Title: Fast learning rate selection for Bayesian non-parametric quantile regression
Authors: Matteo Fasiolo - University of Bristol (United Kingdom) [presenting]
Abstract: Quantile regression (QR) models are often fitted to data by minimising the so-called check or pinball loss. In a Bayesian framework, quantile regression can be based on the asymmetric Laplace (AL) distribution, because the resulting negative log-likelihood corresponds to the pinball loss. In a non-parametric spline smoothing context, it is tempting to use (a smooth generalization of) the AL distribution in conjunction with standard likelihood-based methods to fit non-parametric QR models. We will explain that this leads to poor results both in terms of smoothness of the fit and of frequentist coverage of the resulting credible intervals. We will also discuss how the issue can be alleviated via a calibration step aimed at efficiently selecting the learning rate balancing the relative weights of the loss based likelihood and of the smoothing priors.