Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problems

TL;DR

This paper introduces a deep learning method that jointly models multiple conditional quantiles and the mean for spatio-temporal data, improving predictive density understanding and outperforming existing quantile regression techniques.

Contribution

It proposes a multi-output deep learning approach for joint mean and quantile regression, addressing quantile crossing and enhancing prediction accuracy in spatio-temporal problems.

Findings

Outperforms state-of-the-art quantile regression methods.

Effectively solves the quantile crossing problem.

Provides a richer description of predictive density.

Abstract

Spatio-temporal problems are ubiquitous and of vital importance in many research fields. Despite the potential already demonstrated by deep learning methods in modeling spatio-temporal data, typical approaches tend to focus solely on conditional expectations of the output variables being modeled. In this paper, we propose a multi-output multi-quantile deep learning approach for jointly modeling several conditional quantiles together with the conditional expectation as a way to provide a more complete "picture" of the predictive density in spatio-temporal problems. Using two large-scale datasets from the transportation domain, we empirically demonstrate that, by approaching the quantile regression problem from a multi-task learning perspective, it is possible to solve the embarrassing quantile crossings problem, while simultaneously significantly outperforming state-of-the-art quantile regression methods. Moreover, we show that jointly modeling the mean and several conditional quantiles not only provides a rich description about the predictive density that can capture heteroscedastic properties at a neglectable computational overhead, but also leads to improved predictions of the conditional expectation due to the extra information and a regularization effect induced by the added quantiles.