Conformal Histogral Regression

Published in pre-print, 2021

Recommended citation: Sesia and Romano (2021). "Conformal Histogral Regression." arXiv. https://arxiv.org/abs/2105.08747

Abstract

This paper develops a conformal method to compute prediction intervals for non-parametric regression that can automatically adapt to skewed data. Leveragingblack-box machine learning algorithms to estimate the conditional distribution ofthe outcome using histograms, it translates their output into the shortest predictionintervals with approximate conditional coverage. The resulting prediction intervalsprovably have marginal coverage in finite samples, while asymptotically achiev-ing conditional coverage and optimal length if the black-box model is consistent.Numerical experiments with simulated and real data demonstrate improved perfor-mance compared to state-of-the-art alternatives, including conformalized quantileregression and other distributional conformal prediction approaches.