Nonparametric predictive distributions based on conformal prediction

Vladimir Vovk, Jieli Shen, Valery Manokhin, Minge Xie

Research output: Chapter in Book/Report/Conference proceedingChapter


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.
Original languageEnglish
Title of host publicationProceedings of Machine Learning Research
Subtitle of host publicationProceedings of COPA 2016 (Sixth Symposium on Conformal and Probabilistic Prediction and Applications)
EditorsAlex Gammerman, Vladimir Vovk, Zhiyuan Luo, Harris Papadopoulos
Number of pages21
Publication statusPublished - 2017


  • Conformal prediction.
  • Least Squares
  • predictive distributions
  • regression

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