{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37935",
  "author_total": 3,
  "authors": [
    {
      "name": "Cao Le Cong Thanh"
    },
    {
      "name": "Dang Quang Vinh"
    },
    {
      "name": "Vo Nguyen Le Duy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3hkv0s9bctsfd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37935",
  "fulltext_url": null,
  "id": "3hkv0s9bctsfd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37935",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Anomaly Detection Techniques and Applications"
    ]
  ],
  "openalex": "W7214963119",
  "pdf_url": "https://arxiv.org/pdf/2609.37935",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3hkv0s9bctsfd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:41Z",
      "native_id": "2609.37935",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37935"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Post-Anomaly Detection Inference for Deep SVDD",
  "title_text": "Post-Anomaly Detection Inference for Deep SVDD",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/3hkv0s9bctsfd",
  "venue": "arXiv",
  "versions": []
}