Optimum Multi-Stream Sequential Change-Point Detection With Sampling Control

• Published in: IEEE transactions on information theory Vol. 67; no. 11; pp. 7627 - 7636
• Main Authors: Xu, Qunzhi, Mei, Yajun, Moustakides, George V.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic optimality; change-point detection; CUSUM; Delays; False alarms; Mathematical model; myopic sampling; Nonhomogeneous media; Optimization; Process control; quickest detection; Sampling; Switches; Testing
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2021.3074961

In multi-stream sequential change-point detection it is assumed that there are <inline-formula> <tex-math notation="LaTeX">M </tex-math></inline-formula> processes in a system and at some unknown time, an occurring event changes the distribution of the samples of a particular process. In this article, we consider this problem under a sampling control constraint when one is allowed, at each point in time, to sample a single process. The objective is to raise an alarm as quickly as possible subject to a proper false alarm constraint. We show that under sampling control, a simple myopic-sampling-based sequential change-point detection strategy is second-order asymptotically optimal when the number <inline-formula> <tex-math notation="LaTeX">M </tex-math></inline-formula> of processes is fixed. This means that the proposed detector, even by sampling with a rate <inline-formula> <tex-math notation="LaTeX">1/M </tex-math></inline-formula> of the full rate, enjoys the same detection delay, up to some additive finite constant, as the optimal procedure. Simulation experiments corroborate our theoretical results.