Conformal Inference for Missing Data Under Multiple Robust Learning

We develop a novel approach to address the common but challenging problem of conformal inference for missing data in machine learning, focusing on Missing at Random (MAR) data.We propose a new procedure, Conformal Prediction for Missing Data under Multiple Robust Learning (CM-MRL), which combines split conformal calibration with a multiple robust empirical-likelihood (EL) reweighting scheme.The method proceeds via a double calibration by reweighting the complete-case scores by EL so that their distribution matches the full calibration distribution implied by MAR, even when some working models are misspecified.We demonstrate the asymptotic behavior of our estimators through empirical process theory, provide reliable coverage for our prediction intervals, both marginally and conditionally, and further show an interval-length dominance result.We demonstrate the effectiveness of the proposed method through several numerical experiments in the presence of missing data.