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普遍存在且至关重要。尽管深度学习方法已经展示了时空数据建模的潜力，但典型的方法往往只关注所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，用于对多个条件分位数和条件期望进行联合建模，作为提供时空问题中预测密度的更完整“图片”的方法。使用来自交通领域的两个大规模数据集，我们凭经验证明，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，同时显着优于最先进的技术分位数回归方法。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提供了关于预测密度的丰富描述，可以以可忽略的计算开销捕获异方差属性，而且由于额外的信息和由添加的分位数引起的正则化效应。