This paper proposes a novel approach that approximates the resulting joint uncertainty using a low-rank plus diagonal covariance structure, capturing essential output correlations while avoiding the computational burdens of full covariance matrices.
Abstract
Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-dimensional output spaces. This paper addresses the dual nature of uncertainty -- aleatoric and epistemic -- focusing on their joint integration in high-dimensional regression tasks. For example, in applications like medical image segmentation or restoration, aleatoric uncertainty captures inherent data noise, while epistemic uncertainty quantifies the model's confidence in unfamiliar conditions. Modeling both jointly enables more reliable predictions by reflecting both unavoidable variability and knowledge gaps, whereas modeling only one limits transparency and robustness. We propose a novel approach that approximates the resulting joint uncertainty using a low-rank plus diagonal covariance structure, capturing essential output correlations while avoiding the computational burdens of full covariance matrices. Unlike prior work, our method explicitly combines aleatoric and epistemic uncertainties into a unified second-order distribution that supports robust downstream analyses like sampling and log-likelihood evaluation. We further introduce stabilization strategies for efficient training and inference, achieving superior UQ in the tasks of image inpainting, colorization, optical flow, and depth estimation.
These findings expose a fundamental mismatch between the theoretical promise of aleatoric uncertainty and its practical behavior, and suggest that practitioners should not rely on entropy-based uncertainty as a proxy for clinical ambiguity in safety-critical applications.
Simon Baur, Arne Schernich, Ekin Böke et al.· 1 citation
UCBound-Net is introduced, a continual segmentation framework that exploits Monte Carlo (MC) Dropout uncertainty as a spatial proxy for forgetting risk and outperforms baseline methods without requiring task-boundary supervision.
Diffusion Magnetic Resonance Imaging (dMRI) is a powerful tool for probing brain microstructure, but clinical acquisitions are often limited by low out-of-plane resolution, resulting in degraded structural information and reduced utility for advanced analysis. We introduce SIINR (Structurally Informed Implicit Neural Representations), a general framework for super-resoltion of clinical dMRI datasets while quantifying uncertainty in the reconstructed outputs. SIINR utilizes a supervised 3D U-net as a prior and combines it with a self-supervised implicit neural representation (INR) that fuses the high-resolution prior and the original low-resolution data. The INR enables joint modeling across spatial and angular domains, enforces data consistency, and provides analytic approximate posterior distributions for downstream uncertainty quantification. We validate the framework on a diverse set of open-access dMRI datasets, demonstrating that SIINR outperforms standard interpolation methods in both quantitative error metrics and qualitative anatomical fidelity. Experiments on clinical cases, including subjects with multiple sclerosis and brain lesions, illustrate the framework its ability to propagate intensity changes and flag uncertain regions in challenging scenarios. SIINR is flexible, modular, and can be adapted to different upsampling ratios and downstream tasks, providing a principled approach for enhancing clinical dMRI and supporting robust interpretation of derived neuroimaging metrics.
Tom Hendriks, William Consagra, Anna Vilanova et al.· arXiv.org· 0 citations
A comprehensive survey of UQ techniques in medical image segmentation is presented, categorizing existing approaches into Bayesian methods, deep ensembles, deterministic methods, test-time data augmentation, and hybrid models, while treating foundation-model-based UQ as a separate cross-cutting category.
Seyed Sina Ziaee, K. Ovens· Journal of Imaging· 0 citations
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction error and strongly influence engineering decisions. Because distinguishing and representing each source separately is often infeasible, their combined effect is typically analyzed using a unified model-error framework. Model error directly affects model credibility and predictive reliability, yet its characterization remains challenging. To address this need, we introduce a bootstrap-based stochastic subspace model for characterizing model error in the stochastic reduced-order modeling framework. Given a snapshot matrix of state vectors, the method leverages the empirical data distribution to induce a sampling distribution over principal subspaces for reduced order modeling. The resulting stochastic model enables improved characterization of model error in computational mechanics compared with existing approaches. The method offers several advantages: (1) it is assumption-free and leverages the empirical data distribution; (2) it enforces linear constraints (such as boundary conditions) by construction; (3) it requires only one hyperparameter, significantly simplifying the training process; and (4) its algorithm is straightforward to implement. We evaluate the method’s performance against existing approaches using numerical examples in computational mechanics and structural dynamics.
Quantitative MRI (qMRI) provides standardised tissue parameter maps, but the reliability of deep learning-based qMRI mapping methods is often not explicitly characterised. In this work we systematically evaluate uncertainty maps for quantitative MRI derived from multiple inferences of a data-consistent diffusion model-based qMRI framework. Evaluation on synthetic test data assessed error-awareness, high-error detection, selective prediction, and Gaussian interval calibration. Diffusion model-derived uncertainty was positively associated with the mapping error, while risk-coverage analysis showed that excluding high-uncertainty voxels reduced the retained error. However, the raw uncertainty was poorly calibrated for quantitative interval interpretation. Calibration was substantially improved using a post-hoc procedure combining prediction-value-dependent bias correction with scalar uncertainty scaling. Qualitative evaluation on a healthy volunteer showed spatially meaningful uncertainty patterns. These results indicate that diffusion model-derived uncertainty is informative for reliability assessment and selective prediction, but requires calibration for quantitative interval interpretation.
Shishuai Wang, S. Klein, J. Hernandez-Tamames et al.· 0 citations
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