Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "10574"
  #_source: array:26 [
    "id" => "10574"
    "slug" => "adaptive-multinomial-matrix-completion"
    "yearMonth" => "2015-01"
    "year" => "2015"
    "title" => "Adaptive Multinomial Matrix Completion"
    "description" => "KLOPP, O., LAFOND, J., MOULINES, E. et SALMON, J. (2015). Adaptive Multinomial Matrix Completion. <i>The Electronic Journal of Statistics</i>, 9(2), pp. 2950-2975."
    "authors" => array:4 [
      0 => array:3 [
        "name" => "KLOPP Olga"
        "bid" => "B00732676"
        "slug" => "klopp-olga"
      ]
      1 => array:1 [
        "name" => "LAFOND J."
      ]
      2 => array:1 [
        "name" => "MOULINES E."
      ]
      3 => array:1 [
        "name" => "SALMON J."
      ]
    ]
    "ouvrage" => ""
    "keywords" => []
    "updatedAt" => "2021-07-13 14:31:38"
    "publicationUrl" => "https://projecteuclid.org/download/pdfview_1/euclid.ejs/1452004956"
    "publicationInfo" => array:3 [
      "pages" => "2950-2975"
      "volume" => "9"
      "number" => "2"
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => """
        The task of estimating a matrix given a sample of observed\n
        entries is known as the matrix completion problem. Most works on matrix\n
        completion have focused on recovering an unknown real-valued low-rank\n
        matrix from a random sample of its entries. Here, we investigate the case\n
        of highly quantized observations when the measurements can take only a\n
        small number of values. These quantized outputs are generated according to\n
        a probability distribution parametrized by the unknown matrix of interest.\n
        This model corresponds, for example, to ratings in recommender systems\n
        or labels in multi-class classification. We consider a general, non-uniform,\n
        sampling scheme and give theoretical guarantees on the performance of a\n
        constrained, nuclear norm penalized maximum likelihood estimator. One\n
        important advantage of this estimator is that it does not require knowledge\n
        of the rank or an upper bound on the nuclear norm of the unknown matrix\n
        and, thus, it is adaptive. We provide lower bounds showing that our\n
        estimator is minimax optimal. An efficient algorithm based on lifted coordinate\n
        gradient descent is proposed to compute the estimator. A limited\n
        Monte-Carlo experiment, using both simulated and real data is provided to\n
        support our claims.
        """
      "en" => """
        The task of estimating a matrix given a sample of observed\n
        entries is known as the matrix completion problem. Most works on matrix\n
        completion have focused on recovering an unknown real-valued low-rank\n
        matrix from a random sample of its entries. Here, we investigate the case\n
        of highly quantized observations when the measurements can take only a\n
        small number of values. These quantized outputs are generated according to\n
        a probability distribution parametrized by the unknown matrix of interest.\n
        This model corresponds, for example, to ratings in recommender systems\n
        or labels in multi-class classification. We consider a general, non-uniform,\n
        sampling scheme and give theoretical guarantees on the performance of a\n
        constrained, nuclear norm penalized maximum likelihood estimator. One\n
        important advantage of this estimator is that it does not require knowledge\n
        of the rank or an upper bound on the nuclear norm of the unknown matrix\n
        and, thus, it is adaptive. We provide lower bounds showing that our\n
        estimator is minimax optimal. An efficient algorithm based on lifted coordinate\n
        gradient descent is proposed to compute the estimator. A limited\n
        Monte-Carlo experiment, using both simulated and real data is provided to\n
        support our claims.
        """
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-11-21T10:21:50.000Z"
    "docTitle" => "Adaptive Multinomial Matrix Completion"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/klopp-olga">KLOPP Olga</a>, LAFOND J., MOULINES E., SALMON J."
    "docDescription" => "<span class="document-property-authors">KLOPP Olga, LAFOND J., MOULINES E., SALMON J.</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2015</span>"
    "keywordList" => ""
    "docPreview" => "<b>Adaptive Multinomial Matrix Completion</b><br><span>2015-01 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://projecteuclid.org/download/pdfview_1/euclid.ejs/1452004956" target="_blank">Adaptive Multinomial Matrix Completion</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 9.064929
  +"parent": null
}