Nonparametric predictive distributions based on conformal prediction

Vladimir Vovk, Jieli Shen, Valery Manokhin, Min-ge Xie

Research output: Contribution to journalArticlepeer-review


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
Early online date17 Aug 2018
Publication statusPublished - 15 Mar 2019


  • Conformal prediction
  • Least Squares
  • Predictive distributions
  • Regression
  • Nonparametric regression

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