  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.
