  Conformal predictive systems are a recent modification of conformal
predictors that output, in regression problems, probability distributions for
labels of test observations rather than set predictions. The extra information
provided by conformal predictive systems may be useful, e.g., in decision
making problems. Conformal predictive systems inherit the relative
computational inefficiency of conformal predictors. In this paper we discuss
two computationally efficient versions of conformal predictive systems, which
we call split conformal predictive systems and cross-conformal predictive
systems. The main advantage of split conformal predictive systems is their
guaranteed validity, whereas for cross-conformal predictive systems validity
only holds empirically and in the absence of excessive randomization. The main
advantage of cross-conformal predictive systems is their greater predictive
efficiency.
