Nonparametric predictive distributions based on conformal prediction

This paper applies conformal prediction to derive predictive distributions that are valid under a nonparametric assumption. Namely, we introduce and explore predictive distribution functions that always satisfy a natural property of validity in terms of guaranteed coverage for IID observations. The focus is on a prediction algorithm that we call the Least Squares Prediction Machine (LSPM). The LSPM generalizes the classical Dempster-Hill predictive distributions to nonparametric regression problems. If the standard parametric assumptions for Least Squares linear regression hold, the LSPM is as efficient as the Dempster-Hill procedure, in a natural sense. And if those parametric assumptions fail, the LSPM is still valid, provided the observations are IID.