ATHENA INSTITUTE SEMINAR: Sampling and Prediction for Extreme Events

Multivariate extreme value distributions 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.

We will discuss our ongoing activities in applying machine learning techniques for prediction and generation of extreme value data. To this end, we will discuss

(i) A new neural network architecture referred to as $d$-max-decreasing neural networks that to the best of our knowledge

is the first class of non-parametric estimators for MEVs that preserve their essential shape constraints. We show that our architecture approximates the dependence structure encoded by MEVs at parametric rate.

(ii) 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.

(iii) we consider certain classes of copulas known as Archimedean and hierarchical Archimedean copulas, popular for their parsimonious representation and ability to model different tail dependencies. We consider their representation as mixture models with Laplace transforms of latent random variables from generative neural networks. Building on our methods, we consider Archimax copulas that combine the benefits of Archimedean and extreme-value copulas by modeling asymmetries and non-extreme data, while being fully flexible in the extremes. We propose a non-parametric inference method and sampling algorithm for Archimax copulas. Experimental studies demonstrate the efficacy of the proposed approach both in learning and sampling.

BIO:
Vahid Tarokh worked at AT&T Labs-Research until 2000. From 2000-2002, he was an Associate Professor at Massachusetts Institute of Technology (MIT). In 2002, he joined Harvard University as a Hammond Vinton Hayes Senior Fellow of Electrical Engineering and Perkins Professor of Applied Mathematics. He was a Gordon Moore Distinguished Research Fellow at CALTECH in 2018. He joined Duke University in Jan 2018 where he is the Rhodes Family Professor of Electrical and Computer Engineering and Mathematics (secondary).