# WAIC, but Why? Generative Ensembles for Robust Anomaly Detection

arXiv: https://arxiv.org/abs/1810.01392 · HTML: https://mlsanity.com/paper/1810.01392/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2018.

## Built on by (most cited first, 25 of 25)

- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challenges](https://mlsanity.com/paper/2110.14051/) (2021)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [A Style and Semantic Memory Mechanism for Domain Generalization](https://mlsanity.com/paper/2112.07517/) (2021)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Igeood: An Information Geometry Approach to Out-of-Distribution Detection](https://mlsanity.com/paper/2203.07798/) (2022)
- [Towards Textual Out-of-Domain Detection without In-Domain Labels](https://mlsanity.com/paper/2203.11396/) (2022)
- [Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributions](https://mlsanity.com/paper/2105.04471/) (2021)
- [Out-of-distribution detection algorithms for robust insect classification](https://mlsanity.com/paper/2305.01823/) (2023)
- [OOD Aware Supervised Contrastive Learning](https://mlsanity.com/paper/2310.01942/) (2023)
- [Distribution Awareness for AI System Testing](https://mlsanity.com/paper/2105.02540/) (2021)
- [Unsupervised Class-Incremental Learning Through Confusion](https://mlsanity.com/paper/2104.04450/) (2021)
- [PViT: Prior-augmented Vision Transformer for Out-of-distribution Detection](https://mlsanity.com/paper/2410.20631/) (2024)
- [DOSE3 : Diffusion-based Out-of-distribution detection on SE(3) trajectories](https://mlsanity.com/paper/2502.16725/) (2025)
- [Robust Out-of-Distribution Detection on Deep Probabilistic Generative Models](https://mlsanity.com/paper/2106.07903/) (2021)
- [Gradient-based Counterfactual Explanations using Tractable Probabilistic Models](https://mlsanity.com/paper/2205.07774/) (2022)
- [A Functional Data Perspective and Baseline On Multi-Layer Out-of-Distribution Detection](https://mlsanity.com/paper/2306.03522/) (2023)
- [Out-of-distribution Object Detection through Bayesian Uncertainty Estimation](https://mlsanity.com/paper/2310.19119/) (2023)
- [Advancing Out-of-Distribution Detection through Data Purification and Dynamic Activation Function Design](https://mlsanity.com/paper/2403.03412/) (2024)
- [SincVAE: A new semi-supervised approach to improve anomaly detection on EEG data using SincNet and variational autoencoder](https://mlsanity.com/paper/2406.17537/) (2024)
- [Tree-based Ensemble Learning for Out-of-distribution Detection](https://mlsanity.com/paper/2405.03060/) (2024)
- [Statistical inference for quantum singular models](https://mlsanity.com/paper/2411.16396/) (2024)
- [Predictive Sample Assignment for Semantically Coherent Out-of-Distribution Detection](https://mlsanity.com/paper/2512.12906/) (2025)
- [DAVIS: OOD Detection via Dominant Activations and Variance for Increased Separation](https://mlsanity.com/paper/2601.22703/) (2026)

## Abstract (arXiv)

Machine learning models encounter Out-of-Distribution (OoD) errors when the data seen at test time are generated from a different stochastic generator than the one used to generate the training data. One proposal to scale OoD detection to high-dimensional data is to learn a tractable likelihood approximation of the training distribution, and use it to reject unlikely inputs. However, likelihood models on natural data are themselves susceptible to OoD errors, and even assign large likelihoods to samples from other datasets. To mitigate this problem, we propose Generative Ensembles, which robustify density-based OoD detection by way of estimating epistemic uncertainty of the likelihood model. We present a puzzling observation in need of an explanation -- although likelihood measures cannot account for the typical set of a distribution, and therefore should not be suitable on their own for OoD detection, WAIC performs surprisingly well in practice.