# Aleatoric uncertainty for Errors-in-Variables models in deep regression

arXiv: https://arxiv.org/abs/2105.09095 · HTML: https://mlsanity.com/paper/2105.09095/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 19 May 2021.

## Builds on (most cited first, 18 of 18)

- [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)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [The Limits and Potentials of Deep Learning for Robotics](https://mlsanity.com/paper/1804.06557/) (2018)
- [Noisy Natural Gradient as Variational Inference](https://mlsanity.com/paper/1712.02390/) (2017)
- [Deep Learning in Robotics: A Review of Recent Research](https://mlsanity.com/paper/1707.07217/) (2017)
- [Early Stopping is Nonparametric Variational Inference](https://mlsanity.com/paper/1504.01344/) (2015)
- [Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurements](https://mlsanity.com/paper/2103.01259/) (2021)
- [Input Modeling and Uncertainty Quantification for Improving Volatile Residential Load Forecasting](https://mlsanity.com/paper/1905.06773/) (2019)

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

- [A metrological framework for uncertainty evaluation in machine learning classification models](https://mlsanity.com/paper/2504.03359/) (2025)
- [Analytical results for uncertainty propagation through trained machine learning regression models](https://mlsanity.com/paper/2404.11224/) (2024)
- [An uncertainty-aware Bayesian framework for machine learning classification models: A case study in land cover classification](https://mlsanity.com/paper/2503.21510/) (2025)
- [Quantifying Uncertainty in Deep Learning Classification with Noise in Discrete Inputs for Risk-Based Decision Making](https://mlsanity.com/paper/2310.06105/) (2023)

## Abstract (arXiv)

A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also account for the uncertainty associated with the input of the employed neural network. The presented approach thereby exploits a relevant, but generally overlooked, source of uncertainty and yields a decomposition of the predictive uncertainty into an aleatoric and epistemic part that is more complete and, in many cases, more consistent from a statistical perspective. We discuss the approach along various simulated and real examples and observe that using an Errors-in-Variables model leads to an increase in the uncertainty while preserving the prediction performance of models without Errors-in-Variables. For examples with known regression function we observe that this ground truth is substantially better covered by the Errors-in-Variables model, indicating that the presented approach leads to a more reliable uncertainty estimation.