Quasi-random sampling for multivariate distributions via generative neural networks

TL;DR

This paper introduces GMMNs, a neural network-based method for generating quasi-random samples from complex multivariate distributions, enabling efficient variance reduction in expectation estimates, especially for models with intricate dependence structures.

Contribution

The paper presents a novel use of generative moment matching networks to produce quasi-random samples for a wide range of multivariate distributions, surpassing previous limitations.

Findings

Effective variance reduction demonstrated in numerical experiments.

Applicable to real data with complex dependence structures.

Fast and flexible sampling method suitable for risk management applications.

Abstract

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.