# Neural Bayesian Anomaly Mitigation: A Robust Loss that Doubles as an Unsupervised Contamination Classifier

arXiv: https://arxiv.org/abs/2606.16524 · HTML: https://mlsanity.com/paper/2606.16524/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Probabilistic End-to-end Noise Correction for Learning with Noisy Labels](https://mlsanity.com/paper/1903.07788/) (2019)
- [Radiometer Calibration using Machine Learning](https://mlsanity.com/paper/2504.16791/) (2025)
- [Towards the Identifiability in Noisy Label Learning: A Multinomial Mixture Modelling Approach](https://mlsanity.com/paper/2301.01405/) (2023)
- [Conditional Neural Bayes Ratio Estimation for Experimental Design Optimisation](https://mlsanity.com/paper/2603.26489/) (2026)

## Abstract (arXiv)

Engineered robust losses such as Huber, Student-t, and generalised cross-entropy make supervised models tolerant of contamination but cannot answer which observations are corrupted. We introduce Neural Bayesian Anomaly Mitigation (NBAM), a general-purpose drop-in loss derived from a Bayesian latent-switch mixture model: the marginal likelihood defines a robust supervised loss, and the associated posterior defines an unsupervised contamination classifier. Like Huber or Student-t, NBAM can replace the standard training loss in any supervised pipeline; unlike them, it additionally learns a structured contamination model and returns a calibrated per-sample contamination posterior. A learned input-dependent prior πφ(x) captures the spatial locality of contamination, so that samples near known corruptions are more likely to be flagged, while an Occam penalty emerges automatically and regularises against over-flagging. On CIFAR-10 with asymmetric label contamination, NBAM recovers the structure of the corruption process without supervision: the contamination posterior separates clean from corrupted samples, and the learned anomaly head identifies the direction of every label-flip pair. Alongside these capabilities, NBAM outperforms the four robust-loss baselines considered here at contamination rates 0.2-0.6.