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Nonparametric Density Estimation under Adversarial Losses

arXiv 1805.08836 ↗First posted 22 May 2018math.ST cs.IT math.ITcited by 26

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Abstract (arXiv)

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical Lp losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 May 2018.

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Citing papers per year: 2020: 1; 2021: 5; 2022: 4; 2023: 6; 2024: 3; 2025: 4; 2026: 3.

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  1. 2021Unsupervised Multi-source Domain Adaptation Without Access to Source Datacited by 76
  2. 2021An error analysis of generative adversarial networks for learning distributionscited by 36
  3. 2022Approximation bounds for norm constrained neural networks with applications to regression and GANscited by 22
  4. 2023Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theorycited by 16
  5. 2023PAC-Bayesian Generalization Bounds for Adversarial Generative Modelscited by 13
  6. 2023Sample Complexity Bounds for Estimating Probability Divergences under Invariancescited by 12
  7. 2021On Energy-Based Models with Overparametrized Shallow Neural Networkscited by 8
  8. 2024Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learningcited by 7
  9. 2022Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANscited by 6
  10. 2020Support-weighted Adversarial Imitation Learningcited by 3
  11. 2021Statistical inference for generative adversarial networks and other minimax problemscited by 3
  12. 2022Optimal 1-Wasserstein Distance for WGANscited by 3
14 more
  1. 2024Breaking the curse of dimensionality in structured density estimationcited by 3
  2. 2021Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GANcited by 2
  3. 2022Adversarial Estimatorscited by 2
  4. 2023Sobolev Space Regularised Pre Density Modelscited by 2
  5. 2025A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solverscited by 2
  6. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2
  7. 2025Scalable Sobolev IPM for Probability Measures on a Graphcited by 1
  8. 2025DAMM-Diffusion: Learning Divergence-Aware Multi-Modal Diffusion Model for Nanoparticles Distribution Predictioncited by 1
  9. 2023A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rulescited by 0
  10. 2023Generalization error property of infoGAN for two-layer neural networkcited by 0
  11. 2024Collaborative Multi-source Domain Adaptation Through Optimal Transportcited by 0
  12. 2025Generalized Sobolev IPM for Graph-Based Measurescited by 0
  13. 2026Optimizing Computational-Statistical Runtime for Wasserstein Distance Estimationcited by 0
  14. 2026Sparse Priors for Efficient Distribution Learningcited by 0