Anomaly Detection for a Large Number of Streams: A Permutation-Based Higher Criticism Approach

• 成果类型: Article
• 署名作者: Stoepker, Ivo, V; Castro, Rui M.; Arias-Castro, Ery; van den Heuvel, Edwin
• 署名单位: Eindhoven University of Technology; University of California System; University of California San Diego; University of California System; University of California San Diego
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2126361
• 发表日期: 2024
• 页码: 461-474
• 关键词: false discovery rate; tests; rare

摘要

Anomaly detection when observing a large number of data streams is essential in a variety of applications, ranging from epidemiological studies to monitoring of complex systems. High-dimensional scenarios are usually tackled with scan-statistics and related methods, requiring stringent modeling assumptions for proper calibration. In this work we take a nonparametric stance, and propose a permutation-based variant of the higher criticism statistic not requiring knowledge of the null distribution. This results in an exact test in finite samples which is asymptotically optimal in the wide class of exponential models. We demonstrate the power loss in finite samples is minimal with respect to the oracle test. Furthermore, since the proposed statistic does not rely on asymptotic approximations it typically performs better than popular variants of higher criticism that rely on such approximations. We include recommendations such that the test can be readily applied in practice, and demonstrate its applicability in monitoring the content uniformity of an active ingredient for a batch-produced drug product. for this article are available online.