Bayesian Uncertainty Estimation by Hamiltonian Monte Carlo: Applications to Cardiac MRI Segmentation
This work addresses the critical need for reliable uncertainty estimation in deep learning for medical imaging to enhance trustworthiness in clinical applications, though it is incremental as it builds on existing Bayesian methods.
The paper tackles the problem of overconfidence and miscalibration in deep neural networks for medical image segmentation, which can lead to risky silent failures in clinical applications, by proposing a Bayesian learning framework using Hamiltonian Monte Carlo with cold posterior (HMC-CP) that improves segmentation accuracy and uncertainty estimation for in- and out-of-domain cardiac MRI data compared to baseline methods like Monte Carlo Dropout and Deep Ensembles.
Deep learning (DL)-based methods have achieved state-of-the-art performance for many medical image segmentation tasks. Nevertheless, recent studies show that deep neural networks (DNNs) can be miscalibrated and overconfident, leading to "silent failures" that are risky for clinical applications. Bayesian DL provides an intuitive approach to DL failure detection, based on posterior probability estimation. However, the posterior is intractable for large medical image segmentation DNNs. To tackle this challenge, we propose a Bayesian learning framework using Hamiltonian Monte Carlo (HMC), tempered by cold posterior (CP) to accommodate medical data augmentation, named HMC-CP. For HMC computation, we further propose a cyclical annealing strategy, capturing both local and global geometries of the posterior distribution, enabling highly efficient Bayesian DNN training with the same computational budget as training a single DNN. The resulting Bayesian DNN outputs an ensemble segmentation along with the segmentation uncertainty. We evaluate the proposed HMC-CP extensively on cardiac magnetic resonance image (MRI) segmentation, using in-domain steady-state free precession (SSFP) cine images as well as out-of-domain datasets of quantitative T1 and T2 mapping. Our results show that the proposed method improves both segmentation accuracy and uncertainty estimation for in- and out-of-domain data, compared with well-established baseline methods such as Monte Carlo Dropout and Deep Ensembles. Additionally, we establish a conceptual link between HMC and the commonly known stochastic gradient descent (SGD) and provide general insight into the uncertainty of DL. This uncertainty is implicitly encoded in the training dynamics but often overlooked. With reliable uncertainty estimation, our method provides a promising direction toward trustworthy DL in clinical applications.