Learning extremal graphical structures in high dimensions

Extremal graphical models encode the conditional independence structure of multivariate extremes. 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. We derive explicit conditions that ensure consistent graph recovery for general connected graphs. A key statistic in our method is the empirical extremal variogram. We prove non-asymptotic concentration bounds for this quantity that hold for general multivariate Pareto distributions and are of independent interest.