Conformal Prediction under Exponential-Tilt Joint Shift

Seungjin Choi

Conformal prediction can lose coverage when the data distribution changes after deployment. We study adaptation using labeled source data and unlabeled target inputs, allowing both the input distribution and its relationship with outcomes to change. We use Exponential Tilt Reweighting Alignment (ExTRA), introduced for classification by Maity et al. (2023), to estimate structured distribution shifts. We compare using its estimated weights in conformal calibration with additionally tilting the source predictive distribution. Shared learned predictors, estimated weights, calibration samples, and test observations isolate the effect of tilting. Existing theory gives both procedures target coverage with true weights and a common coverage bound with estimated weights. Identification calculations and an analysis of how scoring interacts with weight estimation error help explain why their performance can nevertheless differ. In a synthetic regression setting where the assumed models match the data-generating process and target inputs are informative about the shift, tilting reduces mean set length by about $30\%$ relative to weighting alone, with both methods attaining coverage near…