# Bayesian Uncertainty Estimation by Hamiltonian Monte Carlo: Applications to Cardiac MRI Segmentation

arXiv: https://arxiv.org/abs/2403.02311 · HTML: https://mlsanity.com/paper/2403.02311/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 67 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Builds on (most cited first, 30 of 39)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Aleatoric uncertainty estimation with test-time augmentation for medical image segmentation with convolutional neural networks](https://mlsanity.com/paper/1807.07356/) (2018)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Confidence Calibration and Predictive Uncertainty Estimation for Deep Medical Image Segmentation](https://mlsanity.com/paper/1911.13273/) (2019)
- [Deep learning for cardiac image segmentation: A review](https://mlsanity.com/paper/1911.03723/) (2019)
- [PHiSeg: Capturing Uncertainty in Medical Image Segmentation](https://mlsanity.com/paper/1906.04045/) (2019)
- [Assessing Reliability and Challenges of Uncertainty Estimations for Medical Image Segmentation](https://mlsanity.com/paper/1907.03338/) (2019)
- [Is SGD a Bayesian sampler? Well, almost](https://mlsanity.com/paper/2006.15191/) (2020)
- [On Uncertainty, Tempering, and Data Augmentation in Bayesian Classification](https://mlsanity.com/paper/2203.16481/) (2022)
- [BayeSeg: Bayesian Modeling for Medical Image Segmentation with Interpretable Generalizability](https://mlsanity.com/paper/2303.01710/) (2023)

## Built on by (most cited first, 1 of 1)

- [Lost in Tracking: Uncertainty-guided Cardiac Cine MRI Segmentation at Right Ventricle Base](https://mlsanity.com/paper/2410.03320/) (2024)

## Abstract (arXiv)

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.