Quasi-random sampling for multivariate distributions via generative neural networks

2018/11/01 by Marius Hofert, Hofert, Marius, Avinash Prasad +3 · 2 citations
Computer Science · Decision Sciences · Mathematics · #00A72 #60E05 #62H99 #65C10 #65C60 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Approximation and Integration #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1811.00683

openalex publication_date 2018/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the difficulty of training Recurrent Neural Networks
• Remarks on a Multivariate Transformation
• MODELLING ASYMMETRIC EXCHANGE RATE DEPENDENCE*

Cited by

• Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies
• Adaptive generative moment matching networks for improved learning of dependence structures

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• Multivariate time-series modeling with generative neural networks