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Approximating Probability Distributions by using Wasserstein Generative Adversarial Networks

arXiv 2103.10060 ↗First posted 18 Mar 2021cs.LG stat.MLcited by 0

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Abstract (arXiv)

Studied here are Wasserstein generative adversarial networks (WGANs) with GroupSort neural networks as their discriminators. It is shown that the error bound of the approximation for the target distribution depends on the width and depth (capacity) of the generators and discriminators and the number of samples in training. A quantified generalization bound is established for the Wasserstein distance between the generated and target distributions. According to the theoretical results, WGANs have a higher requirement for the capacity of discriminators than that of generators, which is consistent with some existing results. More importantly, the results with overly deep and wide (high-capacity) generators may be worse than those with low-capacity generators if discriminators are insufficiently strong. Numerical results obtained using Swiss roll and MNIST datasets confirm the theoretical results.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 15 of its 32 references that are in the map. First posted on arXiv 18 Mar 2021.

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References · 15

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  12. 2018Approximability of Discriminators Implies Diversity in GANscited by 28
3 more
  1. 2020Approximating Lipschitz continuous functions with GroupSort neural networkscited by 27
  2. 2021Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributionscited by 22
  3. 2021On the capacity of deep generative networks for approximating distributionscited by 19

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