Well-Calibrated Regression Uncertainty in Medical Imaging with Deep Learning

The consideration of predictive uncertainty in medical imaging with deep learning is of utmost importance. We apply estimation of predictive uncertainty by variational Bayesian inference with Monte Carlo dropout to regression tasks and show why predictive uncertainty is systematically underestimated. We suggest using $ \sigma $ {\em scaling} with a single scalar value; a simple, yet effective calibration method for both aleatoric and epistemic 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 all 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: {https://github.com/mlaves/well-calibrated-regression-uncertainty}