Abstract

We develop a novel deep-learning method for statistical inference of multivariate extreme events by combining the framework of geometric extreme value theory with that of normalising flows on hyperspheres. Relying on a radial-angular decomposition of a random vector of interest, we define new models bridging parsimony and flexibility by enforcing theoretically-justified links between parameters that determine the limit distributions upon which our framework is built. Leveraging the generative properties of normalising flows, we efficiently generate new events from our fitted models and perform probability estimation for arbitrary extremal regions of the multivariate space. The merits of our method are demonstrated via a simulation study in up to 10 dimensions and a case study of low and high wind extremes in relation to electricity production across the Pacific Northwest region of the United States.