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理论扩展至生成模型，并基于Wasserstein距离和全变差距离建立了模型的泛化界。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降维优势。上述结果自然适用于Wasserstein GANs与Energy-Based GANs，所提出的界为这两种模型提供了新的训练目标。尽管本研究以理论为主，我们仍通过数值实验展示了Wasserstein GANs在合成数据集上的非平凡泛化界。