提出基于距离的量化方法，区分并计算机器学习中的两种不确定性。
Quantification of Credal Uncertainty: A Distance-Based Approach
- 用积分概率度量框架定义不确定性度量，理论清晰且可计算。
- 在多分类任务中实现总不确定性和两类子不确定性的量化，计算高效。
- 适用于需要可靠置信度估计的场景，如医疗诊断或自动驾驶。
可信集（credal sets），即概率测度的闭凸集，为机器学习中的随机性与认知不确定性提供了自然的表达框架。然而，如何对给定的可信集量化这两种不确定性，特别是在多分类任务中，仍缺乏深入研究。本文提出一种基于距离的框架，用于量化可信集的总不确定性、随机性不确定性与认知不确定性。具体地，我们在积分概率度量（IPMs）框架下引入一类度量方法，所得结果具有明确语义、满足自然理论性质，且对常见的IPM选择保持计算可处理性。我们以总变差距离为例进行实例化，在多分类任务中得到简单高效的不确定性度量；在二分类情形下，该方法恢复了已有成熟度量，而此前尚无严谨的多分类推广。实验验证了其实际有效性，在低计算成本下表现优异。
原文摘要 · Abstract (English)
Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.
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