Colored graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of coloring for extremal graphical models on multivariate Pareto distributions, a natural class of limiting distributions for threshold exceedances. Thanks to a stability property of the multivariate Pareto distributions, colored extremal tree models can be defined fully nonparametrically. For more general graphs, the parametric family of H\"usler--Reiss distributions allows for two alternative approaches to colored graphical models. We study both model classes and introduce statistical methodology for parameter estimation. It turns out that for H\"usler--Reiss tree models the different definitions of colored graphical models coincide. In addition, we show a general parametric description of extremal conditional independence statements for H\"usler--Reiss distributions. Finally, we demonstrate that our methodology outperforms existing approaches on a real data set.

翻译：彩色图形模型通过利用模型参数中的对称性，为高维数据建模提供了一种简约化的方法。本文针对多元帕累托分布（阈值超出的自然极限分布类）上的极值图形模型，引入了着色概念。凭借多元帕累托分布的稳定性，可完全非参数化地定义彩色极值树模型。对于更一般的图形，Hüsler–Reiss分布的参数族为彩色图形模型提供了两种替代方法。我们研究了这两类模型，并提出了参数估计的统计方法。结果表明，对于Hüsler–Reiss树模型，彩色图形模型的不同定义是一致的。此外，我们揭示了Hüsler–Reiss分布中极值条件独立性陈述的一般参数化描述。最后，我们在实际数据集上验证了所提方法优于现有方法。