Active Hypothesis Testing for Anomaly Detection

• Published in: IEEE transactions on information theory Vol. 61; no. 3; pp. 1432 - 1450
• Main Authors: Cohen, Kobi, Qing Zhao
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: active hypothesis testing; anomaly detection; Asymptotic methods; controlled sensing; dynamic search; Error probability; Errors; Hypothesis testing; Indexes; Probability; Search problems; Sensors; Sequential detection; Testing; Upper bound; Vectors; controlled sensing; anomaly detection; dynamic search; Sequential detection; active hypothesis testing
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2014.2387857

The problem of detecting a single anomalous process among a finite number M of processes is considered. At each time, a subset of the processes can be observed, and the observations from each chosen process follow two different distributions, depending on whether the process is normal or abnormal. The objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint. This problem can be considered as a special case of active hypothesis testing first considered by Chernoff where a randomized strategy, referred to as the Chernoff test, was proposed and shown to be asymptotically (as the error probability approaches zero) optimal. For the special case considered in this paper, we show that a simple deterministic test achieves asymptotic optimality and offers better performance in the finite regime. We further extend the problem to the case where multiple anomalous processes are present. In particular, we examine the case where only an upper bound on the number of anomalous processes is known.