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Structure learning for extremal tree models
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AI
DOI：10.1111/rssb.12556.png)
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摘要
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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.
Keyword:
domain of attraction
extreme value theory
graphical models
minimum spanning tree
multivariate Pareto distribution
期刊
J
IF:
3.6
论文数:
1.5K
被引数:
3.2W
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