Post-Anomaly Detection Inference for Deep SVDD

Abstract

Deep Support Vector Data Description (Deep SVDD) has become a prominent framework for unsupervised anomaly detection by learning latent representations that compactly characterize normal data around a center. Despite its empirical success, anomaly decisions produced by Deep SVDD are typically made solely based on anomaly scores without rigorous statistical guarantees, thereby limiting their reliability in safety-critical and high-stakes applications where false positives must be strictly controlled. In this paper, we propose PADI (Post-Anomaly Detection Inference), a novel framework that equips a trained and frozen Deep SVDD detector with statistically valid inference by leveraging the Selective Inference framework. Specifically, PADI performs inference conditional on the event that a test instance is identified as anomalous by Deep SVDD, thereby enabling rigorous statistical assessment of anomaly decisions. Based on this formulation, we derive valid selective p-values that quantify the statistical significance of the detected anomaly. Using these p-values, we theoretically establish control of the false positive rate (FPR) at a user-specified significance level α (e.g., α=0.05). Furthermore, we extend the proposed framework to Deep Semi-Supervised Anomaly Detection (Deep SAD), providing a principled approach for statistically reliable inference in semi-supervised anomaly detection settings. Extensive experiments on both synthetic and real-world benchmark datasets robustly support the theoretical findings. The results demonstrate that PADI consistently achieves proper FPR control while attaining superior true positive rates compared with existing approaches.

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Cite

BibTeX RIS

BibTeX

@misc{thanh2026postanomaly,
  title = {{Post-Anomaly Detection Inference for Deep SVDD}},
  author = {Cao Le Cong Thanh and Dang Quang Vinh and Vo Nguyen Le Duy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37935},
  eprint = {2609.37935},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37935},
}

RIS

TY  - UNPB
TI  - Post-Anomaly Detection Inference for Deep SVDD
AU  - Cao Le Cong Thanh
AU  - Dang Quang Vinh
AU  - Vo Nguyen Le Duy
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37935
UR  - https://arxiv.org/abs/2609.37935
AB  - Deep Support Vector Data Description (Deep SVDD) has become a prominent framework for unsupervised anomaly detection by learning latent representations that compactly characterize normal data around a center. Despite its empirical success, anomaly decisions produced by Deep SVDD are typically made solely based on anomaly scores without rigorous statistical guarantees, thereby limiting their reliability in safety-critical and high-stakes applications where false positives must be strictly controlled. In this paper, we propose PADI (Post-Anomaly Detection Inference), a novel framework that equips a trained and frozen Deep SVDD detector with statistically valid inference by leveraging the Selective Inference framework. Specifically, PADI performs inference conditional on the event that a test instance is identified as anomalous by Deep SVDD, thereby enabling rigorous statistical assessment of anomaly decisions. Based on this formulation, we derive valid selective p-values that quantify the statistical significance of the detected anomaly. Using these p-values, we theoretically establish control of the false positive rate (FPR) at a user-specified significance level α (e.g., α=0.05). Furthermore, we extend the proposed framework to Deep Semi-Supervised Anomaly Detection (Deep SAD), providing a principled approach for statistically reliable inference in semi-supervised anomaly detection settings. Extensive experiments on both synthetic and real-world benchmark datasets robustly support the theoretical findings. The results demonstrate that PADI consistently achieves proper FPR control while attaining superior true positive rates compared with existing approaches.
ER  -

Abstract

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