Towards Robust and Efficient Conformal Prediction Under Covariate Shift

Conformal prediction provides model-agnostic prediction sets with nominal coverage, enabling rigorous uncertainty quantification for machine-learning predictions. A major challenge in conformal prediction is covariate shift, where source and target covariate distributions differ while the conditional outcome distribution remains unchanged. Existing methods often fail to balance robustness and efficiency: weighted conformal prediction (WCP) may yield excessively wide or infinite sets under severe covariate shift, whereas doubly robust prediction (DRP) may substantially undercover because it relies on a single pair of component-model estimates whose finite-sample errors can reinforce one another. We propose doubly propagated calibration (DPC) to attain nominal target coverage while keeping prediction sets informative. DPC repeatedly regenerates the DRP component-model estimates across data splits and propagates the resulting finite-sample estimation uncertainty through downstream calibration. Within each regeneration run, DPC balances source and target samples on estimated coverage probabilities and then takes the union of candidate sets across runs, so that one reliable candidate can protect final coverage. Across severe-shift simulations and California Housing experiments, DPC attains near-nominal 90% coverage in settings where DRP substantially undercovers, with intervals about 40% narrower than WCP in simulations and widths less than 9% above the oracle benchmark on California Housing.