Combining strengths from deep learning and extreme value theory can help describe complex relationships between variables where extreme events have significant impacts (e.g., environmental or financial applications). Neural networks learn complicated nonlinear relationships from large datasets under limited parametric assumptions. By definition, the number of occurrences of extreme events is small, which limits the ability of the data-hungry, nonparametric neural network to describe rare events. Inspired by recent extreme cold winter weather events in North America caused by atmospheric blocking, we examine several probabilistic generative models for the entire multivariate probability distribution of daily boreal winter surface air temperature. We propose metrics to measure spatial asymmetries, such as long-range anticorrelated patterns that commonly appear in temperature fields during blocking events. Compared to vine copulas, the statistical standard for multivariate copula modeling, deep learning methods show improved ability to reproduce complicated asymmetries in the spatial distribution of ERA5 temperature reanalysis, including the spatial extent of in-sample extreme events.

翻译：结合深度学习与极值理论的各自优势，有助于描述极端事件引发显著影响（如环境或金融应用）的变量间复杂关系。神经网络能在有限参数假设下，从大型数据集中学习复杂的非线性关系。然而，极端事件的发生次数本就不多，这限制了数据饥渴型的非参数神经网络对罕见事件的描述能力。受近期由大气阻塞引发的北美极端冬季寒冷天气事件启发，我们研究了多种概率生成模型，用于描述北半球冬季地表气温的完整多元概率分布。我们提出了衡量空间不对称性的指标，例如阻塞事件期间温度场中常见的远距离反相关模式。与多元连接函数建模的统计标准——藤连接函数相比，深度学习方法在再现ERA5温度再分析资料中复杂的空间不对称性（包括样本内极端事件的空间范围）方面表现出更强的能力。