  Generative moment matching networks (GMMNs) are introduced for generating
quasi-random samples from multivariate models with any underlying copula in
order to compute estimates under variance reduction. So far, quasi-random
sampling for multivariate distributions required a careful design, exploiting
specific properties (such as conditional distributions) of the implied
parametric copula or the underlying quasi-Monte Carlo (QMC) point set, and was
only tractable for a small number of models. Utilizing GMMNs allows one to
construct quasi-random samples for a much larger variety of multivariate
distributions without such restrictions, including empirical ones from real
data with dependence structures not well captured by parametric copulas. Once
trained on pseudo-random samples from a parametric model or on real data, these
neural networks only require a multivariate standard uniform randomized QMC
point set as input and are thus fast in estimating expectations of interest
under dependence with variance reduction. Numerical examples are considered to
demonstrate the approach, including applications inspired by risk management
practice. All results are reproducible with the demos GMMN_QMC_paper,
GMMN_QMC_data and GMMN_QMC_timings as part of the R package gnn.
