# Quasi-random sampling for multivariate distributions via generative neural networks

arXiv: https://arxiv.org/abs/1811.00683 · HTML: https://mlsanity.com/paper/1811.00683/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2018.

## Built on by (most cited first, 9 of 9)

- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernel](https://mlsanity.com/paper/2111.10722/) (2021)
- [RafterNet: Probabilistic predictions in multi-response regression](https://mlsanity.com/paper/2112.03377/) (2021)
- [Dependence model assessment and selection with DecoupleNets](https://mlsanity.com/paper/2202.03406/) (2022)
- [Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencoder](https://mlsanity.com/paper/2309.09916/) (2023)
- [A Generative Approach to Quasi-Random Sampling from Copulas via Space-Filling Designs](https://mlsanity.com/paper/2403.05281/) (2024)
- [Adaptive generative moment matching networks for improved learning of dependence structures](https://mlsanity.com/paper/2508.21531/) (2025)

## Abstract (arXiv)

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.