A Wasserstein perspective of Vanilla GANs
The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for good dimension reduction properties. Statistical results for Vanilla GANs, the original optimization problem, are still rather limited and require assumptions such as smooth activation functions and equal dimensions of the latent space and the ambient space. To bridge this gap, we draw a connection from Vanilla GANs to the Wasserstein distance. By doing so, existing results for Wasserstein GANs can be extended to Vanilla GANs. In particular, we obtain an oracle inequality for Vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be satisfied by network architectures commonly used in practice, such as feedforward ReLU networks. By providing a quantitative result for the approximation of a Lipschitz function by a feedforward ReLU network with bounded H\"older norm, we conclude a rate of convergence for Vanilla GANs as well as Wasserstein GANs as estimators of the unknown probability distribution.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionSimilar Papers 제목 키워드 기반
Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance b…
Benchmarking Vanilla GAN, DCGAN, and WGAN Architectures for MRI Reconstruction: A Quantitative Analysis
Magnetic Resonance Imaging (MRI) is a crucial imaging modality for viewing internal body structures. This research work analyses the performance of popular GAN models for accurate and precise MRI reconstruction by enhanc…
Image ReconstructionMRI ReconstructionStability Analysis Framework for Particle-based Distance GANs with Wasserstein Gradient Flow
In this paper, we investigate the training process of generative networks that use a type of probability density distance named particle-based distance as the objective function, e.g. MMD GAN, Cram\'er GAN, EIEG GAN. How…
Gradient penalty from a maximum margin perspective
A popular heuristic for improved performance in Generative adversarial networks (GANs) is to use some form of gradient penalty on the discriminator. This gradient penalty was originally motivated by a Wasserstein distanc…
Image GenerationLipschitz Generative Adversarial Nets
In this paper, we study the convergence of generative adversarial networks (GANs) from the perspective of the informativeness of the gradient of the optimal discriminative function. We show that GANs without restriction …
Informativeness