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Journal articles (2019), Bernoulli: A Journal of Mathematical Statistics and Probability, 4B (25), pp. 3883-3911

Structured Matrix Estimation and Completion

KLOPP Olga , LU Y., TSYBAKOV A. B., ZHOU H. H.

We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and dictionary learning. We consider the optimal convergence rates in a minimax sense for estimation of the signal matrix under the Frobenius norm and under the spectral norm. As a consequence of our general result we obtain minimax optimal rates of convergence for various special models. Link to the article

KLOPP, O., LU, Y., TSYBAKOV, A.B. and ZHOU, H.H. (2019). Structured Matrix Estimation and Completion. Bernoulli: A Journal of Mathematical Statistics and Probability, 4B(25), pp. 3883-3911.