# Statistical inference for generative adversarial networks and other minimax problems

arXiv: https://arxiv.org/abs/2104.10601 · HTML: https://mlsanity.com/paper/2104.10601/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 79 references that are in the map.
- First posted on arXiv 21 Apr 2021.

## Builds on (most cited first, 27 of 27)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulation](https://mlsanity.com/paper/2003.13659/) (2020)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization](https://mlsanity.com/paper/2011.00364/) (2020)
- [Learning to Simulate Dynamic Environments with GameGAN](https://mlsanity.com/paper/2005.12126/) (2020)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [Precise Tradeoffs in Adversarial Training for Linear Regression](https://mlsanity.com/paper/2002.10477/) (2020)
- [Gradient descent GAN optimization is locally stable](https://mlsanity.com/paper/1706.04156/) (2017)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [Hybrid Block Successive Approximation for One-Sided Non-Convex Min-Max Problems: Algorithms and Applications](https://mlsanity.com/paper/1902.08294/) (2019)
- [Deep Network Interpolation for Continuous Imagery Effect Transition](https://mlsanity.com/paper/1811.10515/) (2018)
- [Multi-Agent Reinforcement Learning via Double Averaging Primal-Dual Optimization](https://mlsanity.com/paper/1806.00877/) (2018)
- [Approximation and Convergence Properties of Generative Adversarial Learning](https://mlsanity.com/paper/1705.08991/) (2017)
- [Some Theoretical Insights into Wasserstein GANs](https://mlsanity.com/paper/2006.02682/) (2020)
- [Some Theoretical Properties of GANs](https://mlsanity.com/paper/1803.07819/) (2018)
- [Statistical guarantees for generative models without domination](https://mlsanity.com/paper/2010.09237/) (2020)
- [Generative Adversarial Networks recover features in astrophysical images of galaxies beyond the deconvolution limit](https://mlsanity.com/paper/1702.00403/) (2017)
- [Nonparametric Density Estimation under Adversarial Losses](https://mlsanity.com/paper/1805.08836/) (2018)
- [Significance Tests for Neural Networks](https://mlsanity.com/paper/1902.06021/) (2019)
- [Rates of convergence for density estimation with generative adversarial networks](https://mlsanity.com/paper/2102.00199/) (2021)

## Built on by (most cited first, 3 of 3)

- [Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-art](https://mlsanity.com/paper/2308.16316/) (2023)
- [Adaptive Learning of the Latent Space of Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/2409.18374/) (2024)
- [Generative Predictive Distributions for Time Series](https://mlsanity.com/paper/2606.16773/) (2026)

## 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.