用主观风险分解重新定义不确定性量化，统一了多种测量方法的理论基础。
Subjective Risk Decomposition: A New View for Uncertainty Quantification
- 从严格适当的损失函数出发，通过主观风险分解推导出不确定性项。
- 恢复了经典信息论中的认知与随机不确定性，且覆盖众多已有度量。
- 为不确定性量化提供学习理论视角，适合研究者构建统一框架。
我们提出一种全新的不确定性量化视角：不确定性度量并非需要公理和论证的原始概念，而是高层建模决策的衍生结果。我们展示如何通过基于严格适当损失函数的主观风险分解，推导出认知不确定性与随机不确定性。逆交叉熵是一个显著例子，其分解可重现经典的信息论不确定性项。该方法还能复现文献中大量已提出的度量，为其提供统一的理论基础。这提示了一种新的不确定性量化路径：给定建模场景与严格适当损失，对应的认知与随机项由主观风险分解自然诱导。进一步地，我们将此观点扩展至学习理论，引入并分析了主观风险对超额风险、近似误差与估计误差的类比，揭示其与不确定性量化的内在联系。本文标志着向完整的学习理论框架迈进的第一步。
原文摘要 · Abstract (English)
We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty terms. The same approach recovers numerous measures previously proposed across the UQ literature, providing them a common theoretical foundation. This suggests a new approach to UQ: given a modelling scenario and strictly proper loss, the corresponding epistemic and aleatoric terms are induced by the subjective-risk decomposition. We then extend our view to learning theory: we introduce and analyse subjective risk analogues of excess risk, approximation error and estimation error, and identify the connections to UQ. We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.
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