提出统一框架，用核函数量化回归不确定性。
Uncertainty Quantification for Regression: A Unified Framework based on kernel scores
- 基于严格合适的核得分，构建多维回归的不确定性度量
- 不同核函数导致不同权衡，实验验证其在分布外检测等任务有效
- 为安全关键领域提供可解释的不确定性设计指南
回归任务，特别是在安全关键领域，需要可靠的不确定性量化，但现有研究仍以分类为主。为此，我们基于严格合适的核得分，提出一类用于多维回归的总不确定性、随机性不确定性和认知不确定性度量。该框架为设计新不确定性度量提供系统方法，其行为（如尾部敏感性或分布外响应）由底层核函数决定，同时将现有度量纳入统一分析。我们证明了核函数性质与度量行为之间的显式对应关系，为实践者提供具体设计指导。在结构化回归任务（包括空间和函数域）上的大量实验表明，该方法在分布外检测和主动学习等下游任务中表现优异，且不同核选择带来不同权衡，为任务特定选型提供依据。
原文摘要 · Abstract (English)
Regression tasks, notably in safety-critical domains, require reliable uncertainty quantification, yet the literature remains largely classification-focused. To address this, we introduce a family of measures for total, aleatoric, and epistemic uncertainty in multivariate regression based on strictly proper kernel scores. The framework provides a principled recipe for designing new uncertainty measures whose behavior, such as tail sensitivity or out-of-distribution responsiveness, is governed by the choice of the underlying kernel, while also encompassing existing measures under a joint analysis. We prove explicit correspondences between properties of the kernel and behavior of resulting uncertainty measures, yielding concrete design guidelines for practitioners. Extensive experiments across structured regression tasks, including spatial and functional domains, demonstrate effectiveness on downstream tasks such as out-of-distribution detection and active learning, and reveal that different kernel choices lead to distinct trade-offs, offering practitioners guidance for task-specific selection.
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