Fixed-Horizon Active Hypothesis Testing and Anomaly Detection

Dhruva Kartik, Urbashi Mitra

Abstract: Determining the presence of an anomaly or whether a system is safe or not is a problem with wide applicability. The model adopted for this problem is that of verifying whether a multi-component system has anomalies or not. Components can be probed over time individually or as groups in a data-driven manner. The collected observations are noisy and contain information on whether the selected group contains an anomaly or not. The aim is to minimize the probability of incorrectly declaring the system to be free of anomalies while ensuring that the probability of correctly declaring it to be safe is sufficiently large. This problem is modeled as an active hypothesis testing problem in the Neyman-Pearson setting. Asymptotically optimal rates and strategies are characterized. The general strategies are data driven and outperform previously proposed asymptotically optimal methods in the finite sample regime. Furthermore, novel component-selection are designed and analyzed in the non-asymptotic regime. For a specific class of problems admitting a key form of symmetry, strong non-asymptotic converse and achievability bounds are provided which are tighter than previously proposed bounds.