Fast Calibrated Additive Quantile Regression

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).

Comparing abundance distributions and range maps in spatial conservation planning for migratory species

“…The model therefore estimated the lower and upper quartiles of proportions of populations included in selected sites, enabling us to identify times of year where several species have particularly low or high estimates. We fitted these models in R package qgam (Fasiolo et al 2018).…”

The shape of abundance distributions across temperature gradients in reef fishes

“…For each species we extracted the residuals from the firststage models, and then modelled the relationship between temperature and residual-abundance using quantile generalised additive models in the R package 'qgam' (Fasiolo et al 2017). The use of generalised additive models rather than linear models allowed a flexible fit to highly variable abundance data.…”

Scalable Visualization Methods for Modern Generalized Additive Models

“…The object-oriented layer-based framework implemented by mgcViz aims at facilitating future extensions of the visualisation methods proposed here. In particular, while the package already contains diagnostic layers that are specific to quantile GAMs (Fasiolo et al, 2017), we plan to develop bespoke methods for other non-standard models, such as functional GAMs (McLean et al, 2014). More demanding extensions would be providing general methods for creating animated version of current plot types, which would be useful for smooth effect uncertainty visualisation (Bowman, 2018), and tools for comparing plots generated under different GAM models.…”