Robust W-GAN-Based Estimation Under Wasserstein Contamination

TL;DR

This paper introduces computationally feasible Wasserstein GAN-based estimators for robust statistical tasks like location, covariance, and regression, achieving minimax optimality under Wasserstein contamination with promising numerical results.

Contribution

It proposes novel Wasserstein GAN-inspired estimators for robust statistics that are both computationally tractable and minimax optimal, advancing the field.

Findings

Estimators are minimax optimal in many scenarios.

Numerical results demonstrate estimator effectiveness.

Proposed methods are computationally feasible.

Abstract

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.