Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction

Ensuring model calibration is critical for reliable predictions, yet popular distribution-free methods, such as histogram binning and isotonic regression, provide only asymptotic guarantees. We introduce a unified framework for Venn and Venn-Abers calibration, generalizing Vovk's binary classification approach to arbitrary prediction tasks and loss functions. Venn calibration leverages binning calibrators to construct prediction sets that contain at least one marginally perfectly calibrated point prediction in finite samples, capturing epistemic uncertainty in the calibration process. The width of these sets shrinks asymptotically to zero, converging to a conditionally calibrated point prediction. Furthermore, we propose Venn multicalibration, a novel methodology for finite-sample calibration across subpopulations. For quantile loss, group-conditional and multicalibrated conformal prediction arise as special cases of Venn multicalibration, and Venn calibration produces novel conformal prediction intervals that achieve quantile-conditional coverage. As a separate contribution, we extend distribution-free conditional calibration guarantees of histogram binning and isotonic calibration to general losses.