Nonparametric predictive distributions based on conformal prediction. / Vovk, Vladimir; Shen, Jieli; Manokhin, Valery; Xie, Minge.

In: Machine Learning, Vol. 108, No. 3, 03.2019, p. 445-474.

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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 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.
Original languageEnglish
Pages (from-to)445-474
Number of pages30
JournalMachine Learning
Volume108
Issue number3
Early online date17 Aug 2018
DOIs
Publication statusPublished - Mar 2019

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