# A Generative Approach to Quasi-Random Sampling from Copulas via Space-Filling Designs

arXiv: https://arxiv.org/abs/2403.05281 · HTML: https://mlsanity.com/paper/2403.05281/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 8 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Deep Network Approximation Characterized by Number of Neurons](https://mlsanity.com/paper/1906.05497/) (2019)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Copula-based transferable models for synthetic population generation](https://mlsanity.com/paper/2302.09193/) (2023)
- [Quasi-random sampling for multivariate distributions via generative neural networks](https://mlsanity.com/paper/1811.00683/) (2018)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)

## Abstract (arXiv)

Exploring the dependence between covariates across distributions is crucial for many applications. Copulas serve as a powerful tool for modeling joint variable dependencies and have been effectively applied in various practical contexts due to their intuitive properties. However, existing computational methods lack the capability for feasible inference and sampling of any copula, preventing their widespread use. This paper introduces an innovative quasi-random sampling approach for copulas, utilizing generative adversarial networks (GANs) and space-filling designs. The proposed framework constructs a direct mapping from low-dimensional uniform distributions to high-dimensional copula structures using GANs, and generates quasi-random samples for any copula structure from points set of space-filling designs. In the high-dimensional situations with limited data, the proposed approach significantly enhances sampling accuracy and computational efficiency compared to existing methods. Additionally, we develop convergence rate theory for quasi-Monte Carlo estimators, providing rigorous upper bounds for bias and variance. Both simulated experiments and practical implementations, particularly in risk management, validate the proposed method and showcase its superiority over existing alternatives.