Valid prediction intervals for regression problems
This work addresses the calibration problem for prediction intervals in regression, which is important for reliable uncertainty quantification in various domains, but it is incremental as it reviews and applies existing methods.
The paper reviews four classes of methods for estimating prediction intervals in regression, finding large performance fluctuations across datasets due to violated assumptions, and shows how conformal prediction can calibrate poorly performing methods.
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.