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-贝叶斯理论扩展至生成式模型，并基于Wasserstein距离和总变差距离建立了模型的泛化界。关于Wasserstein距离的首个结果假设实例空间有界，第二个结果则利用了降维的优势。我们的结论自然适用于Wasserstein生成对抗网络与基于能量的生成对抗网络，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，但我们通过数值实验展示了Wasserstein生成对抗网络在合成数据集上的非平凡泛化界。