Generative modelling of multivariate geometric extremes using normalising flows

TL;DR

This paper introduces a deep learning approach using normalising flows on hyperspheres to accurately model and extrapolate multivariate geometric extremes, capturing complex dependence structures in high dimensions.

Contribution

It presents a novel methodology combining geometric multivariate extremes with normalising flows, enabling efficient joint tail extrapolation and probability estimation in higher dimensions.

Findings

Effective modeling of multivariate extremes up to 10 dimensions.

Accurate probability estimation for complex extreme events.

Application to wind speed extremes reveals data structure.

Abstract

Leveraging the recently emerging geometric approach to multivariate extremes and the flexibility of normalising flows on the hypersphere, we propose a principled deep-learning-based methodology that enables accurate joint tail extrapolation in all directions. We exploit theoretical links between intrinsic model parameters defined as functions on hyperspheres to construct models ranging from high flexibility to parsimony, thereby enabling the efficient modelling of multivariate extremes displaying complex dependence structures in higher dimensions with reasonable sample sizes. We use the generative feature of normalising flows to perform fast probability estimation for arbitrary Borel risk regions via an efficient Monte Carlo integration scheme. The good properties of our estimators are demonstrated via a simulation study in up to ten dimensions. We apply our methodology to the analysis of low and high extremes of wind speeds. In particular, we find that our methodology enables probability estimation for non-trivial extreme events in relation to electricity production via wind turbines and reveals interesting structure in the underlying data.