Modeling Extremes with $d$-max-decreasing Neural Networks

Ali Hasan, Khalil Elkhalil, Yuting Ng, João M. Pereira, Sina Farsiu, Jose Blanchet, Vahid Tarokh

Keywords: extreme value theory, copula, sampling

TL;DR: We propose neural network architectures for representing high dimensional extreme value distributions.

Abstract: We propose a neural network architecture that enables non-parametric calibration and generation of multivariate extreme value distributions (MEVs). MEVs arise from Extreme Value Theory (EVT) as the necessary class of models when extrapolating a distributional fit over large spatial and temporal scales based on data observed in intermediate scales. In turn, EVT dictates that $d$-max-decreasing, a stronger form of convexity, is an essential shape constraint in the characterization of MEVs. As far as we know, our proposed architecture provides the first class of non-parametric estimators for MEVs which preserve these essential shape constraints. We show that our architecture approximates the dependence structure encoded by MEVs at parametric rate. Moreover, we present a new method for sampling high-dimensional MEVs using a generative model. We demonstrate our methodology on a wide range of experimental settings, ranging from environmental sciences to financial mathematics and verify the structural properties of MEVs are retained compared to existing methods.