发表机构
The University of Manchester; University of Warwick（曼彻斯特大学; 沃里克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出不确定性量化新观点，基于严格恰当损失通过主观风险分解推导认知和偶然不确定性度量，恢复众多UQ度量并提供理论基础，还扩展到学习理论，为不确定性量化完整学习理论框架迈出第一步。
AI 中文摘要
我们提出了一种用于不确定性量化的新观点。不确定性度量并非需要公理和论证的基本要素，而是更高层次建模决策的结果。我们展示了如何基于严格恰当损失，通过主观风险分解来推导认知和偶然不确定性度量。反向交叉熵就是一个突出例子，分解可恢复经典信息论不确定性项。同样的方法能恢复UQ文献中先前提出的众多度量，为它们提供共同理论基础。从实践角度看，这为UQ提出了新方法：给定建模场景和严格恰当损失，由主观风险分解诱导出相应认知和偶然项。我们还将观点扩展到学习理论：引入并分析了超额风险、近似误差和估计误差的主观风险类似物，并确定了它们与UQ的联系。我们认为这是迈向不确定性量化完整学习理论框架的第一步。
英文摘要
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.
Comments36 pages (including bibliography/appendix)
