Modeling Extremes with d-max-decreasing Neural Networks

TL;DR

This paper introduces a new neural network architecture for non-parametric modeling of multivariate extreme value distributions, preserving essential shape constraints and enabling high-dimensional sampling, with applications across various scientific fields.

Contribution

The paper presents the first non-parametric neural network estimator for MEVs that maintains $d$-max-decreasing shape constraints and approximates dependence structures at parametric rates.

Findings

Successfully models multivariate extreme value distributions.

Preserves $d$-max-decreasing shape constraints.

Effective in high-dimensional sampling and diverse applications.

Abstract

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.