Deep svdd gets reliable statistical tests for anomaly detection
Post-Anomaly Detection Inference for Deep SVDD
Machine Learning
Summary
Sometimes, computer systems need to find unusual or strange data points called anomalies. The authors build on a popular method called Deep SVDD that finds odd data by learning what normal data looks like. Usually, this method just guesses if a point is strange without telling how confident it is, which can be risky in important situations. The authors propose a new way called PADI to add reliable statistical checks that show how likely an anomaly detection is truly unusual or just random noise. This makes it safer to trust the decisions, especially when making high-stakes calls.
What this means in practice
- •For security monitoring teams: Control false alarms precisely in anomaly detection systems to improve trustworthiness when spotting cyber or physical threats.
- •For medical device engineers: Use statistically validated anomaly alerts in device data to reduce risky false positive warnings in critical health systems.
Authors
Cao Le Cong Thanh, Dang Quang Vinh, Vo Nguyen Le Duy
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.