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Modeling Spatial Extremes via Ensemble-of-Trees of Pairwise Copulas

机译：通过成对的Copulas集合树对空间极端进行建模

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摘要

Assessing the risk of extreme events in a spatial domain, such as hurricanes, floods, and droughts, presents a unique significance in practice. Unfortunately, the existing extreme-value statistical models are typically not feasible for practical large-scale problems. Graphical models, on the other hand, are capable of handling sizable number of variables, but have yet to be explored in the realm of extreme-value analysis. To bridge the gap, an extreme-value graphical model is introduced in this paper, i.e., an ensemble-of-trees of pairwise copulas (ETPC). In the proposed graphical model, extreme-value marginal distributions are stitched together by means of a pairwise copulas, which in turn are the building blocks of the ensemble of trees. Novel linear-complexity stochastic gradient-based algorithms are then developed for learning the ETPC model and inferring missing data. As a result, the ETPC model is applicable to extreme-value problems with thousands of variables. It can be proven that, under mild conditions, the ETPC model exhibits the favorable property of tail-dependence between an arbitrary pair of sites (variables); consequently, the model is able to reliably capture statistical dependence between extreme values at different sites. Experimental results for both synthetic and real data demonstrate the advantages of the ETPC model in modeling fitting, imputation, and computational efficiency.
机译：评估空间范围内极端事件的风险，例如飓风，洪水和干旱，在实践中具有独特的意义。不幸的是，现有的极值统计模型通常对于实际的大规模问题是不可行的。另一方面，图形模型能够处理大量变量，但尚未在极值分析领域中进行探索。为了弥合差距，本文引入了一个极值图形模型，即成对系动词树（ETPC）的集合树。在提出的图形模型中，极值边际分布通过成对的copulas缝合在一起，而copulas又是树木集合的组成部分。然后，开发了基于线性复杂度随机梯度的新型算法，以学习ETPC模型并推断缺失数据。因此，ETPC模型适用于具有数千个变量的极值问题。可以证明，在温和的条件下，ETPC模型在任意一对位点（变量）之间表现出良好的尾部依赖性。因此，该模型能够可靠地捕获不同位置的极值之间的统计依赖性。综合数据和真实数据的实验结果证明了ETPC模型在拟合拟合，估算和计算效率方面的优势。

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