提出基于高密度区域的不确定性量化新方法，更符合实际决策需求。
On the QUEST for Uncertainty Quantification via Highest Density Regions
- 用分布峰值附近最可能子集的体积衡量不确定性
- 在多个基准上优于方差和微分熵等传统指标
- 满足不确定性量化的可扩展性与平移不变性等公理
不确定性量化（UQ）对安全关键场景中的概率机器学习至关重要。现有标量UQ方法（如基于合适评分规则的方法）通过点预测风险度量不确定性，但在目标统计量非条件期望时可能导致反直觉结果。本文提出新框架QUEST（基于最高密度区域的不确定性量化），以分布支撑集上最可能子集的勒贝格测度集中程度来刻画不确定性，通过一个或多个鲁棒参数α进行评估。该方法与信息论和经济学中的经典统计量建立联系，并证明其在认知不确定性和随机不确定性度量上满足一组经适配的公理，包括分布扩散下的单调性及位置平移不变性。选择性预测基准测试表明，QUEST在性能上优于方差、微分熵等标准方法。
原文摘要 · Abstract (English)
Uncertainty quantification (UQ) is essential for reliable decision-making in safety-critical applications in probabilistic machine learning. For regression problems, dominant scalar UQ approaches - notably, those based on proper scoring rules - measure uncertainty via pointwise predictive risk. This can lead to counterintuitive results when the target statistic is not the conditional expectation. We propose an alternative framework, in which uncertainty is characterised by the volume of the most probable subset of a distribution's support. QUEST (Quantifying Uncertainty via highest dEnSiTy regions) is a novel approach to UQ based on the concentration of Lebesgue measure at a distribution's peak(s), evaluated at one or more values of a robustness parameter $α$. We establish connections between our measures and classical statistics from information theory and economics. We show that, unlike popular alternatives based on proper scoring rules, QUEST measures of epistemic and aleatoric uncertainty satisfy a set of axioms adapted from the UQ literature, including monotonicity under distributional spread and invariance to location shifts. Selective prediction benchmarks confirm that QUEST performs favourably against standard measures such as variance and differential entropy.
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