Quasi-random number generators for multivariate distributions based on generative neural networks

Generative moment matching networks are introduced as quasi-random number generators for multivariate distributions. So far, quasi-random number generators for non-uniform multivariate distributions require a careful design, often need to exploit specific properties of the distribution or quasi-random number sequence under consideration, and are limited to few models. Utilizing generative neural networks, in particular, generative moment matching networks, allows one to construct quasi-random number generators for a much larger variety of multivariate distributions without such restrictions. Once trained, the presented generators only require independent quasi-random numbers as input and are thus fast in generating non-uniform multivariate quasi-random number sequences from the target distribution. Various numerical examples are considered to demonstrate the approach, including applications inspired by risk management practice.