# Statistical Test for Anomaly Detections by Variational Auto-Encoders

arXiv: https://arxiv.org/abs/2402.03724 · HTML: https://mlsanity.com/paper/2402.03724/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 37 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Autoencoders for Unsupervised Anomaly Segmentation in Brain MR Images: A Comparative Study](https://mlsanity.com/paper/2004.03271/) (2020)
- [Deep Autoencoding Models for Unsupervised Anomaly Segmentation in Brain MR Images](https://mlsanity.com/paper/1804.04488/) (2018)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Unsupervised Detection of Lesions in Brain MRI using constrained adversarial auto-encoders](https://mlsanity.com/paper/1806.04972/) (2018)
- [Association of genomic subtypes of lower-grade gliomas with shape features automatically extracted by a deep learning algorithm](https://mlsanity.com/paper/1906.03720/) (2019)
- [Deep Learning for Unsupervised Anomaly Localization in Industrial Images: A Survey](https://mlsanity.com/paper/2207.10298/) (2022)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Iterative energy-based projection on a normal data manifold for anomaly localization](https://mlsanity.com/paper/2002.03734/) (2020)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Valid Inference Corrected for Outlier Removal](https://mlsanity.com/paper/1711.10635/) (2017)
- [Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programming](https://mlsanity.com/paper/2002.09132/) (2020)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Computing Valid p-values for Image Segmentation by Selective Inference](https://mlsanity.com/paper/1906.00629/) (2019)
- [Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inference](https://mlsanity.com/paper/2010.01823/) (2020)
- [Anomaly Detection for Skin Disease Images Using Variational Autoencoder](https://mlsanity.com/paper/1807.01349/) (2018)
- [Selecting the number of principal components: estimation of the true rank of a noisy matrix](https://mlsanity.com/paper/1410.8260/) (2014)
- [A significance test for forward stepwise model selection](https://mlsanity.com/paper/1405.3920/) (2014)
- [Selective Sequential Model Selection](https://mlsanity.com/paper/1512.02565/) (2015)
- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [adVAE: A self-adversarial variational autoencoder with Gaussian anomaly prior knowledge for anomaly detection](https://mlsanity.com/paper/1903.00904/) (2019)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Statistical Test for Attention Map in Vision Transformer](https://mlsanity.com/paper/2401.08169/) (2024)

## Built on by (most cited first, 7 of 7)

- [Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inference](https://mlsanity.com/paper/2502.12978/) (2025)
- [Statistical Test for Diffusion-Based Anomaly Localization via Selective Inference](https://mlsanity.com/paper/2402.11789/) (2024)
- [Statistical Test for Saliency Maps of Graph Neural Networks via Selective Inference](https://mlsanity.com/paper/2505.16893/) (2025)
- [Selective Inference for Deep Clustering in Latent Spaces](https://mlsanity.com/paper/2609.28756/) (2026)
- [Statistical testing on generative AI anomaly detection tools in Alzheimer's Disease diagnosis](https://mlsanity.com/paper/2410.13363/) (2024)
- [A statistical perspective on transformers for small longitudinal cohort data](https://mlsanity.com/paper/2602.16914/) (2026)
- [Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selection](https://mlsanity.com/paper/2608.04667/) (2026)

## Abstract (arXiv)

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.