Fast calibrated additive quantile regression

TL;DR

This paper introduces a fast, statistically rigorous additive quantile regression framework with automatic smoothing parameter estimation, calibrated inference, and an application to electricity load forecasting, implemented in the qgam R package.

Contribution

It presents a novel, computationally efficient method for additive quantile regression with calibrated inference and automatic smoothing, improving over existing approaches.

Findings

The method provides well-calibrated conditional quantile estimates.

It achieves fast estimation suitable for large datasets.

Application to electricity load forecasting demonstrates practical utility.

Abstract

We 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 GAMs, 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 et al. (2016) to loss based inference, but compute by adapting the stable fitting methods of Wood et al. (2016). We show how the pinball loss is statistically suboptimal relative to a novel smooth generalisation, 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).