Robust W-GAN-Based Estimation Under Wasserstein Contamination
This addresses the problem of robust estimation for statisticians and machine learning practitioners by providing efficient methods that overcome computational intractability in existing optimal estimators.
The paper tackles robust estimation under Wasserstein contamination by proposing computationally tractable estimators based on Wasserstein GANs for problems like location estimation, covariance matrix estimation, and linear regression, showing they achieve minimax optimality in many scenarios.
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.