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We propose a new method for modeling the distribution function of high dimensional extreme value distributions. The Pickands dependence function models the relationship between the covariates in the tails, and we learn this function using a neural network that is designed to satisfy its required properties. Moreover, we present new methods for recovering the spectral representation of extreme distributions and propose a generative model for sampling from extreme copulas. Numerical examples are provided demonstrating the efficacy and promise of our proposed methods.
Game-theoretic attribution techniques based on Shapley values are used extensively to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the comput
This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n to infty$ with fixed kernel size $k$. Under some regularity conditions, we demonstra
Variational Inference (VI) is a popular alternative to asymptotically exact sampling in Bayesian inference. Its main workhorse is optimization over a reverse Kullback-Leibler divergence (RKL), which typically underestimates the tail of the posterior
In order to compute fast approximations to the singular value decompositions (SVD) of very large matrices, randomized sketching algorithms have become a leading approach. However, a key practical difficulty of sketching an SVD is that the user does n
As part of Probabilistic Risk Assessment studies, it is necessary to study the fragility of mechanical and civil engineered structures when subjected to seismic loads. This risk can be measured with fragility curves, which express the probability of