论文标题
极端树模型的结构学习
Structure learning for extremal tree models
论文作者
论文摘要
极端图形模型是多元极端事件的稀疏统计模型。基础图编码有条件的独立性，并可以对复杂的极端依赖结构进行视觉解释。对于树模型的重要情况，我们开发了一种数据驱动的方法来学习图形结构。我们表明，极端相关性的示例版本和我们称为极端变化图的新摘要统计量可以用作最小跨越树的权重，以始终如一地恢复真实的基础树。值得注意的是，这意味着可以通过使用简单的摘要统计数据以完全非参数的方式学习极端树模型，而无需假设离散分布，存在密度或用于双变量分布的参数模型。
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the important case of tree models, we develop a data-driven methodology for learning the graphical structure. We show that sample versions of the extremal correlation and a new summary statistic, which we call the extremal variogram, can be used as weights for a minimum spanning tree to consistently recover the true underlying tree. Remarkably, this implies that extremal tree models can be learned in a completely non-parametric fashion by using simple summary statistics and without the need to assume discrete distributions, existence of densities, or parametric models for bivariate distributions.
