Fast Calibrated Additive Quantile Regression
Matteo Fasiolo, Simon N. Wood, Margaux Zaffran, Raphaël Nedellec, Yannig Goude · Journal of the American Statistical Association · 2020
Matteo Fasioloa*, Simon N. Wooda , Margaux Zaffranb, Raphaël Nedellecc & Yannig Goudec a School of Mathematics, University of Bristol , Bristol , UK;; b ENSTA ParisTech , Paris , France;; c Électricité de France R&D , Paris , France Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA. Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.CONTACT Matteo Fasiolo [email protected] GA.17, Fry Building, Woodland Road , BS8 1UG , University of Bristol , UK.AbstractWe propose a novel framework for fitting additive quantile regression models, which provides well-calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as diverse as those usable with distributional generalized additive models, while maintaining equivalent numerical efficiency and stability. The proposed methods are at once statistically rigorous and computationally efficient, because they are based on the general belief updating framework of Bissiri, Holmes, and Walker to loss based inference, but compute by adapting the stable fitting methods of Wood, Pya, and Säfken. We show how the pinball loss is statistically suboptimal relative to a novel smooth generalization, which also gives access to fast estimation methods. Further, we provide a novel calibration method for efficiently selecting the “learning rate” balancing the loss with the smoothing priors during inference, thereby obtaining reliable quantile uncertainty estimates. Our work was motivated by a probabilistic electricity load forecasting application, used here to demonstrate the proposed approach. The methods described here are implemented by the qgam R package, available on the Comprehensive R Archive Network (CRAN). Supplementary materials for this article are available online.