mlsanityData to 7 Oct 2026

Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inference

arXiv 2502.12978 ↗First posted 18 Feb 2025stat.ML cs.LGcited by 3

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Abstract (arXiv)

In real-world applications, anomaly detection (AD) often operates without access to anomalous data, necessitating semi-supervised methods that rely solely on normal data. Among these methods, deep k-nearest neighbor (deep kNN) AD stands out for its interpretability and flexibility, leveraging distance-based scoring in deep latent spaces.Despite its strong performance, deep kNN lacks a mechanism to quantify uncertainty-an essential feature for critical applications such as industrial inspection. To address this limitation, we propose a statistical framework that quantifies the significance of detected anomalies in the form of p-values, thereby enabling control over false positive rates at a user-specified significance level (e.g.,0.05). A central challenge lies in managing selection bias, which we tackle using Selective Inference-a principled method for conducting inference conditioned on data-driven selections. We evaluate our method on diverse datasets and demonstrate that it provides reliable AD well-suited for industrial use cases.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 38 of its 62 references that are in the map. First posted on arXiv 18 Feb 2025.

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38 of 62 references.

References · 38

  1. 2018GANomaly: Semi-Supervised Anomaly Detection via Adversarial Trainingcited by 409
  2. 2022Diffusion Models for Medical Anomaly Detectioncited by 231
  3. 2018Adversarially Learned One-Class Classifier for Novelty Detectioncited by 202
  4. 2020Deep Nearest Neighbor Anomaly Detectioncited by 103
  5. 2013Exact post-selection inference, with application to the lassocited by 90
  6. 2014Optimal Inference After Model Selectioncited by 63
  7. 2014Exact Post-Selection Inference for Sequential Regression Procedurescited by 47
  8. 2020Selective Inference for Hierarchical Clusteringcited by 37
  9. 2017Valid Inference Corrected for Outlier Removalcited by 25
  10. 2019Testing for a Change in Mean After Changepoint Detectioncited by 25
  11. 2020Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programmingcited by 25
  12. 2019Computing Valid p-values for Image Segmentation by Selective Inferencecited by 24
26 more
  1. 2021More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programmingcited by 24
  2. 2016Selective Inference for Group-Sparse Linear Modelscited by 21
  3. 2020Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inferencecited by 21
  4. 2022Selective inference for k-means clusteringcited by 21
  5. 2023Valid P-Value for Deep Learning-Driven Salient Regioncited by 17
  6. 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuationcited by 16
  7. 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Modelcited by 15
  8. 2021Applications of Generative Adversarial Networks in Anomaly Detection: A Systematic Literature Reviewcited by 15
  9. 2014Exact Post Model Selection Inference for Marginal Screeningcited by 12
  10. 2018Image Anomalies: a Review and Synthesis of Detection Methodscited by 10
  11. 2023CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inferencecited by 10
  12. 2023REB: Reducing Biases in Representation for Industrial Anomaly Detectioncited by 9
  13. 2016Integrative Methods for Post-Selection Inference Under Convex Constraintscited by 7
  14. 2020More Powerful and General Selective Inference for Stepwise Feature Selection using the Homotopy Continuation Approachcited by 6
  15. 2024Statistical Test for Anomaly Detections by Variational Auto-Encoderscited by 6
  16. 2017Selective inference for the problem of regions via multiscale bootstrapcited by 5
  17. 2015Selective inference after cross-validationcited by 4
  18. 2020Approximate Post-Selective Inference for Regression with the Group LASSOcited by 4
  19. 2023Selective Inference for Changepoint detection by Recurrent Neural Networkcited by 4
  20. 2025si4onnx: A Python package for Selective Inference in Deep Learning Modelscited by 4
  21. 2016Exact Post-Selection Inference for Changepoint Detection and Other Generalized Lasso Problemscited by 3
  22. 2020Selective Inference for Latent Block Modelscited by 3
  23. 2024Statistical Test for Auto Feature Engineering by Selective Inferencecited by 3
  24. 2020Selective Inference for Additive and Linear Mixed Modelscited by 2
  25. 2024Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptationcited by 2
  26. 2025Change Point Detection in the Frequency Domain with Statistical Reliabilitycited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2025Statistical Inference for Clustering-based Anomaly Detectioncited by 0
  2. 2026Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathologycited by 0
  3. 2026Post-Anomaly Detection Inference for Deep SVDDcited by 0