[Forum SIS] Seminario Dott. Engelke 9-5-2019

[Dip. Scienze Statistiche - Mi]

Dipartimento di Scienze statistiche e Dipartimento di Politica Economica- Università Cattolica del Sacro Cuore, Milano

AVVISO DI SEMINARIO
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Giovedì 9 Maggio dalle ore 11,30

in Aula SA 324



Università Cattolica del Sacro Cuore - Milano

Via Sant'Agnese, 2


Dott. Sebastian Engelke, Università di Ginevra



Graphical Models and Structural Learning for Extremes

Abstract
Conditional independence, graphical models and sparsity are key notions for parsimonious models in high dimensions and for learning structural relationships in the data. The theory of multivariate and spatial extremes describes the risk of rare events through asymptotically justi_ed limit models such as max-stable and multivariate Pareto distributions. Statistical modeling in this _eld has been limited to moderate dimensions so far, owing to complicated likelihoods and a lack of understanding of the underlying probabilistic structures.
We introduce a general theory of conditional independence for multivariate Pareto distributions that allows to de_ne graphical models and sparsity for extremes. New parametric models can be built in a modular way and statistical inference can be simpli_ed to lower-dimensional margins. We de_ne the extremal variogram, a new summary statistics that turns out to be a tree metric and therefore allows to e_ciently learn an underlying tree structure through Prim's algorithm. For a popular parametric class of multivariate Pareto distributions we show that, similarly to the Gaussian case, the sparsity pattern of a general graphical model can be easily read of from suitable inverse covariance matrices. This enables the de_nition of an extremal graphical lasso that enforces sparsity in the dependence structure. We illustrate the results with an application to ood risk assessment on the Danube river.

This is joint work with Adrien Hitz. Preprint available on https://arxiv.org/abs/1812.01734.




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