Valid prediction intervals for regression problems

TL;DR

This paper reviews various methods for estimating prediction intervals in regression, emphasizing calibration issues and demonstrating how conformal prediction can improve calibration across different methods and datasets.

Contribution

It provides a comprehensive conceptual and experimental review of four main classes of prediction interval methods and highlights the role of conformal prediction for calibration.

Findings

Performance varies significantly across datasets.

Violations of assumptions affect method reliability.

Conformal prediction effectively calibrates poor-performing methods.

Abstract

Over the last few decades, various methods have been proposed for estimating prediction intervals in regression settings, including Bayesian methods, ensemble methods, direct interval estimation methods and conformal prediction methods. An important issue is the calibration of these methods: the generated prediction intervals should have a predefined coverage level, without being overly conservative. In this work, we review the above four classes of methods from a conceptual and experimental point of view. Results on benchmark data sets from various domains highlight large fluctuations in performance from one data set to another. These observations can be attributed to the violation of certain assumptions that are inherent to some classes of methods. We illustrate how conformal prediction can be used as a general calibration procedure for methods that deliver poor results without a calibration step.