视情况而定：纳入高维输出空间的偶然不确定性与认知不确定性的相关性
It depends: Incorporating correlations for joint aleatoric and epistemic uncertainties of high-dimensional output spaces
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中文总结 AI 辅助
该研究针对高维输出空间的深度学习，提出低秩加对角协方差结构的联合不确定性建模方法，实现偶然与认知不确定性的统一，在多项视觉任务中提升了不确定性量化效果。
中文摘要 AI 辅助
不确定性量化（UQ）对于提升深度学习模型预测的可靠性至关重要，尤其适用于高维输出空间场景。本文针对不确定性的双重属性——偶然不确定性与认知不确定性，聚焦于二者在高维回归任务中的联合整合。例如，在医学图像分割或复原等应用中，偶然不确定性捕捉固有数据噪声，认知不确定性量化模型对陌生场景的置信度。联合建模二者可通过反映不可避免的变异性与知识缺口，实现更可靠的预测，而仅建模其中一种则会降低透明度与鲁棒性。我们提出一种新方法，采用低秩加对角协方差结构近似联合不确定性，在捕捉关键输出相关性的同时，避免了全协方差矩阵的计算负担。与现有工作不同，我们的方法明确将偶然与认知不确定性整合为统一的二阶分布，支持采样、对数似然评估等鲁棒下游分析。我们进一步引入稳定策略以实现高效训练与推理，在图像修复、上色、光流及深度估计任务中取得了优异的不确定性量化效果。
英文摘要
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.
