Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way to use variance-based measures to quantify uncertainty on the basis of second-order distributions in classification problems. A distinctive feature of the measures is the ability to reason about uncertainties on a class-based level, which is useful in situations where nuanced decision-making is required. Recalling some properties from the literature, we highlight that the variance-based measures satisfy important (axiomatic) properties. In addition to this axiomatic approach, we present empirical results showing the measures to be effective and competitive to commonly used entropy-based measures.

翻译：不确定性量化是机器学习模型的关键方面，能提供预测可靠性的重要见解，并辅助实际应用中的决策过程。本文提出了一种基于方差测度的新方法，用于在分类问题中基于二阶分布量化不确定性。该方法的一个显著特点是能够在类别层面推理不确定性，这在需要精细化决策的场景中尤为有用。通过回顾文献中的若干性质，我们强调方差测度满足重要的（公理性）属性。除公理方法外，我们还展示了实证结果，表明这些测度有效且与常用的基于熵的测度相比具有竞争力。