为聚类异常检测提供统计推断框架，确保误报率可控。
Statistical Inference for Clustering-based Anomaly Detection
- 基于选择性推断理论，分析聚类异常检测的选中机制。
- 在显著性水平α=0.05下严格控制误报率。
- 提升真实异常检出率，适合对可靠性要求高的场景。
无监督异常检测是机器学习与统计学中的基础问题。聚类驱动的异常检测方法虽常用，但缺乏对检测结果可靠性的保障。本文提出SI-CLAD（Statistical Inference for CLustering-based Anomaly Detection），一种用于检验聚类异常检测结果的新统计框架。其核心优势在于可严格控制虚假异常识别的概率，使其低于预设显著性水平α（如α=0.05）。通过分析聚类异常检测中固有的选择机制，并结合选择性推断（Selective Inference, SI）框架，我们证明了误报控制的可行性。此外，引入策略提升真实异常检出率，增强整体性能。在合成数据与真实数据集上的大量实验验证了理论结果，展示了该方法的优越性。
原文摘要 · Abstract (English)
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 $α$ (e.g., $α= 0.05$). 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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