A1094
Title: High-dimensional sequential change detection
Authors: Dogyoon Song - University of California Davis (United States) [presenting]
Abstract: The aim is to address the quickest change detection (QCD) problem for multivariate Gaussian time series in which post-change parameters are unknown and must be estimated from a limited data window. The focus is on the high-dimensional regime where the dimension p grows proportionally with the window size n. Extending the window-limited CuSum (WLCuSum) procedure to this setting, it is shown that its asymptotic performance is governed by a novel information-theoretic metric, which is termed the normalized high-dimensional Kullback-Leibler (NHDKL) divergence. Specifically, the detection delay is inversely proportional to the difference between the NHDKL of the post-change versus pre-change distributions and the NHDKL attributable to estimation error. This characterization reveals the suboptimality of plug-in estimators. By minimizing the estimation-error component of the NHDKL, the Ledoit-Wolf quadratic inverse Steins shrinkage estimator (LWISE) is identified as asymptotically optimal within a broad class of shrinkage estimators. Coupled with the sample mean, LWISE yields a practical WLCuSum detector that provably achieves the optimal tradeoff between detection delay and false-alarm rate.
