Modeling extremes with $d$-max-decreasing neural networks
Ali Hasan, Khalil Elkhalil, Yuting Ng, João M. Pereira, Sina Farsiu, Jose Blanchet, Vahid Tarokh
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 that preserve these essential shape constraints. We show that the 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.
BibTeX
@InProceedings{pmlr-v180-hasan22a,
title = {Modeling extremes with $d$-max-decreasing neural networks},
author = {Hasan, Ali and Elkhalil, Khalil and Ng, Yuting and Pereira, Jo\~ao M. and Farsiu, Sina and Blanchet, Jose and Tarokh, Vahid},
booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence},
pages = {759--768},
year = {2022},
editor = {Cussens, James and Zhang, Kun},
volume = {180},
series = {Proceedings of Machine Learning Research},
month = {01--05 Aug},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v180/hasan22a/hasan22a.pdf},
url = {https://proceedings.mlr.press/v180/hasan22a.html},
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 that preserve these essential shape constraints. We show that the 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.}
}