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.

翻译：本研究探讨了使用变分自编码器（VAE）进行异常检测（AD）的可靠性评估问题。近十年来，基于VAE的异常检测从方法开发到应用研究已在多角度得到广泛探索。然而，当异常检测结果被用于医疗诊断等高风险决策时，必须确保所检出异常的可信度。本研究提出VAE-AD检验法，通过在统计检验框架内量化基于VAE的异常检测的统计可靠性。利用VAE-AD检验，VAE检出的异常区域可靠性可以以p值形式量化。这意味着当p值低于特定阈值时判定异常，可将误检概率控制在期望水平。由于VAE-AD检验基于称为选择性推断的新型统计推断框架构建，其有效性在有限样本条件下具有理论保证。为验证所提VAE-AD检验的有效性，本研究在人工数据上进行了数值实验，并开展了脑影像分析的实际应用。