High-dimensional Quickest Change Detection with Adaptive Window-Based Subset Estimation

Music City Center 

A large scale multichannel sequential detection is considered, where an event occurs at some unknown time and affects the distributions of an unknown subset of independent data streams, possibly at a different time each of them. The goal is to detect this change as quickly as possible for any possible affected set of streams, while controlling the false alarm rate. A computationally scalable adaptive CuSum procedure is proposed. Its performance is analyzed in various high-dimensional regimes where the number of streams, the unknown number of affected streams, and the unknown delays in the emergence of the change all go to infinity as the false alarm rate goes to zero. Analytically, it is compared favorably to existing schemes in the literature with similar computational complexity and it is shown to enjoy various kinds of asymptotic optimality properties in certain sparse and moderately high dimensional regimes. Finally, performance of the proposed procedure for a Gaussian mean-shift problem is compared with other methods in a simulation study.

High-dimensional

Sequential change detection

Adaptive

CuSum

Multistream

Window-based 

Quality and Productivity Section