Asymptotic Statistical Analysis of $f$-divergence GAN

Understand

Generative Adversarial Networks (GANs) have achieved great success in data generation.

• However, its statistical properties are not fully understood.
• In this paper, we consider the statistical behavior of the general $f$-divergence formulation of GAN, which includes the Kullback--Leibler divergence that is closely related to the maximum likelihood principle.
• We show that for parametric generative models that are correctly specified, all $f$-divergence GANs with the same discriminator classes are asymptotically equivalent under suitable regularity conditions.