# Robust W-GAN-Based Estimation Under Wasserstein Contamination

arXiv: https://arxiv.org/abs/2101.07969 · HTML: https://mlsanity.com/paper/2101.07969/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 20 Jan 2021.

## Builds on (most cited first, 14 of 14)

- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Wasserstein Adversarial Examples via Projected Sinkhorn Iterations](https://mlsanity.com/paper/1902.07906/) (2019)
- [Sliced Gromov-Wasserstein](https://mlsanity.com/paper/1905.10124/) (2019)
- [Banach Wasserstein GAN](https://mlsanity.com/paper/1806.06621/) (2018)
- [Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model](https://mlsanity.com/paper/1506.00691/) (2015)
- [Generalized Resilience and Robust Statistics](https://mlsanity.com/paper/1909.08755/) (2019)
- [Multi-marginal Wasserstein GAN](https://mlsanity.com/paper/1911.00888/) (2019)
- [Deconstructing Generative Adversarial Networks](https://mlsanity.com/paper/1901.09465/) (2019)
- [Generative Adversarial Nets for Robust Scatter Estimation: A Proper Scoring Rule Perspective](https://mlsanity.com/paper/1903.01944/) (2019)
- [Robust Estimation and Generative Adversarial Nets](https://mlsanity.com/paper/1810.02030/) (2018)

## Built on by (most cited first, 9 of 9)

- [General Synthetic-Powered Inference](https://mlsanity.com/paper/2509.20345/) (2025)
- [Solving a Research Problem in Mathematical Statistics with AI Assistance](https://mlsanity.com/paper/2511.18828/) (2025)
- [Wasserstein Distributionally Robust Nonparametric Regression](https://mlsanity.com/paper/2505.07967/) (2025)
- [Optimal Robust Estimation under Local and Global Corruptions: Stronger Adversary and Smaller Error](https://mlsanity.com/paper/2410.17230/) (2024)
- [Minimax Statistical Estimation under Wasserstein Contamination](https://mlsanity.com/paper/2308.01853/) (2023)
- [Robust Estimation for Kernel Exponential Families with Smoothed Total Variation Distances](https://mlsanity.com/paper/2410.20760/) (2024)
- [Estimation of Stochastic Optimal Transport Maps](https://mlsanity.com/paper/2512.09499/) (2025)
- [Distribution Estimation of Contaminated Data via DNN-based MoM-GANs](https://mlsanity.com/paper/2212.13741/) (2022)
- [Robust Processing and Learning: Principles, Methods, and Wireless Applications](https://mlsanity.com/paper/2602.09848/) (2026)

## Abstract (arXiv)

Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax rates of estimation have been established in recent years, many existing robust estimators with provably optimal convergence rates are also computationally intractable. In this paper, we study several estimation problems under a Wasserstein contamination model and present computationally tractable estimators motivated by generative adversarial networks (GANs). Specifically, we analyze properties of Wasserstein GAN-based estimators for location estimation, covariance matrix estimation, and linear regression and show that our proposed estimators are minimax optimal in many scenarios. Finally, we present numerical results which demonstrate the effectiveness of our estimators.