Statistical Test for Anomaly Detections using Variational Auto-Encoders by Selective Inference

Daiki Miwa, Tomohiro Shiraishi, Vo Nguyen Le Duy, Teruyuki Katsuoka, Ichiro Takeuchi

Keywords: Variational Autoencoder, Selective Inference, Anomaly Detection, Medical Image Analysis

TL;DR: In this paper, we present a novel statistical test for Variational Autoencoder-based anomaly detection by using selective inference.

Abstract: Over the past decade, Variational Autoencoders (VAE) have become a widely used tool for anomaly detection (AD), with research advancing from algorithm development to real-world applications. However, a critical challenge remains --- the lack of a reliable method to rigorously assess the reliability of detected anomalies, which restricts its use in high-stakes decision-making tasks such as medical diagnostics. To overcome this limitation, we introduce the VAE-AD Test, a novel approach for quantifying the statistical reliability of VAE-based AD. The key advantage of the VAE-AD Test lies in its ability to properly control the probability of misidentifying anomalies under a pre-specified level of guarantee $\alpha$ (e.g., 0.05). Specifically, by carefully analyzing the AD process of VAE, which operates through piecewise-linear functions, and leveraging the Selective Inference (SI) framework to assign valid p-values to the detected anomalies, we prove that theoretical control of the false detection rate is achievable. Experiments conducted on both synthetic and real-world datasets robustly support our theoretical results, showcasing the VAE-AD Test’s superior performance. To our knowledge, this is the first work capable of conducting valid statistical inference to assess the reliability of VAE-based AD.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 9490