Conformal regression provides prediction intervals with global coverage guarantees, but often fails to capture local error distributions, leading to non-homogeneous coverage. We address this with a new adaptive method based on rescaling conformal scores with an estimate of local score distribution, inspired by the Jackknife+ method, which enables the use of calibration data in conformal scores without breaking calibration-test exchangeability. Our approach ensures formal global coverage guarantees and is supported by new theoretical results on local coverage, including an a posteriori bound on any calibration score. The strength of our approach lies in achieving local coverage without sacrificing calibration set size, improving the applicability of conformal prediction intervals in various settings. As a result, our method provides prediction intervals that outperform previous methods, particularly in the low-data regime, making it especially relevant for real-world applications such as healthcare and biomedical domains where uncertainty needs to be quantified accurately despite low sample data.

翻译：保形回归提供了具有全局覆盖保证的预测区间，但往往难以捕捉局部误差分布，导致覆盖率不均匀。我们提出了一种新的自适应方法，通过重缩放保形分数并利用局部分数分布的估计来处理这一问题。该方法受Jackknife+方法的启发，能够在保形分数中使用校准数据而不破坏校准-测试的可交换性。我们的方法保证了形式化的全局覆盖保证，并得到了关于局部覆盖的新理论结果的支持，包括对任意校准分数的后验界。该方法的优势在于无需牺牲校准集大小即可实现局部覆盖，从而提升了保形预测区间在各种场景中的适用性。最终，我们的方法提供的预测区间优于先前的方法，尤其是在低数据量场景下，使其特别适用于医疗健康和生物医学等实际应用领域，这些领域需要在低样本数据下精确量化不确定性。