Abstract

This talk considers the problem of noisy matrix completion, i.e., that of estimation of an unknown matrix from incomplete observation of its entries corrupted by noise. The focus in on high-dimensional setting where the number of observed entries is much smaller than the dimension of the matrix. At the same time, we suppose that its rank or some other sparsity characteristic is small. Several methods of matrix completion under the small rank assumption have been suggested recently, mainly in the non-noisy setting. The aim of this talk is to explore the noisy matrix completion model. The main results consist in deriving oracle inequalities for nuclear norm penalized and rank penalized estimators, and to show that these estimators attain optimal rates in a minimax sense.