Stable Localized Conformal Prediction via Transduction

Existing evaluations of conformal prediction, such as prediction efficiency and test-conditional coverage, are defined in expectation over the calibration data. In practice, when only one calibration set of limited size is available, the prediction sets can exhibit high variability, especially for methods with localization. We formalize this concern as set stability, defined as the variance of the conditional expectation of the set size given the calibration data. To improve stability without requiring additional target-task labels, we propose Stable Localized Conformal Prediction (SLCP), a transfer learning approach that utilizes labeled source-task data and unlabeled target data. Theoretically, we characterize the marginal coverage and stability of SLCP; empirically, it delivers more stable prediction sets than standard conformal prediction methods with localization when calibration data are limited.