Quasi-Random Sampling for Multivariate Distributions via Generative Neural Networks
提出生成矩匹配网络，从任意连接函数的多元分布中生成近似拟随机样本，实现方差缩减，适用于参数模型和真实数据，在风险管理等应用中快速估计期望。
Generative moment matching networks (GMMNs) are introduced for generating approximate quasi-random samples from multivariate models with any underlying copula to compute estimates with 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. Using GMMNs allows one to construct approximate 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.