Generalization Properties of Optimal Transport GANs with Latent Distribution Learning

Generative Adversarial Networks (GAN) are powerful methods for learning probability measures and performing realistic sampling [21]. Algorithms in this class aim to reproduce the sampling behavior of the target distribution, rather than explicitly fitting a density function. This is done by modeling the target probability as the pushforward of a probability measure in a latent space. Since their introduction, GANs have achieved remarkable progress. From a practical perspective, a large number of model architectures have been explored, leading to impressive results in data generation [48, 24, 26]. From the side of theory, attention has been devoted to identify rich metrics for generator training, such as f-divergences [36], integral probability metrics (IPM) [16] or optimal transport distances [3], as well as studying their approximation properties [28, 5, 51]. From the statistical perspective, progression has been slower. While recent work has set the first steps towards a characterization of the generalization properties of GANs with IPM loss functions [4, 51, 27, 41, 45], a full theoretical understanding of the main building blocks of the GAN framework is still missing. In this work, we focus on optimal transport-based loss functions [20] and study the impact of two key quantities of the GANs paradigm on the overall generalization performance.