# Fast calibrated additive quantile regression

arXiv: https://arxiv.org/abs/1707.03307 · HTML: https://mlsanity.com/paper/1707.03307/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2017.

## Built on by (most cited first, 27 of 27)

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## Abstract (arXiv)

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).