Statistical Test for Anomaly Detections by Variational Auto-Encoders

In this study, we consider the reliability assessment of anomaly detection (AD) using Variational Autoencoder (VAE). Over the last decade, VAE-based AD has been actively studied in various perspective, from method development to applied research. However, when the results of ADs are used in high-stakes decision-making, such as in medical diagnosis, it is necessary to ensure the reliability of the detected anomalies. In this study, we propose the VAE-AD Test as a method for quantifying the statistical reliability of VAE-based AD within the framework of statistical testing. Using the VAE-AD Test, the reliability of the anomaly regions detected by a VAE can be quantified in the form of p-values. This means that if an anomaly is declared when the p-value is below a certain threshold, it is possible to control the probability of false detection to a desired level. Since the VAE-AD Test is constructed based on a new statistical inference framework called selective inference, its validity is theoretically guaranteed in finite samples. To demonstrate the validity and effectiveness of the proposed VAE-AD Test, numerical experiments on artificial data and applications to brain image analysis are conducted.