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.

翻译：探究协变量在不同分布间的依赖关系对诸多应用至关重要。Copula作为联合变量依赖性建模的有力工具，因其直观的特性已在多个实际场景中得到有效应用。然而，现有计算方法缺乏对任意Copula进行可行推断与采样的能力，这限制了其广泛使用。本文提出一种创新的适用于Copula的准随机采样方法，该方法利用生成对抗网络（GANs）与空间填充设计。所提框架通过GANs构建从低维均匀分布到高维Copula结构的直接映射，并基于空间填充设计点集为任意Copula结构生成准随机样本。在高维小样本场景下，与现有方法相比，该方法显著提升了采样精度与计算效率。此外，我们发展了准蒙特卡罗估计量的收敛速度理论，为偏差与方差提供了严格的上下界。模拟实验与风险管理的实际应用均验证了所提方法的有效性，并展示了其相较于现有替代方案的优越性。