Nonparametric predictive distributions based on conformal prediction

• Published in: Machine learning Vol. 108; no. 3; pp. 445 - 474
• Main Authors: Vovk, Vladimir, Shen, Jieli, Manokhin, Valery, Xie, Min-ge
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2019; Springer Nature B.V
• Subjects: Artificial Intelligence; Computer Science; Control; Distribution functions; Least squares; Mechatronics; Natural Language Processing (NLP); Nonparametric statistics; Predictions; Regression analysis; Robotics; Simulation and Modeling; Special Issue: Conformal Prediction; Regression; Predictive distributions; Least Squares; Nonparametric regression; Conformal prediction
• ISSN: 0885-6125; 1573-0565
• DOI: 10.1007/s10994-018-5755-8

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.