Bridging Unsupervised and Semi-Supervised Anomaly Detection: A Theoretically-Grounded and Practical Framework with Synthetic Anomalies

TL;DR

This paper introduces a theoretically-grounded semi-supervised anomaly detection framework that leverages synthetic anomalies, providing new convergence guarantees and demonstrating consistent empirical improvements across multiple benchmarks.

Contribution

It extends the anomaly detection principle to semi-supervised settings with a formal mathematical framework and introduces the first theoretical convergence guarantees for neural classifiers in this context.

Findings

Synthetic anomalies improve modeling in low-density regions.

The framework achieves consistent performance gains on five benchmarks.

Theoretical guarantees support the effectiveness of synthetic anomalies in semi-supervised AD.

Abstract

Anomaly detection (AD) is a critical task across domains such as cybersecurity and healthcare. In the unsupervised setting, an effective and theoretically-grounded principle is to train classifiers to distinguish normal data from (synthetic) anomalies. We extend this principle to semi-supervised AD, where training data also include a limited labeled subset of anomalies possibly present in test time. We propose a theoretically-grounded and empirically effective framework for semi-supervised AD that combines known and synthetic anomalies during training. To analyze semi-supervised AD, we introduce the first mathematical formulation of semi-supervised AD, which generalizes unsupervised AD. Here, we show that synthetic anomalies enable (i) better anomaly modeling in low-density regions and (ii) optimal convergence guarantees for neural network classifiers -- the first theoretical result for semi-supervised AD. We empirically validate our framework on five diverse benchmarks, observing consistent performance gains. These improvements also extend beyond our theoretical framework to other classification-based AD methods, validating the generalizability of the synthetic anomaly principle in AD.