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.

本文提出了一种新的自适应方法，基于重新缩放符合规范的分数与本地分数分布的估计，解决了不均匀覆盖率的问题，从而在不破坏校准检验可交换性的情况下利用校准数据进行符合规范的评分。该方法提供了一种新型的预测间隔，具有全局覆盖率保证，并且在低数据情况下表现更优，特别适用于需要准确量化不确定因素的实际应用，如医疗保健领域。