Spatiotemporal problems are ubiquitous and of vital importance in many research fields. Despite the potential already demonstrated by deep learning methods in modeling spatiotemporal data, typical approaches tend to focus solely on conditional expectations of the output variables being modeled. In this article, we propose a multioutput multiquantile 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 spatiotemporal problems. Using two large-scale data sets from the transportation domain, we empirically demonstrate that, by approaching the quantile regression problem from a multitask 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 the regularization effect induced by the added quantiles.

中文翻译：

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超出预期：时空问题的深度联合均值和分位数回归。

时空问题在许多研究领域中无处不在且至关重要。尽管深度学习方法已经在时空数据建模中显示出了潜力，但典型的方法往往只关注于要建模的输出变量的条件期望。在本文中，我们提出了一种多输出多分位数深度学习方法，用于对几个条件分位数以及条件期望值进行联合建模，以此为时空问题提供更完整的``预测密度''``图''。使用交通领域的两个大规模数据集，我们通过经验证明，通过从多任务学习的角度处理分位数回归问题，可以解决令人尴尬的分位数交叉问题，同时显着胜过最新的分位数回归方法。此外，我们表明，对均值和几个条件分位数进行联合建模不仅可以提供关于可以以可忽略的计算开销捕获异方差性质的预测密度的丰富描述，而且还可以由于额外的信息和改进而导致对条件期望的改进预测由增加的分位数引起的正则化效应。