Quickest Change Detection Using Mismatched CUSUM

Abstract: The field of quickest change detection (QCD) concerns design and analysis of algorithms to estimate in real time the time at which an important event takes place and identify properties of the post-change behavior. The goal is to devise a stopping time adapted to the observations that minimizes an $L_1$ loss. Approximately optimal solutions are well known under a variety of assumptions. In the work surveyed here we consider the CUSUM statistic, which is defined as a one-dimensional reflected random walk driven by a functional of the observations. It is known that the optimal functional is a log likelihood ratio subject to special statical assumptions. The paper concerns model free approaches to detection design, considering the following questions: 1. What is the performance for a given functional of the observations? 2. How do the conclusions change when there is dependency between pre- and post-change behavior? 3. How can techniques from statistics and machine learning be adapted to approximate the best functional in a given class?