in the Department of Statistics and AI Degree Program, EECS Department at Oregon State University. His research interests lie in several fields of statistics, including statistical inference of networks, high-dimensional statistical inference, clustering, semiparametric inference, and hypothesis testing. He is also interested in the application of statistical methods in neuroscience, epidemiology, public health, and public policy. Before joining Oregon State University, Dr. Bhattacharyya completed his Ph.D. in Statistics at the University of California, Berkeley, under the supervision of Prof. Peter J. Bickel. Before that, he completed a B.Stat and M.Stat at the Indian Statistical Institute in Kolkata.