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

TL;DR

This paper introduces a permutation-based higher criticism test for anomaly detection across numerous data streams, offering a non-parametric, exact, and asymptotically optimal method that performs well in finite samples without relying on asymptotic approximations.

Contribution

It proposes a novel permutation-based higher criticism statistic that does not require null distribution knowledge, enhancing practical applicability and finite-sample performance.

Findings

Minimal power loss compared to oracle test

Outperforms asymptotic-based variants in finite samples

Effective in real-world drug content monitoring

Abstract

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 non-parametric 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.