# Nonparametric Density Estimation under Adversarial Losses

arXiv: https://arxiv.org/abs/1805.08836 · HTML: https://mlsanity.com/paper/1805.08836/

## Key facts

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

## Built on by (most cited first, 26 of 26)

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- [PAC-Bayesian Generalization Bounds for Adversarial Generative Models](https://mlsanity.com/paper/2302.08942/) (2023)
- [Sample Complexity Bounds for Estimating Probability Divergences under Invariances](https://mlsanity.com/paper/2311.02868/) (2023)
- [On Energy-Based Models with Overparametrized Shallow Neural Networks](https://mlsanity.com/paper/2104.07531/) (2021)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs](https://mlsanity.com/paper/2201.07206/) (2022)
- [Support-weighted Adversarial Imitation Learning](https://mlsanity.com/paper/2002.08803/) (2020)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)
- [Optimal 1-Wasserstein Distance for WGANs](https://mlsanity.com/paper/2201.02824/) (2022)
- [Breaking the curse of dimensionality in structured density estimation](https://mlsanity.com/paper/2410.07685/) (2024)
- [Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GAN](https://mlsanity.com/paper/2110.13680/) (2021)
- [Adversarial Estimators](https://mlsanity.com/paper/2204.10495/) (2022)
- [Sobolev Space Regularised Pre Density Models](https://mlsanity.com/paper/2307.13763/) (2023)
- [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025)
- [Error Analysis of Bayesian Inverse Problems with Generative Priors](https://mlsanity.com/paper/2601.17374/) (2026)
- [Scalable Sobolev IPM for Probability Measures on a Graph](https://mlsanity.com/paper/2502.00737/) (2025)
- [DAMM-Diffusion: Learning Divergence-Aware Multi-Modal Diffusion Model for Nanoparticles Distribution Prediction](https://mlsanity.com/paper/2503.09491/) (2025)
- [A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rules](https://mlsanity.com/paper/2306.13641/) (2023)
- [Generalization error property of infoGAN for two-layer neural network](https://mlsanity.com/paper/2310.00443/) (2023)
- [Collaborative Multi-source Domain Adaptation Through Optimal Transport](https://mlsanity.com/paper/2404.06599/) (2024)
- [Generalized Sobolev IPM for Graph-Based Measures](https://mlsanity.com/paper/2510.25591/) (2025)
- [Optimizing Computational-Statistical Runtime for Wasserstein Distance Estimation](https://mlsanity.com/paper/2605.20122/) (2026)
- [Sparse Priors for Efficient Distribution Learning](https://mlsanity.com/paper/2609.20883/) (2026)

## 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.