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

2026-08-25

AI Summary

本文提出一种新方法，通过低秩加对角协方差结构联合建模高维输出空间中的偶然和认知不确定性，以提高深度学习模型预测的可靠性。

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.

Problem

• Uncertainty Quantification
• high-dimensional output spaces
• aleatoric and epistemic uncertainties
• reliable predictions

Innovation

• uncertainty quantification
• aleatoric and epistemic uncertainties
• low-rank plus diagonal covariance
• high-dimensional output spaces
• stabilization strategies