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.

翻译：典型机器学习回归应用旨在通过平方或绝对误差评分函数训练，报告预测概率分布的均值或中位数。预测概率分布更多泛函（分位数及期望分位数）的重要性已被视为量化预测不确定性的手段。在深度学习应用中，这可通过分位数回归神经网络及期望分位数回归神经网络实现。本文提出深度Huber分位数回归网络，将分位数回归神经网络与期望分位数回归神经网络作为边界情形涵盖其中。深度Huber分位数回归网络能够预测Huber分位数——这是一种更通用的泛函，因其以分位数和期望分位数作为极限情形嵌套其中。核心思想在于利用Huber分位数回归函数训练深度学习算法，该函数对Huber分位数泛函具有一致性。作为概念验证，我们将深度Huber分位数回归网络应用于澳大利亚房价预测。在此背景下，结合经济学案例研究的证据性解释，讨论三种深度学习架构的预测性能。