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：本研究探讨了利用变分自编码器进行异常检测时的可靠性评估问题。过去十年间，基于VAE的异常检测从方法开发到应用研究均取得了长足进展，但当检测结果用于高风险决策场景（如医学诊断）时，确保异常发现的统计可靠性至关重要。本文提出VAE-AD检验方法，在统计检验框架下量化VAE异常检测的统计可靠性。通过该检验方法，VAE检测出的异常区域可靠性能以p值形式量化表达。这意味着当p值低于预设阈值时声明存在异常，可有效控制误检概率至期望水平。由于VAE-AD检验基于选择性推断这一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。通过人工数据数值实验与脑图像分析应用，验证了所提方法的有效性与实用性。