Mean and covariance estimation for anisotropic distributions in the presence of adversarial outliers

Suppose we are observing a sample of independent random vectors, knowing that the original distribution was contaminated, so that a fraction of observations came from a different distribution. How to estimate the mean and the covariance matrix of the original distribution in this case? In this talk, we discuss some recent estimators that achieve the optimal non-asymptotic, dimension-free rate of convergence under the model where the adversary can corrupt a fraction of the samples arbitrarily. The discussion will cover a wide range of distributions including heavy-tailed, sub-Gaussian, and specifically Gaussian distributions.

The talk is based on arXiv:2205.08494 and arXiv:2301.09024.