Quickest Change Detection with Confusing Change
Yu-Zhen Janice Chen, Jinhang Zuo, Venugopal V. Veeravalli, Don Towsley
TL;DR
The paper tackles quickest change detection when a change may be either a target bad event or a confusing event. It formalizes a dual-false-alarm metric and proposes two CuSum-based detectors, S-CuSum and J-CuSum, leveraging two statistics $W[t]$ and $\Lambda[t]$ to reliably detect bad changes while suppressing false alarms from confusing changes. The authors establish a universal lower bound on worst-case average detection delay and provide corresponding upper bounds for both proposed procedures, complemented by numerical results showing robust performance across three regimes. The work offers computationally efficient, recursive-update detectors with strong theoretical guarantees, validated by simulations, and identifies future directions to close remaining gaps between bounds.
Abstract
In the problem of quickest change detection (QCD), a change occurs at some unknown time in the distribution of a sequence of independent observations. This work studies a QCD problem where the change is either a bad change, which we aim to detect, or a confusing change, which is not of our interest. Our objective is to detect a bad change as quickly as possible while avoiding raising a false alarm for pre-change or a confusing change. We identify a specific set of pre-change, bad change, and confusing change distributions that pose challenges beyond the capabilities of standard Cumulative Sum (CuSum) procedures. Proposing novel CuSum-based detection procedures, S-CuSum and J-CuSum, leveraging two CuSum statistics, we offer solutions applicable across all kinds of pre-change, bad change, and confusing change distributions. For both S-CuSum and J-CuSum, we provide analytical performance guarantees and validate them by numerical results. Furthermore, both procedures are computationally efficient as they only require simple recursive updates.