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Structured Matrix Estimation and Completion

Author

Listed:
  • Olga Klopp

    (ESSEC Business School ; CREST)

  • Yu Lu

    (Yale University)

  • Alexandre B. Tsybakov

    (ENSAE, UMR CNRS 9194)

  • Harrison H. Zhou

    (Yale University)

Abstract

We study the problem of matrix estimation and matrix completion for matrices with general clustering structure. We consider an unified model which includes as particular cases gaussian mixture model, mixed membership model, bi-clustering model and dictionary learning. For this general model we obtain 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 recover minimax optimal rates of convergence for the special models mentioned before.

Suggested Citation

  • Olga Klopp & Yu Lu & Alexandre B. Tsybakov & Harrison H. Zhou, 2017. "Structured Matrix Estimation and Completion," Working Papers 2017-43, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-43
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    Keywords

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

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