# Rates of convergence for density estimation with generative adversarial networks

arXiv: https://arxiv.org/abs/2102.00199 · HTML: https://mlsanity.com/paper/2102.00199/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 30 Jan 2021.

## Builds on (most cited first, 18 of 18)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Deep Video Portraits](https://mlsanity.com/paper/1805.11714/) (2018)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [Energy-based Generative Adversarial Network](https://mlsanity.com/paper/1609.03126/) (2016)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [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)
- [Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networks](https://mlsanity.com/paper/2002.03938/) (2020)
- [Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Losses](https://mlsanity.com/paper/1902.03511/) (2019)
- [Generalization Properties of Optimal Transport GANs with Latent Distribution Learning](https://mlsanity.com/paper/2007.14641/) (2020)
- [Understanding GANs: the LQG Setting](https://mlsanity.com/paper/1710.10793/) (2017)
- [A Convenient Infinite Dimensional Framework for Generative Adversarial Learning](https://mlsanity.com/paper/2011.12087/) (2020)

## Built on by (most cited first, 13 of 13)

- [Statistical guarantees for denoising reflected diffusion models](https://mlsanity.com/paper/2411.01563/) (2024)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)
- [Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution](https://mlsanity.com/paper/2307.16422/) (2023)
- [A Wasserstein perspective of Vanilla GANs](https://mlsanity.com/paper/2403.15312/) (2024)
- [Numerical and statistical analysis of NeuralODE with Runge-Kutta time integration](https://mlsanity.com/paper/2503.10729/) (2025)
- [Learning Brenier Potentials with Convex Generative Adversarial Neural Networks](https://mlsanity.com/paper/2504.19779/) (2025)
- [Bounds on Lp errors in density ratio estimation via f-divergence loss functions](https://mlsanity.com/paper/2410.01516/) (2024)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Scaling-based Data Augmentation for Generative Models and its Theoretical Extension](https://mlsanity.com/paper/2410.20780/) (2024)
- [Can Generative Artificial Intelligence Survive Data Contamination? Theoretical Guarantees under Contaminated Recursive Training](https://mlsanity.com/paper/2602.16065/) (2026)
- [Regularity of Solutions to Beckmann's Parametric Optimal Transport](https://mlsanity.com/paper/2603.19755/) (2026)
- [Generative Adversarial Learning from Deterministic Processes](https://mlsanity.com/paper/2605.18425/) (2026)
- [Generative Predictive Distributions for Time Series](https://mlsanity.com/paper/2606.16773/) (2026)

## Abstract (arXiv)

In this work we undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We prove an oracle inequality for the Jensen-Shannon (JS) divergence between the underlying density mathsfp^* and the GAN estimate with a significantly better statistical error term compared to the previously known results. The advantage of our bound becomes clear in application to nonparametric density estimation. We show that the JS-divergence between the GAN estimate and mathsfp^* decays as fast as (logn/n)2β/(2β + d), where n is the sample size and β determines the smoothness of mathsfp^*. This rate of convergence coincides (up to logarithmic factors) with minimax optimal for the considered class of densities.