Statistical Inference for Clustering-based Anomaly Detection

Nguyen Thi Minh Phu; Duong Tan Loc; Vo Nguyen Le Duy

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arXiv · 2504.18633

Statistical Inference for Clustering-based Anomaly Detection

Nguyen Thi Minh Phu·Duong Tan Loc·Vo Nguyen Le Duy

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Abstract

Unsupervised anomaly detection (AD) is a fundamental problem in machine learning and statistics. A popular approach to unsupervised AD is clustering-based detection. However, this method lacks the ability to guarantee the reliability of the detected anomalies. In this paper, we propose SI-CLAD (Statistical Inference for CLustering-based Anomaly Detection), a novel statistical framework for testing the clustering-based AD results. The key strength of SI-CLAD lies in its ability to rigorously control the probability of falsely identifying anomalies, maintaining it below a pre-specified significance level $\alpha$ (e.g., $\alpha = 0.05$). By analyzing the selection mechanism inherent in clustering-based AD and leveraging the Selective Inference (SI) framework, we prove that false detection control is attainable. Moreover, we introduce a strategy to boost the true detection rate, enhancing the overall performance of SI-CLAD. Extensive experiments on synthetic and real-world datasets provide strong empirical support for our theoretical findings, showcasing the superior performance of the proposed method.

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BibTeX RIS

Nguyen Thi Minh Phu, Duong Tan Loc, Vo Nguyen Le Duy. 2025-04-25. Statistical Inference for Clustering-based Anomaly Detection. https://arxiv.org/abs/2504.18633

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