# Recalibration of Aleatoric and Epistemic Regression Uncertainty in Medical Imaging

arXiv: https://arxiv.org/abs/2104.12376 · HTML: https://mlsanity.com/paper/2104.12376/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 26 Apr 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Integrating Spatial Configuration into Heatmap Regression Based CNNs for Landmark Localization](https://mlsanity.com/paper/1908.00748/) (2019)
- [Well-calibrated Model Uncertainty with Temperature Scaling for Dropout Variational Inference](https://mlsanity.com/paper/1909.13550/) (2019)
- [Bayesian Image Quality Transfer with CNNs: Exploring Uncertainty in dMRI Super-Resolution](https://mlsanity.com/paper/1705.00664/) (2017)
- [On the Applicability of Registration Uncertainty](https://mlsanity.com/paper/1803.05266/) (2018)
- [Stochastic Deep Compressive Sensing for the Reconstruction of Diffusion Tensor Cardiac MRI](https://mlsanity.com/paper/1805.12064/) (2018)
- [Calibrating Uncertainties in Object Localization Task](https://mlsanity.com/paper/1811.11210/) (2018)
- [Uncertainty in multitask learning: joint representations for probabilistic MR-only radiotherapy planning](https://mlsanity.com/paper/1806.06595/) (2018)
- [Automatic kidney segmentation in ultrasound images using subsequent boundary distance regression and pixelwise classification networks](https://mlsanity.com/paper/1811.04815/) (2018)
- [A Deep Learning Approach for Pose Estimation from Volumetric OCT Data](https://mlsanity.com/paper/1803.03852/) (2018)

## Built on by (most cited first, 18 of 18)

- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [Uncertainty Estimation and Propagation in Accelerated MRI Reconstruction](https://mlsanity.com/paper/2308.02631/) (2023)
- [An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression](https://mlsanity.com/paper/2504.18433/) (2025)
- [Uncertainty Quantification for Molecular Property Predictions with Graph Neural Architecture Search](https://mlsanity.com/paper/2307.10438/) (2023)
- [Reliable Neural Networks for Regression Uncertainty Estimation](https://mlsanity.com/paper/2109.08213/) (2021)
- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)
- [Overcoming the Limitations of Localization Uncertainty: Efficient & Exact Non-Linear Post-Processing and Calibration](https://mlsanity.com/paper/2306.08981/) (2023)
- [Bayesian optimized deep ensemble for uncertainty quantification of deep neural networks: a system safety case study on sodium fast reactor thermal stratification modeling](https://mlsanity.com/paper/2412.08776/) (2024)
- [Unsupervised Knowledge-Transfer for Learned Image Reconstruction](https://mlsanity.com/paper/2107.02572/) (2021)
- [How inter-rater variability relates to aleatoric and epistemic uncertainty: a case study with deep learning-based paraspinal muscle segmentation](https://mlsanity.com/paper/2308.06964/) (2023)
- [Posterior temperature optimized Bayesian models for inverse problems in medical imaging](https://mlsanity.com/paper/2202.00986/) (2022)
- [Towards Reliable Uncertainty Quantification via Deep Ensembles in Multi-output Regression Task](https://mlsanity.com/paper/2303.16210/) (2023)
- [Cost-Sensitive Uncertainty-Based Failure Recognition for Object Detection](https://mlsanity.com/paper/2404.17427/) (2024)
- [PULPo: Probabilistic Unsupervised Laplacian Pyramid Registration](https://mlsanity.com/paper/2407.10567/) (2024)
- [Reduced Order Probabilistic Emulation for Physics-Based Thermosphere Models](https://mlsanity.com/paper/2211.04392/) (2022)
- [Probabilistic Feature Imputation and Uncertainty-Aware Multimodal Federated Aggregation](https://mlsanity.com/paper/2604.12970/) (2026)
- [Estimation of River Water Surface Elevation Using UAV Photogrammetry and Machine Learning](https://mlsanity.com/paper/2306.06118/) (2023)
- [A Calibration Audit of Confidence in Feed-Forward 3D Reconstruction Models](https://mlsanity.com/paper/2608.29705/) (2026)

## Abstract (arXiv)

The consideration of predictive uncertainty in medical imaging with deep learning is of utmost importance. We apply estimation of both aleatoric and epistemic uncertainty by variational Bayesian inference with Monte Carlo dropout to regression tasks and show that predictive uncertainty is systematically underestimated. We apply  σ  scaling with a single scalar value; a simple, yet effective calibration method for both types of uncertainty. The performance of our approach is evaluated on a variety of common medical regression data sets using different state-of-the-art convolutional network architectures. In our experiments,  σ  scaling is able to reliably recalibrate predictive uncertainty. It is easy to implement and maintains the accuracy. Well-calibrated uncertainty in regression allows robust rejection of unreliable predictions or detection of out-of-distribution samples. Our source code is available at https://github.com/mlaves/well-calibrated-regression-uncertainty