Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration bounds that hold under general domain of attraction conditions. For the popular class of H\"usler--Reiss models, we propose a majority voting algorithm for learning the underlying graph from data through $L^1$ regularized optimization. Our concentration bounds are used to derive explicit conditions that ensure the consistent recovery of any connected graph. The methodology is illustrated through a simulation study as well as the analysis of river discharge and currency exchange data.

翻译：极值图模型编码了多元极值的条件独立性结构。学习极值图结构的关键统计量是经验极值变异函数，我们为其证明了在一般吸引域条件下成立的非渐近集中界。针对流行的Hüsler-Reiss模型类，我们提出一种多数投票算法，通过$L^1$正则化优化从数据中学习底层图结构。利用所得集中界，我们推导出确保任意连通图可一致恢复的显式条件。通过模拟研究及河流流量与汇率数据分析，对所提方法进行了实证说明。