Conference proceeding
Non-Asymptotic Error Bounds for Bidirectional GANs
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 34 (NEURIPS 2021), Vol.34
Advances in Neural Information Processing Systems
01/01/2021
Abstract
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.
Details
- Title: Subtitle
- Non-Asymptotic Error Bounds for Bidirectional GANs
- Creators
- Shiao Liu - Univ Iowa, Dept Stat & Actuarial Sci, Iowa City, IA 52242 USAYunfei Yang - University of Hong KongJian Huang - Univ Iowa, Dept Stat & Actuarial Sci, Iowa City, IA 52242 USAYuling Jiao - Wuhan UniversityYang Wang - University of Hong Kong
- Contributors
- M Ranzato (Editor)A Beygelzimer (Editor)Y Dauphin (Editor)P S Liang (Editor)J W Vaughan (Editor)
- Resource Type
- Conference proceeding
- Publication Details
- ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 34 (NEURIPS 2021), Vol.34
- Publisher
- Neural Information Processing Systems (Nips)
- Series
- Advances in Neural Information Processing Systems
- ISSN
- 1049-5258
- Number of pages
- 12
- Grant note
- Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications 16308518; 16317416 / Hong Kong Research Grant Council; Hong Kong Research Grants Council DMS-1916199 / U.S. NSF; National Science Foundation (NSF) ITS/044/18FX / HK Innovation Technology Fund 11871474 / National Science Foundation of China; National Natural Science Foundation of China (NSFC)
- Language
- English
- Date published
- 01/01/2021
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984400638202771
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