Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in high-dimensional problems. In this work, we provide the fundamental concepts of extremal graphical models and discuss recent advances in the field. Different existing perspectives on graphical extremes are presented in a unified way through graphical models for exponent measures. We discuss the important cases of nonparametric extremal graphical models on simple graph structures, and the parametric class of H\"usler--Reiss models on arbitrary undirected graphs. In both cases, we describe model properties, methods for statistical inference on known graph structures, and structure learning algorithms when the graph is unknown. We illustrate different methods in an application to flight delay data at US airports.

翻译：极值图模型已成为极值依赖建模中一个多样且快速扩展的研究领域。它们支持简约的统计方法，尤其适合在高维问题中强制实施稀疏性。本文提供了极值图模型的基本概念，并讨论了该领域的最新进展。通过指数测度的图模型，以统一的方式呈现了极值图模型的不同现有视角。我们讨论了简单图结构上的非参数极值图模型，以及任意无向图上的参数化Hüsler-Reiss模型这两类重要情形。针对这两种情形，我们描述了模型属性、已知图结构下的统计推断方法，以及图未知时的结构学习算法。我们在美国机场航班延误数据的应用中展示了不同方法。