Deep Huber quantile regression networks

TL;DR

This paper introduces deep Huber quantile regression networks (DHQRN), a flexible neural network framework that predicts a range of distributional functionals including quantiles and expectiles, improving uncertainty quantification in regression tasks.

Contribution

The paper proposes DHQRN, a novel neural network model that generalizes quantile and expectile regression by predicting Huber quantiles, unifying these approaches within a single framework.

Findings

DHQRN effectively predicts house prices in Melbourne and Boston.

DHQRN demonstrates satisfactory performance on real-world datasets.

The model provides interpretable economic insights.

Abstract

Typical machine learning regression applications aim to report the mean or the median of the predictive probability distribution, via training with a squared or an absolute error scoring function. The importance of issuing predictions of more functionals of the predictive probability distribution (quantiles and expectiles) has been recognized as a means to quantify the uncertainty of the prediction. In deep learning (DL) applications, that is possible through quantile and expectile regression neural networks (QRNN and ERNN respectively). Here we introduce deep Huber quantile regression networks (DHQRN) that nest QRNN and ERNN as edge cases. DHQRN can predict Huber quantiles, which are more general functionals in the sense that they nest quantiles and expectiles as limiting cases. The main idea is to train a DL algorithm with the Huber quantile scoring function, which is consistent for the Huber quantile functional. As a proof of concept, DHQRN are applied to predict house prices in Melbourne, Australia and Boston, United States (US). In this context, predictive performances of three DL architectures are discussed along with evidential interpretation of results from two economic case studies. Additional simulation experiments and applications to real-world case studies using open datasets demonstrate a satisfactory absolute performance of DHQRN.