Assume that we observe a small set of entries or linear combinations of entries
of an unknown matrix A corrupted by noise. We propose a new method for
estimating A which does not rely on the knowledge or on an estimation of the
standard deviation of the noise s. Our estimator achieves, up to a logarithmic
factor, optimal rates of convergence under the Frobenius risk and, thus, has the
same prediction performance as previously proposed estimators which rely on the
knowledge of s. Some numerical experiments show the benefits of this approach.
KLOPP, O. et GAIFFAS, S. (2017). High dimensional matrix estimation with unknown variance of the noise. Statistica Sinica, 27(1), pp. 115-145.