We extend PAC-Bayesian theory to generative models and develop generalization bounds for models based on the Wasserstein distance and the total variation distance. Our first result on the Wasserstein distance assumes the instance space is bounded, while our second result takes advantage of dimensionality reduction. Our results naturally apply to Wasserstein GANs and Energy-Based GANs, and our bounds provide new training objectives for these two. Although our work is mainly theoretical, we perform numerical experiments showing non-vacuous generalization bounds for Wasserstein GANs on synthetic datasets.

翻译：我们将PAC-Bayesian理论扩展到生成模型，并针对基于Wasserstein距离和全变差距离的模型推导出泛化界。关于Wasserstein距离的第一个结果假设实例空间有界，而第二个结果则利用了降维优势。我们的结论自然适用于Wasserstein GAN和Energy-Based GAN，并且所提出的界为这两种模型提供了新的训练目标。尽管本研究主要属于理论范畴，我们通过数值实验展示了Wasserstein GAN在合成数据集上的非平凡泛化界。