Abstract: Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix A₀ corrupted by noise. We propose a new method for estimating A₀ that does not rely on the knowledge or on an estimation of the standard deviation of the noise σ. Our estimator achieves, up to a logarithmic factor, optimal rates of convergence under Frobenius risk and, thus, has the same prediction performance as previously proposed estimators that rely on the knowledge of σ. Some numerical experiments show the benefits of this approach.

Key words and phrases: Low rank matrix estimation, matrix completion, matrix regression, unknown variance of the noise.