B1534
Title: Learning extremal graphical structures in high dimensions
Authors: Michael Lalancette - Technical University of Munich (Germany) [presenting]
Sebastian Engelke - University of Geneva (Switzerland)
Stanislav Volgushev - University of Toronto (Canada)
Abstract: Multiple characterizations and models exist for extremal dependence, the dependence structure of multivariate data in unobserved tail regions. However, statistical inference for extremal dependence uses merely a fraction of the available data, drastically reducing the effective sample size and creating challenges even in moderate dimensions. Recently introduced graphical models for multivariate extremes allow for enforced sparsity in moderate- to high-dimensional settings, reducing the effective dimension. We propose a novel, scalable method for the selection of extremal graphical models that makes no assumption on the underlying graph structure, as opposed to existing approaches. It exploits existing tools for Gaussian graphical model selection, such as the graphical lasso and neighborhood selection. Model selection consistency is established in sparse regimes where the dimension is allowed to be exponentially larger than the effective sample size.
