IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2016-14.html
   My bibliography  Save this paper

Robust Matrix Completion

Author

Listed:
  • Olga Klopp

    (CREST, MODAL’X, Université Paris Ouest)

  • Karim Lounici

    (School of Mathematics, Georgia Institute of Technology)

  • Alexandre Tsybakov

    (CREST, ENSAE, CNRS)

Abstract

This paper considers the problem of estimation of a low-rank matrix when most of its entries are not observed and some of the observed en- tries are corrupted. The observations are noisy realizations of a sum of a low-rank matrix, which we wish to estimate, and a second matrix having a complementary sparse structure such as elementwise sparsity or colum- nwise sparsity. We analyze a class of estimators obtained as solutions of a constrained convex optimization problem combining the nuclear norm penalty and a convex relaxation penalty for the sparse constraint. Our assumptions allow for simultaneous presence of random and deterministic patterns in the sampling scheme. We establish rates of convergence for the low-rank component from partial and corrupted observations in the presence of noise and we show that these rates are minimax optimal up to logarithmic factors.

Suggested Citation

  • Olga Klopp & Karim Lounici & Alexandre Tsybakov, 2016. "Robust Matrix Completion," Working Papers 2016-14, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2016-14
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2016-14.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2016-14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.