Quickest Change Detection with Confusing Change
This addresses a specific challenge in statistical signal processing for applications like quality control or anomaly detection, but it is incremental as it builds on existing CuSum methods.
The paper tackles quickest change detection when changes can be either 'bad' (to detect) or 'confusing' (to ignore), identifying distributions where standard methods fail and proposing S-CuSum and J-CuSum procedures that work for all distributions, with analytical guarantees and numerical validation.
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.