Conformal calibrators

Conformal predictive distributions were inspired by the work on predictive distributions inparametric statistics (see, e.g., [7, Chapter 12] and [8]) and first suggested in [14]. As usual, we will refer to algorithms producing conformal predictive distributions as conformal predictive systems (CPS, used in both singular andplural senses). Conformal predictive systems are built on top of traditional prediction algorithms toensure a property of validity usually referred to as calibration in probability [3]. Several versions of the Least Squares Prediction Machine, CPS based on the method of Least Squares, are constructed in [14]. This construction isslightly extended to cover ridge regression and then further extended to nonlinear settings by applying the kernel trick in [12]. However, even after this extension the method is not fully adaptive, even for a universal kernel. As explained in [12, Section 7], the universality of the kernel shows in the ability of the predictive distribution function to take any shape; however, the CPS is still inflexible in that the shape does not depend, or depends weakly, on the test object. Formany base algorithms full CPS (like full conformal predictors in general) are computationally inefficient, and [13] define and study computationally efficient versionsof CPS, namely split-conformal predictive systems (SCPS) and 1 cross-conformal predictive systems (CCPS).