Title: Quasi-Monte Carlo for multivariate distributions via generative neural networks
Authors: Marius Hofert - University of Waterloo (Canada) [presenting]
Mu Zhu - University of Waterloo (Canada)
Avinash Prasad - University of Waterloo (Canada)
Abstract: A novel approach based on generative neural networks is introduced for constructing quasi-random number generators for multivariate models with any underlying copula in order to estimate expectations with variance reduction. So far, quasi-random number generators for multivariate distributions required a careful design, exploiting specific properties (such as conditional distributions) of the implied copula or the underlying quasi-Monte Carlo point set, and were only tractable for a small number of models. Utilizing specific generative neural networks allows one to construct quasi-random number generators for a much larger variety of multivariate distributions without such restrictions. Once trained with a pseudo-random sample, these neural networks only require a multivariate standard uniform randomized quasi-Monte Carlo point set as input and are thus fast in estimating expectations under dependence with variance reduction. Reproducible numerical examples are considered to demonstrate the approach. Emphasis is put on ideas rather than mathematical proofs.