  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 QRNNs and ERNNs 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 deep
learning algorithm with the Huber quantile regression function, which is
consistent for the Huber quantile functional. As a proof of concept, DHQRN are
applied to predict house prices in Australia. In this context, predictive
performances of three DL architectures are discussed along with evidential
interpretation of results from an economic case study.
