This paper considers the problem of estimation of a low-rank matrix
when most of its entries are not observed and some of the observed entries
are corrupted. The observations are noisy realizations of a sum of a
low-rank matrix, which we wish to estimate, and a second matrix having
a complementary sparse structure such as elementwise sparsity or columnwise
sparsity. We analyze a class of estimators obtained as solutions of
a constrained convex optimization problem combining the nuclear norm
penalty and a convex relaxation penalty for the sparse constraint. Our
assumptions allow for simultaneous presence of random and deterministic
patterns in the sampling scheme. We establish rates of convergence for
the low-rank component from partial and corrupted observations in the
presence of noise and we show that these rates are minimax optimal up
to logarithmic factors.
KLOPP, O. (2015). Robust Matrix Completion. Dans: ISNPS Biosciences, Medicine, and novel Non-parametric Methods. Graz.