Hasan, A., Elkhalil, K., Ng, Y., Pereira, J.M., Farsiu, S., Blanchet, J. & Tarokh, V.. (2022). Modeling extremes with $d$-max-decreasing neural networks. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:759-768 Available from 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 -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.
Authors
Ali Hasan, Khalil Elkhalil, Yuting Ng, João M Pereira, Sina Farsiu, Jose Blanchet, Vahid Tarokh
Publication date
2022/8/17
Conference
Uncertainty in Artificial Intelligence
Pages
759-768
Publisher
PMLR
