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.

利用统计检验方法提出了 Variational Autoencoder（VAE）在异常检测中的可靠性评估方法，该方法能够量化通过 VAE 检测到的异常区域的统计可靠性，并且可以控制误检的概率。