A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration, producing narrow but overconfident predictions. However, in safety-critical settings, trustworthy uncertainty estimates are often more valuable than narrow intervals. Realizing the problem, several recent works have focused on post-hoc corrections; however, existing methods either rely on weak notions of calibration (such as PIT uniformity) or impose restrictive parametric assumptions on the nature of the error. To address these limitations, we propose a novel nonparametric re-calibration algorithm based on conditional kernel mean embeddings, capable of correcting calibration error without restrictive modeling assumptions. For efficient inference with real-valued targets, we introduce a novel characteristic kernel over distributions that can be evaluated in $\mathcal{O}(n \log n)$ time for empirical distributions of size $n$. We demonstrate that our method consistently outperforms prior re-calibration approaches across a diverse set of regression benchmarks and model classes.

翻译：概率回归中的一个关键挑战在于确保预测分布能够准确反映真实的经验不确定性。最小化总体预测误差往往促使模型优先考虑信息性而非校准性，从而产生狭窄但过度自信的预测。然而，在安全关键型应用中，可信的不确定性估计通常比狭窄的区间更有价值。认识到这一问题，近期的一些研究聚焦于事后校正方法；然而，现有方法要么依赖于较弱的校准概念（如概率积分变换均匀性），要么对误差性质施加了限制性的参数假设。为应对这些局限性，我们提出了一种基于条件核均值嵌入的新型非参数重校准算法，该算法能够在没有限制性建模假设的情况下校正校准误差。为实现实值目标的高效推断，我们引入了一种新颖的分布特征核，对于规模为 $n$ 的经验分布，其评估时间复杂度为 $\mathcal{O}(n \log n)$。我们通过实验证明，在多种回归基准测试和模型类别中，我们的方法始终优于先前的重校准方法。