Conformal prediction has emerged as a general and versatile framework for constructing prediction sets in regression and classification tasks (Shafer and Vovk, 2008). Unlike traditional methods, which often depend on rigid distributional assumptions, conformal prediction transforms point predictions from any prediction (or black-box) algorithm into prediction sets that guarantee valid finite-sample marginal coverage. Originally introduced by Vovk et al. (2005), it has become increasingly influential, with numerous methods and extensions being proposed since its introduction. In particular, full conformal prediction by Vovk et al. (2005), demonstrates favorable properties regarding the coverage and the size of the prediction set. However, these advantages are counterbalanced by a substantial computational cost, which limits its practical application.

This note introduces the method of cross-conformal prediction, which is a hybrid of the methods of inductive conformal prediction and cross-validation, and studies its validity and predictive efficiency empirically.