Non-Asymptotic Error Bounds for Bidirectional GANs
This addresses the lack of theoretical foundations for BiGANs, offering insights for researchers in generative modeling and machine learning, though it is incremental in extending analysis from unidirectional GANs.
The paper tackles the problem of providing theoretical guarantees for bidirectional GANs (BiGANs) by deriving nearly sharp error bounds for the estimation error under the Dudley distance, without assuming equal dimensions or bounded support for distributions, which are common limitations in prior work.
We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural networks used in the model. To the best of our knowledge, this is the first theoretical guarantee for the bidirectional GAN learning approach. An appealing feature of our results is that they do not assume the reference and the data distributions to have the same dimensions or these distributions to have bounded support. These assumptions are commonly assumed in the existing convergence analysis of the unidirectional GANs but may not be satisfied in practice. Our results are also applicable to the Wasserstein bidirectional GAN if the target distribution is assumed to have a bounded support. To prove these results, we construct neural network functions that push forward an empirical distribution to another arbitrary empirical distribution on a possibly different-dimensional space. We also develop a novel decomposition of the integral probability metric for the error analysis of bidirectional GANs. These basic theoretical results are of independent interest and can be applied to other related learning problems.