  We propose a novel 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
that 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 that the structural properties of MEVs are retained
compared to existing methods.
