Quantized matrix completion for low rank matrices

In this paper, we consider the recovery of a low rank matrix M given a subset of noisy quantized (or ordinal) measurements. We consider a constrained maximum likelihood estimation of M, under a constraint on the entry-wise infinity-norm of M and an exact rank constraint. We provide an upper bound on the Frobenius norm of the matrix estimation error under this model. Past theoretical investigations have been restricted to binary quantizers, and based on convex relaxation of the rank. We propose a globally convergent optimization algorithm exploiting existing work on low rank matrix factorization, and validate the method on synthetic data, with improved performance over past methods.