Generalization Properties of Optimal Transport GANs with Latent Distribution Learning
This work addresses a theoretical gap in GANs for researchers, but it appears incremental as it builds on existing frameworks.
The paper tackles the problem of understanding how the latent distribution and generator complexity affect performance in Optimal Transport GANs, and shows that learning the latent distribution can lead to significant advantages in sample complexity.
The Generative Adversarial Networks (GAN) framework is a well-established paradigm for probability matching and realistic sample generation. While recent attention has been devoted to studying the theoretical properties of such models, a full theoretical understanding of the main building blocks is still missing. Focusing on generative models with Optimal Transport metrics as discriminators, in this work we study how the interplay between the latent distribution and the complexity of the pushforward map (generator) affects performance, from both statistical and modelling perspectives. Motivated by our analysis, we advocate learning the latent distribution as well as the pushforward map within the GAN paradigm. We prove that this can lead to significant advantages in terms of sample complexity.