It depends: Incorporating correlations for joint aleatoric and epistemic uncertainties of high-dimensional output spaces

TMLR Paper6948 Authors

Abstract: Uncertainty Quantification 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 Uncertainty Quantification in the tasks of image inpainting, colorization, and optical flow estimation.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Jes_Frellsen1

Submission Number: 6948