Statistical Error Bounds for GANs with Nonlinear Objective Functionals
Authors: Jeremiah Birrell
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work we derive statistical error bounds for (f, Γ)-GANs for general classes of f and Γ in the form of finite-sample concentration inequalities. These results prove the statistical consistency of (f, Γ)-GANs... In this paper we develop theory that allows us to prove statistical consistency of the (f, Γ)-GANs, in the form of finite-sample concentration inequalities. The key technical hurdle is the nonlinearity of the objective functional due to the presence of the generalized cumulant generating function (4). Section 2 is dedicated to properties of and bounds on ΛP f which will be needed in Section 3 to derive concentration inequalities for (f, Γ)-GANs. |
| Researcher Affiliation | Academia | Jeremiah Birrell EMAIL Department of Mathematics Texas State University San Marcos, TX 78666, USA |
| Pseudocode | No | The paper contains mathematical formulations and proofs, but no clearly structured pseudocode or algorithm blocks are present. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to a code repository for the methodology described. |
| Open Datasets | No | The paper is theoretical and focuses on deriving statistical error bounds for GANs. It does not describe experiments that use specific datasets, nor does it provide access information for any open datasets. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments with dataset splits. Therefore, no information on training/test/validation splits is provided. |
| Hardware Specification | No | The paper is theoretical and does not describe experiments that require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not detail an experimental implementation. Therefore, no specific software dependencies with version numbers are provided. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup with hyperparameters or training configurations. |