为回归任务的不确定性度量提供理论框架，验证常用方法的优劣。
An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
- 构建连续空间的参数化不确定性表示，支持严格分析
- 提出一套公理体系，可评估总不确定、偶然和认知不确定性
- 对比熵与方差度量，揭示其在回归中的局限性，适合模型可信度研究者
不确定性量化在机器学习中至关重要，但现有（公理化）研究多集中于分类任务，回归场景缺乏形式化依据和评估。本文提出一种连续空间的通用参数化不确定性表示，支持可计算的分析与评估。在此框架下，我们定义了一组公理，用于严格检验总不确定、偶然不确定和认知不确定的度量方法。以典型预测模型为例，我们比较了广泛使用的基于熵和方差的度量方法，分析其在不确定性量化中的局限与挑战。本工作为监督回归中的不确定性度量提供了原则性方法，提供了理论洞见与可靠评估的实践指南。
原文摘要 · Abstract (English)
Uncertainty quantification is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this work, we provide a formal way of representing uncertainty in continuous space, using a general parametric formulation, allowing for tractable analysis and evaluation of uncertainty measures. Within this framework, we propose a set of axioms that enable rigorous assessment of total, aleatoric, and epistemic uncertainty measures. Together, this allows for a theoretical examination of uncertainty measures and their corresponding properties. As a specific example, we compare the widely used entropy- and variance-based measures with respect to established predictive models and analyze their limitations and challenges in uncertainty quantification. Our work provides a principled way to understand and develop uncertainty measures in supervised regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.
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