Recalibration of Aleatoric and EpistemicRegression Uncertainty in Medical Imaging

Max-Heinrich Laves1,20000-0003-0156-7247, Sontje Ihler2, Jacob F. Fast2,30000-0002-0651-8279, Lüder A. Kahrs4,50000-0001-5506-2768, Tobias Ortmaier20000-0003-1644-3685
1: Institute of Medical Technology and Intelligent Systems, Hamburg University of Technology, 2: Institute of Mechatronic Systems, Leibniz Universit ̈at Hannover, 3: Hannover Medical School, 4: Centre for Image Guided Innovation and Therapeutic Intervention, The Hospital for Sick Children, Toronto, 5: Department of Mathematical and Computational Sciences, University of Toronto Mississauga
Publication date: 2021/04/28
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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 sigma 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, sigma 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:


bayesian approximation · variational inference

Bibtex @article{melba:2021:008:laves, title = "Recalibration of Aleatoric and EpistemicRegression Uncertainty in Medical Imaging", author = "Laves, Max-Heinrich and Ihler, Sontje and Fast, Jacob F. and Kahrs, Lüder A. and Ortmaier, Tobias", journal = "Machine Learning for Biomedical Imaging", volume = "1", issue = "MIDL 2020 special issue", year = "2021", pages = "1--26", issn = "2766-905X", doi = "", url = "" }
RISTY - JOUR AU - Laves, Max-Heinrich AU - Ihler, Sontje AU - Fast, Jacob F. AU - Kahrs, Lüder A. AU - Ortmaier, Tobias PY - 2021 TI - Recalibration of Aleatoric and EpistemicRegression Uncertainty in Medical Imaging T2 - Machine Learning for Biomedical Imaging VL - 1 IS - MIDL 2020 special issue SP - 1 EP - 26 SN - 2766-905X DO - UR - ER -

2021:008 cover