Statistically Optimal Robust Mean and Covariance Estimation for Anisotropic Gaussians

Orateur: Arshak Minasyan
Localisation: ,
Type: Séminaire de probabilités et statistiques
Site: UGE , 4B 125
Date de début: 24/01/2023 - 10:30

We study the problem of robust mean and covariance estimation of an anisotropic Gaussian distribution under adversarial contamination. In the adversarial contamination model the adversary is allowed to change $\varepsilon$ fraction of observations arbitrarily. In this work, we construct estimators both for mean vector and covariance matrix that are both dimension-free and have optimal dependence on the contamination level $\varepsilon$, hence they have optimal minimax rate. Despite the recent significant interest in robust statistics, achieving dimension-free bound with optimal dependence on $\varepsilon$ in the canonical Gaussian case remained open. In fact, previously known results were either dimension-dependent and required covariance matrix to be close to identity, or had a sub-optimal dependence on the contamination level.