Structure learning for extremal tree models
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.06179
- arXiv:
- arXiv:2012.06179
- Bibcode:
- 2020arXiv201206179E
- Keywords:
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- Statistics - Methodology