Modeling Extremes with d-max-decreasing Neural Networks
This work addresses the challenge of extrapolating distributional fits over large scales in extreme value theory, providing a non-parametric method for researchers and practitioners in domains like environmental science and finance, though it is incremental as it builds on existing EVT constraints.
The authors tackled the problem of modeling multivariate extreme value distributions (MEVs) by proposing a novel neural network architecture that enables non-parametric calibration and generation while preserving essential shape constraints like d-max-decreasing, achieving parametric rate approximation and demonstrating applicability in fields such as environmental sciences and financial mathematics.
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.