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arXiv · 2111.00840

Learning extremal graphical structures in high dimensions

Sebastian Engelke·Michaël Lalancette·Stanislav Volgushev
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Abstract

Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration bounds that hold under general domain of attraction conditions. 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. Our concentration bounds are used to derive explicit conditions that ensure the consistent recovery of any connected graph. The methodology is illustrated through a simulation study as well as the analysis of river discharge and currency exchange data.

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Sebastian Engelke, Michaël Lalancette, Stanislav Volgushev. 2021-11-01. Learning extremal graphical structures in high dimensions. https://arxiv.org/abs/2111.00840

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