High dimensional matrix estimation with unknown variance of the noise
نویسنده
چکیده
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 which does not rely on the knowledge or an estimation of the standard deviation of the noise σ. 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 σ.
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