# Adaptive generative moment matching networks for improved learning of dependence structures

arXiv: https://arxiv.org/abs/2508.21531 · HTML: https://mlsanity.com/paper/2508.21531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 29 Aug 2025.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [On gradient regularizers for MMD GANs](https://mlsanity.com/paper/1805.11565/) (2018)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing](https://mlsanity.com/paper/1508.00655/) (2015)
- [Quasi-random sampling for multivariate distributions via generative neural networks](https://mlsanity.com/paper/1811.00683/) (2018)
- [Exact simulation of max-stable processes](https://mlsanity.com/paper/1506.04430/) (2015)
- [Multivariate time-series modeling with generative neural networks](https://mlsanity.com/paper/2002.10645/) (2020)
- [Right-truncated Archimedean and related copulas](https://mlsanity.com/paper/2006.10107/) (2020)
- [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)
- [Index-mixed copulas](https://mlsanity.com/paper/2306.10663/) (2023)

## Abstract (arXiv)

An adaptive bandwidth selection procedure for the mixture kernel in the maximum mean discrepancy (MMD) for fitting generative moment matching networks (GMMNs) is introduced, and improved learning of copula random number generators is demonstrated. Based on the relative error of the training loss, the number of kernels is increased during training; additionally, the relative error of the validation loss is used as an early stopping criterion. While training time remains similar, adaptively training GMMNs (AGMMNs) significantly increases training performance, which is shown based on validation MMD trajectories, samples and validation MMD values. Superiority of AGMMNs over GMMNs and parametric copula models is also demonstrated in terms of three applications. First, convergence rates of estimators based on quasi-random versus pseudo-random samples from copulas are investigated in dimensions as large as 100 for the first time. Second, replicated validation MMDs, as well as Monte Carlo and quasi-Monte Carlo applications demonstrate the improved training of AGMMNs for a copula model implied by the 50 constituents of the S&P 500 index after deGARCHing. Last, both the latter dataset and 50 constituents of the FTSE 100 are used to demonstrate that the improved training of AGMMNs indeed translates to an improved model prediction.