# Diffusion Tensor Estimation with Uncertainty Calibration

arXiv: https://arxiv.org/abs/2111.10847 · HTML: https://mlsanity.com/paper/2111.10847/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 54 references that are in the map.
- First posted on arXiv 21 Nov 2021.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Uncertainty Toolbox: an Open-Source Library for Assessing, Visualizing, and Improving Uncertainty Quantification](https://mlsanity.com/paper/2109.10254/) (2021)
- [Individual Calibration with Randomized Forecasting](https://mlsanity.com/paper/2006.10288/) (2020)
- [Calibrated Reliable Regression using Maximum Mean Discrepancy](https://mlsanity.com/paper/2006.10255/) (2020)
- [SuperDTI: Ultrafast diffusion tensor imaging and fiber tractography with deep learning](https://mlsanity.com/paper/2002.01031/) (2020)

## Abstract (arXiv)

It is highly desirable to know how uncertain a model's predictions are, especially for models that are complex and hard to understand as in deep learning. Although there has been a growing interest in using deep learning methods in diffusion-weighted MRI, prior works have not addressed the issue of model uncertainty. Here, we propose a deep learning method to estimate the diffusion tensor and compute the estimation uncertainty. Data-dependent uncertainty is computed directly by the network and learned via loss attenuation. Model uncertainty is computed using Monte Carlo dropout. We also propose a new method for evaluating the quality of predicted uncertainties. We compare the new method with the standard least-squares tensor estimation and bootstrap-based uncertainty computation techniques. Our experiments show that when the number of measurements is small the deep learning method is more accurate and its uncertainty predictions are better calibrated than the standard methods. We show that the estimation uncertainties computed by the new method can highlight the model's biases, detect domain shift, and reflect the strength of noise in the measurements. Our study shows the importance and practical value of modeling prediction uncertainties in deep learning-based diffusion MRI analysis.