Structure learning for extremal tree models

12/11/2020
by   Sebastian Engelke, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/01/2023

Parametric and nonparametric symmetries in graphical models for extremes

Colored graphical models provide a parsimonious approach to modeling hig...
research
12/04/2018

Graphical Models for Extremes

Conditional independence, graphical models and sparsity are key notions ...
research
05/31/2018

Learning Tree Distributions by Hidden Markov Models

Hidden tree Markov models allow learning distributions for tree structur...
research
10/25/2022

Statistical Inference for Hüsler-Reiss Graphical Models Through Matrix Completions

The severity of multivariate extreme events is driven by the dependence ...
research
11/01/2021

Concentration bounds for the extremal variogram

In extreme value theory, the extremal variogram is a summary of the tail...
research
03/11/2023

A Geometric Statistic for Quantifying Correlation Between Tree-Shaped Datasets

The magnitude of Pearson correlation between two scalar random variables...
research
06/21/2020

Learning of Discrete Graphical Models with Neural Networks

Graphical models are widely used in science to represent joint probabili...

Please sign up or login with your details

Forgot password? Click here to reset