# Bayesian autoencoders with uncertainty quantification: Towards trustworthy anomaly detection

arXiv: https://arxiv.org/abs/2202.12653 · HTML: https://mlsanity.com/paper/2202.12653/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 61 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [Edge AI: On-Demand Accelerating Deep Neural Network Inference via Edge Computing](https://mlsanity.com/paper/1910.05316/) (2019)
- [Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty](https://mlsanity.com/paper/2011.07586/) (2020)
- [Deep Learning for Medical Anomaly Detection -- A Survey](https://mlsanity.com/paper/2012.02364/) (2020)
- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Bayesian Variational Autoencoders for Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/1912.05651/) (2019)
- [Revisiting Bayesian Autoencoders with MCMC](https://mlsanity.com/paper/2104.05915/) (2021)
- [Model Selection for Bayesian Autoencoders](https://mlsanity.com/paper/2106.06245/) (2021)
- [Bayesian Autoencoders for Drift Detection in Industrial Environments](https://mlsanity.com/paper/2107.13249/) (2021)
- [Instance Selection Improves Geometric Mean Accuracy: A Study on Imbalanced Data Classification](https://mlsanity.com/paper/1804.07155/) (2018)
- [Bayesian Autoencoders: Analysing and Fixing the Bernoulli likelihood for Out-of-Distribution Detection](https://mlsanity.com/paper/2107.13304/) (2021)

## Built on by (most cited first, 4 of 4)

- [Explainability through uncertainty: Trustworthy decision-making with neural networks](https://mlsanity.com/paper/2403.10168/) (2024)
- [Graph Evidential Learning for Anomaly Detection](https://mlsanity.com/paper/2506.00594/) (2025)
- [Leveraging Unsupervised Learning for Cost-Effective Visual Anomaly Detection](https://mlsanity.com/paper/2409.15980/) (2024)
- [MSS-PAE: Saving Autoencoder-based Outlier Detection from Unexpected Reconstruction](https://mlsanity.com/paper/2304.00709/) (2023)

## Abstract (arXiv)

Despite numerous studies of deep autoencoders (AEs) for unsupervised anomaly detection, AEs still lack a way to express uncertainty in their predictions, crucial for ensuring safe and trustworthy machine learning systems in high-stake applications. Therefore, in this work, the formulation of Bayesian autoencoders (BAEs) is adopted to quantify the total anomaly uncertainty, comprising epistemic and aleatoric uncertainties. To evaluate the quality of uncertainty, we consider the task of classifying anomalies with the additional option of rejecting predictions of high uncertainty. In addition, we use the accuracy-rejection curve and propose the weighted average accuracy as a performance metric. Our experiments demonstrate the effectiveness of the BAE and total anomaly uncertainty on a set of benchmark datasets and two real datasets for manufacturing: one for condition monitoring, the other for quality inspection.