Building on the success of deep learning, two modern approaches to learn a probability model of the observed data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-bound on the log-likelihood function. GANs, however, compute a generative model by minimizing a distance between observed and generated probability distributions without considering an explicit model for the observed data. The lack of having explicit probability models in GANs prohibits computation of sample likelihoods in their frameworks and limits their use in statistical inference problems. In this work, we show that an optimal transport GAN with the entropy regularization can be viewed as a generative model that maximizes a lower-bound on average sample likelihoods, an approach that VAEs are based on. In particular, our proof constructs an explicit probability model for GANs that can be used to compute likelihood statistics within GAN's framework. Our numerical results on several datasets demonstrate consistent trends with the proposed theory.

通过构建一种显式的概率模型，将沃瑟斯坦GANs与熵正则化视为基于变分下界的生成模型，从而使得GANs和VAEs之间建立了有理论支持的联系。同时，作者还在多个数据集上计算了GANs的似然统计量，验证了该理论结果。

熵生成对抗网络与变分自编码器相遇：计算GAN样本似然的统计方法