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# Nonparametric predictive distributions based on conformal prediction

*Proceedings of the Sixth Workshop on Conformal and Probabilistic Prediction and Applications*, PMLR 60:82-102, 2017.

#### Abstract

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 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.