# Maximum Likelihood Uncertainty Estimation: Robustness to Outliers

arXiv: https://arxiv.org/abs/2202.03870 · HTML: https://mlsanity.com/paper/2202.03870/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 27 of 27)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [Image Classification with Deep Learning in the Presence of Noisy Labels: A Survey](https://mlsanity.com/paper/1912.05170/) (2019)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Analyzing the Role of Model Uncertainty for Electronic Health Records](https://mlsanity.com/paper/1906.03842/) (2019)
- [Safely Entering the Deep: A Review of Verification and Validation for Machine Learning and a Challenge Elicitation in the Automotive Industry](https://mlsanity.com/paper/1812.05389/) (2018)
- [On the Robustness of Monte Carlo Dropout Trained with Noisy Labels](https://mlsanity.com/paper/2103.12002/) (2021)
- [DeepGUM: Learning Deep Robust Regression with a Gaussian-Uniform Mixture Model](https://mlsanity.com/paper/1808.09211/) (2018)
- [Robust and Accurate Inference via a Mixture of Gaussian and Student's t Errors](https://mlsanity.com/paper/1707.03057/) (2017)
- [Towards Using Probabilistic Models to Design Software Systems with Inherent Uncertainty](https://mlsanity.com/paper/2008.03046/) (2020)

## Built on by (most cited first, 6 of 6)

- [A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation Estimation](https://mlsanity.com/paper/2303.01743/) (2023)
- [Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution](https://mlsanity.com/paper/2305.10465/) (2023)
- [Robust Long-Range Perception Against Sensor Misalignment in Autonomous Vehicles](https://mlsanity.com/paper/2408.11196/) (2024)
- [A Deep Learning Approach to Estimate Canopy Height and Uncertainty by Integrating Seasonal Optical, SAR and Limited GEDI LiDAR Data over Northern Forests](https://mlsanity.com/paper/2410.18108/) (2024)
- [Probabilistic MIMO U-Net: Efficient and Accurate Uncertainty Estimation for Pixel-wise Regression](https://mlsanity.com/paper/2308.07477/) (2023)
- [Fundamentals of Regression](https://mlsanity.com/paper/2512.01920/) (2025)

## Abstract (arXiv)

We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect estimation of uncertainty. We propose the use of a heavy-tailed distribution (Laplace distribution) to improve the robustness to outliers. This property is evaluated using standard regression benchmarks and on a high-dimensional regression task of monocular depth estimation, both containing outliers. In particular, heavy-tailed distribution based maximum likelihood provides better uncertainty estimates, better separation in uncertainty for out-of-distribution data, as well as better detection of adversarial attacks in the presence of outliers.