Deep Learning of Multivariate Extremes via a Geometric Representation

TL;DR

This paper introduces a deep learning framework for modeling multivariate extremes using geometric representations, enabling flexible analysis of high-dimensional extremal dependence beyond low-dimensional limitations.

Contribution

It develops the first deep learning-based method for modeling limit sets in geometric extremes, extending inference capabilities to high-dimensional data.

Findings

Successfully modeled complex extremal dependencies in North Sea meteorological data.

Demonstrated the flexibility and scalability of neural network-based extremal dependence models.

Provided theoretical results supporting the asymptotic validity of the proposed deep learning approach.

Abstract

The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes, termed limit sets, link together several popular extremal dependence modelling frameworks. Although the geometric approach is becoming an increasingly popular modelling tool, current inference techniques are limited to a low dimensional setting (d < 5), and generally require rigid modelling assumptions. In this work, we propose a range of novel theoretical results to aid with the implementation of the geometric extremes framework and introduce the first approach to modelling limit sets using deep learning. By leveraging neural networks, we construct asymptotically-justified yet flexible semi-parametric models for extremal dependence of high-dimensional data. We showcase the efficacy of our deep approach by modelling the complex extremal dependencies between meteorological and oceanographic variables in the North Sea off the coast of the UK.