Beyond Remasking: Probabilistic Tabular Prediction under Recording Shift

A tabular model can reconstruct hidden entries accurately yet predict the wrong distribution for genuinely missing values. We address recording shift, where selective data collection makes observed outcomes unrepresentative of those requiring prediction. Our approach uses additional information retained in labelled source records and an unlabelled deployment sample, even when that information is unavailable for individual predictions. Building on existing identification results, we develop two probabilistic adaptation routes under conditional stability and source support. Direct reweights learning or labelled contexts. Supported fine-law adaptation (SFLA) combines state-conditional distributions using deployment probabilities. We implement these routes through deployment-targeted flow matching (DT-FM) for joint continuous prediction and through adaptation of frozen tabular foundation models. Our analysis separates correctable population mismatch from information lost at inference and explains how estimation errors affect the benefit of correction. Controlled experiments recover conditional changes invisible to marginal correction and associations lost by point prediction. Experiments on real datasets under imposed recording shifts demonstrate gains over native predictors, with controls identifying the contribution of recording correction.