A0482
Title: A deep geometric approach to modelling multivariate extremes
Authors: Callum Murphy-Barltrop - Technische Universitat Dresden (Germany)
Reetam Majumder - North Carolina State University (United States)
Jordan Richards - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Abstract: The geometric representation for multivariate extremes, where data is split into radial and angular components and the radial component is modelled conditionally on the angle, provides an exciting new approach to modelling the extremes of multivariate data. Through a consideration of scaled sample clouds and limit sets, it provides a flexible, semi-parametric model for extremes that connects multiple classical extremal dependence measures; these include the coefficients of tail dependence and asymptotic independence and parameters of the conditional extremes framework. Although the geometric approach is becoming an increasingly popular modelling tool for multivariate extremes, inference with this framework is limited to a low dimensional setting $(d < 4)$. The first deep representation is proposed for geometric extremes. By leveraging the predictive power and computational scalability of neural networks, asymptotically-justified yet flexible semi-parametric models are constructed for extremal dependence of high-dimensional data. The efficacy of the deep approach is showcased by modelling the complex extremal dependence between metocean variables sampled from the North Sea.
