Active Change Point Anomaly Detection Over Composite Hypotheses

The problem of detecting a single anomalous process among a finite number M of processes is considered. We examine a composite hypothesis case, where observations of a process follow a common distribution with an unknown parameter (vector). The parameter value resides in either normal or abnormal parameter spaces, contingent on the process state. Until the change point, all processes are in a normal state, and after the change point, one process transitions to an abnormal state. Our goal is to develop a sequential search strategy that minimizes the expected detection time since the anomaly occurred subject to an error probability constraint. We develop a novel anomaly detection algorithm, named Searching for Change Point Anomaly (SCPA), with the following desired properties. Firstly, when no additional side information on the process states is available, the proposed algorithm is asymptotically optimal in terms of minimizing the detection delay as the error probability approaches zero. Secondly, in the scenario where the parameter value under the null hypothesis is known and equal for all normal processes, the proposed algorithm is also asymptotically optimal and demonstrates improved detection time determined by the true null state. Finally, we establish an upper bound on the error probability under the proposed algorithm for the finite sample regime.