自适应调整核函数带宽，让生成模型更精准捕捉变量依赖关系。
Adaptive generative moment matching networks for improved learning of dependence structures
- 根据训练损失误差动态增加混合核数量，优化生成模型学习过程。
- 在100维场景下验证，自适应模型收敛速度和生成样本质量显著提升。
- 适合需要高维依赖结构建模的金融风险分析与量化应用。
提出一种针对最大均值差异（MMD）中混合核的自适应带宽选择方法，用于改进生成矩匹配网络（GMMN）对依赖结构的学习。基于训练损失相对误差，训练过程中动态增加核数量；同时利用验证损失相对误差作为早停准则。尽管训练时间相近，自适应训练的GMMN（AGMMN）在验证MMD轨迹、样本质量和验证MMD值上均有显著提升。在三个应用场景中，AGMMN均优于传统GMMN及参数化拷贝拉模型：首次在高达100维下比较了拟随机与伪随机抽样生成器的估计器收敛速率；在对经过deGARCH处理的标普500指数50只成分股隐含拷贝拉模型的训练中，通过重复验证MMD及蒙特卡洛/准蒙特卡洛应用证明了性能提升；最后，使用标普500与富时100各50只成分股数据表明，AGMMN的训练改进确实转化为更优的模型预测能力。
原文摘要 · Abstract (English)
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.
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