Adaptive Conformal Regression with Jackknife+ Rescaled Scores

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.