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Stuctured Matrix Estimation and Completion

Author

Listed:
  • Olga Klopp

    (ESSEC;CREST)

  • Yu Lu

    (Yale University)

  • Alexandre Tsybakov

    (ENSAE;CNRS)

  • Harrison H. Zhou

Abstract

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. ;Classification-JEL: 62J99, 62H12, 60B20, 15A83

Suggested Citation

  • Olga Klopp & Yu Lu & Alexandre Tsybakov & Harrison H. Zhou, 2017. "Stuctured Matrix Estimation and Completion," Working Papers 2017-24, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2017-24
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    Keywords

    matrix completion; matrix estimation; minimax optimality;
    All these keywords.

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