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Statistical Inference for Clustering-based Anomaly Detection

arXiv 2504.18633 ↗First posted 25 Apr 2025stat.ML cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 25 of its 49 references that are in the map. First posted on arXiv 25 Apr 2025.

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25 of 49 references.

References · 25

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13 more
  1. 2014A significance test for forward stepwise model selectioncited by 17
  2. 2015Selective Sequential Model Selectioncited by 17
  3. 2023Valid P-Value for Deep Learning-Driven Salient Regioncited by 17
  4. 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuationcited by 16
  5. 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Modelcited by 15
  6. 2021Tree-Values: selective inference for regression treescited by 15
  7. 2016Post Selection Inference with Kernelscited by 13
  8. 2017Selective Inference for Change Point Detection in Multi-dimensional Sequencescited by 11
  9. 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inferencecited by 10
  10. 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inferencecited by 7
  11. 2024Statistical Test for Attention Map in Vision Transformercited by 6
  12. 2025Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inferencecited by 3
  13. 2024Controllable RANSAC-based Anomaly Detection via Hypothesis Testingcited by 2

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