Statistical inference for generative adversarial networks and other minimax problems
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Abstract (arXiv)
This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are estimated to solve a particular minimax problem. This minimax problem typically has a multitude of solutions and the focus of this paper are the statistical properties of these solutions. We address two key statistical issues for the generator and discriminator network parameters, consistent estimation and confidence sets. We first show that the set of solutions to the sample GAN problem is a (Hausdorff) consistent estimator of the set of solutions to the corresponding population GAN problem. We then devise a computationally intensive procedure to form confidence sets and show that these sets contain the population GAN solutions with the desired coverage probability. Small numerical experiments and a Monte Carlo study illustrate our results and verify our theoretical findings. We also show that our results apply in general minimax problems that may be non-convex, non-concave, and have multiple solutions.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 27 of its 79 references that are in the map. First posted on arXiv 21 Apr 2021.
Builds on
27 of 79 references.
References · 27
- 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
- 2018Which Training Methods for GANs do actually Converge?cited by 672
- 2017Generative Adversarial Networks: An Overviewcited by 588
- 2019Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithmscited by 555
- 2015Weight Uncertainty in Neural Networkscited by 554
- 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 460
- 2019Agnostic Federated Learningcited by 451
- 2018Learning Models with Uniform Performance via Distributionally Robust Optimizationcited by 334
- 2020Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulationcited by 225
- 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 165
- 2020Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimizationcited by 94
- 2020Learning to Simulate Dynamic Environments with GameGANcited by 86
15 more
- 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
- 2020Precise Tradeoffs in Adversarial Training for Linear Regressioncited by 76
- 2017Gradient descent GAN optimization is locally stablecited by 65
- 2017Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeterscited by 55
- 2019Hybrid Block Successive Approximation for One-Sided Non-Convex Min-Max Problems: Algorithms and Applicationscited by 55
- 2018Deep Network Interpolation for Continuous Imagery Effect Transitioncited by 47
- 2018Multi-Agent Reinforcement Learning via Double Averaging Primal-Dual Optimizationcited by 40
- 2017Approximation and Convergence Properties of Generative Adversarial Learningcited by 28
- 2020Some Theoretical Insights into Wasserstein GANscited by 28
- 2018Some Theoretical Properties of GANscited by 27
- 2020Statistical guarantees for generative models without dominationcited by 27
- 2017Generative Adversarial Networks recover features in astrophysical images of galaxies beyond the deconvolution limitcited by 26
- 2018Nonparametric Density Estimation under Adversarial Lossescited by 26
- 2019Significance Tests for Neural Networkscited by 17
- 2021Rates of convergence for density estimation with generative adversarial networkscited by 13
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Citing papers per year: 2023: 1; 2024: 1; 2025: 0; 2026: 1.
3 papers.