Quickest Change Detection with Confusing Change

TL;DR

This paper addresses the challenge of quickest change detection when confusing changes occur, proposing novel CuSum-based procedures that distinguish between bad and confusing changes efficiently and with proven guarantees.

Contribution

It introduces S-CuSum and J-CuSum procedures that handle confusing changes in QCD, extending standard methods with analytical guarantees and computational efficiency.

Findings

Proposed S-CuSum and J-CuSum outperform standard CuSum in complex scenarios.

Analytical performance guarantees are established for the new procedures.

Numerical results validate the effectiveness and efficiency of the methods.

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.