Uncertainty Quantification for Regression: A Unified Framework based on kernel scores
This work addresses uncertainty quantification for regression in safety-critical domains, offering a principled framework that is incremental in unifying and extending existing methods.
The paper tackles the problem of uncertainty quantification in regression tasks, which is underdeveloped compared to classification, by introducing a unified framework based on kernel scores that unifies existing measures and provides design guidelines, with experiments showing effectiveness in downstream tasks and trade-offs among instantiations.
Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic uncertainty based on proper scoring rules, with a particular emphasis on kernel scores. The framework unifies several well-known measures and provides a principled recipe for designing new ones whose behavior, such as tail sensitivity, robustness, and out-of-distribution responsiveness, is governed by the choice of kernel. We prove explicit correspondences between kernel-score characteristics and downstream behavior, yielding concrete design guidelines for task-specific measures. Extensive experiments demonstrate that these measures are effective in downstream tasks and reveal clear trade-offs among instantiations, including robustness and out-of-distribution detection performance.