Statistical Test for Anomaly Detections by Variational Auto-Encoders
Daiki Miwa Tomohiro Shiraishi Vo Nguyen Le Duy Teruyuki Katsuoka Ichiro Takeuchi
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.