Quantile Super Learning for independent and online settings with application to solar power forecasting

Abstract

Estimating quantiles of an outcome conditional on covariates is of fundamental interest in statistics with broad application in probabilistic prediction and forecasting. An ensemble method for conditional quantile estimation is proposed, Quantile Super Learning, that combines predictions from multiple candidate algorithms based on their empirical performance measured with respect to a cross-validated empirical risk of the quantile loss function. Theoretical guarantees for both i.i.d. and online data scenarios are presented. The performance of this approach for quantile estimation and in forming prediction intervals is tested in simulation studies. Two case studies related to solar energy are used to illustrate Quantile Super Learning: in an i.i.d. setting, we predict the physical properties of perovskite materials for photovoltaic cells, and in an online setting we forecast ground solar irradiance based on output from dynamic weather ensemble models.