深度SVDD的异常检测后推断

中文摘要 AI 辅助

深度支持向量数据描述（Deep SVDD）已成为无监督异常检测的重要框架，其通过学习围绕中心紧凑表征正常数据的潜在表示。尽管经验上取得了成功，Deep SVDD 产生的异常决策通常仅基于异常分数，缺乏严格的统计保证，从而限制了其在必须严格控制误报的安全关键和高风险应用中的可靠性。在本文中，我们提出 PADI（异常检测后推断），一种新颖的框架，通过利用选择性推断框架，为训练好的且冻结的 Deep SVDD 检测器配备统计有效的推断。具体来说，PADI 在测试实例被 Deep SVDD 识别为异常的事件条件下进行推断，从而能够对异常决策进行严格的统计评估。基于此公式，我们推导出有效的选择性 p 值，用以量化检测到的异常的统计显著性。利用这些 p 值，我们在理论上确立了在用户指定的显著性水平 α（例如，α=0.05）下对误报率（FPR）的控制。此外，我们将所提出的框架扩展到深度半监督异常检测（Deep SAD），为半监督异常检测设置中的统计可靠推断提供了一种原则性方法。在合成和真实世界基准数据集上的大量实验有力地支持了理论发现。结果表明，与现有方法相比，PADI 持续实现适当的 FPR 控制，同时获得更高的真阳性率。

英文摘要

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.

发表机构

• University of Information Technology（信息技术大学）
• Vietnam National University, Ho Chi Minh City（胡志明市越南国家大学）

机构由 AI 辅助整理，请以论文原文为准。