mlsanityData to 7 Oct 2026

Rates of convergence for density estimation with generative adversarial networks

arXiv 2102.00199 ↗First posted 30 Jan 2021math.ST stat.ML stat.THcited by 13

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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.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 18 of its 51 references that are in the map. First posted on arXiv 30 Jan 2021.

Builds on

18 of 51 references.

References · 18

  1. 2016Improved Techniques for Training GANscited by 2,938
  2. 2017Improved Training of Wasserstein GANscited by 2,223
  3. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,898
  4. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  5. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  6. 2018Deep Video Portraitscited by 265
  7. 2015Training generative neural networks via Maximum Mean Discrepancy optimizationcited by 149
  8. 2016Mode Regularized Generative Adversarial Networkscited by 123
  9. 2016Energy-based Generative Adversarial Networkcited by 119
  10. 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
  11. 2020Some Theoretical Insights into Wasserstein GANscited by 28
  12. 2018Some Theoretical Properties of GANscited by 27
6 more
  1. 2020Statistical guarantees for generative models without dominationcited by 27
  2. 2020Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networkscited by 23
  3. 2019Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Lossescited by 22
  4. 2020Generalization Properties of Optimal Transport GANs with Latent Distribution Learningcited by 13
  5. 2017Understanding GANs: the LQG Settingcited by 12
  6. 2020A Convenient Infinite Dimensional Framework for Generative Adversarial Learningcited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 1; 2024: 4; 2025: 2; 2026: 4.

13 papers.

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  1. 2024Statistical guarantees for denoising reflected diffusion modelscited by 6
  2. 2021Statistical inference for generative adversarial networks and other minimax problemscited by 3
  3. 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
  4. 2024A Wasserstein perspective of Vanilla GANscited by 3
  5. 2025Numerical and statistical analysis of NeuralODE with Runge-Kutta time integrationcited by 3
  6. 2025Learning Brenier Potentials with Convex Generative Adversarial Neural Networkscited by 3
  7. 2024Bounds on Lp errors in density ratio estimation via f-divergence loss functionscited by 2
  8. 2022Noise-contrastive Online Change Point Detectioncited by 0
  9. 2024Scaling-based Data Augmentation for Generative Models and its Theoretical Extensioncited by 0
  10. 2026Can Generative Artificial Intelligence Survive Data Contamination? Theoretical Guarantees under Contaminated Recursive Trainingcited by 0
  11. 2026Regularity of Solutions to Beckmann's Parametric Optimal Transportcited by 0
  12. 2026Generative Adversarial Learning from Deterministic Processescited by 0
1 more
  1. 2026Generative Predictive Distributions for Time Seriescited by 0