Statistical Error Bounds for GANs with Nonlinear Objective Functionals
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Abstract (arXiv)
Generative adversarial networks (GANs) are unsupervised learning methods for training a generator distribution to produce samples that approximate those drawn from a target distribution. Many such methods can be formulated as minimization of a metric or divergence between probability distributions. Recent works have derived statistical error bounds for GANs that are based on integral probability metrics (IPMs), e.g., WGAN which is based on the 1-Wasserstein metric. In general, IPMs are defined by optimizing a linear functional (difference of expectations) over a space of discriminators. A much larger class of GANs, which we here call (f,Gamma)-GANs, can be constructed using f-divergences (e.g., Jensen-Shannon, KL, or α-divergences) together with a regularizing discriminator space Gamma (e.g., 1-Lipschitz functions). These GANs have nonlinear objective functions, depending on the choice of f, and have been shown to exhibit improved performance in a number of applications. In this work we derive statistical error bounds for (f,Gamma)-GANs for general classes of f and Gamma in the form of finite-sample concentration inequalities. These results prove the statistical consistency of (f,Gamma)-GANs and reduce to the known results for IPM-GANs in the appropriate limit. Our results use novel Rademacher complexity bounds which provide new insight into the performance of IPM-GANs for distributions with unbounded support and have application to statistical learning tasks beyond GANs.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 22 of its 36 references that are in the map. First posted on arXiv 24 Jun 2024.
Builds on
22 of 36 references.
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.