Essec\Faculty\Model\Contribution {#2205
  #_index: "academ_contributions"
  #_id: "14700"
  #_source: array:26 [
    "id" => "14700"
    "slug" => "dimension-free-bounds-for-sums-of-dependend-matrices-and-operators-with-heavy-tailed-distribution"
    "yearMonth" => "2024-02"
    "year" => "2024"
    "title" => "Dimension-free bounds for sums of dependend matrices and operators with heavy-tailed distribution"
    "description" => "NAKAKITA, S., ALQUIER, P. et IMAIZUMI, M. (2024). Dimension-free bounds for sums of dependend matrices and operators with heavy-tailed distribution. <i>The Electronic Journal of Statistics</i>, 18(1), pp. 1130-1159."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "ALQUIER Pierre"
        "bid" => "B00809923"
        "slug" => "alquier-pierre"
      ]
      1 => array:1 [
        "name" => "NAKAKITA Shogo"
      ]
      2 => array:1 [
        "name" => "IMAIZUMI Masaaki"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:4 [
      0 => "Dependent process"
      1 => "heavy-tailed distribution"
      2 => "high-dimension"
      3 => "random matrix"
    ]
    "updatedAt" => "2024-03-27 13:14:16"
    "publicationUrl" => "https://doi.org/10.1214/24-EJS2224"
    "publicationInfo" => array:3 [
      "pages" => "1130-1159"
      "volume" => "18"
      "number" => "1"
    ]
    "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" => "We study the deviation inequality for a sum of high-dimensional random matrices and operators with dependence and arbitrary heavy tails. There is an increase in the importance of the problem of estimating high-dimensional matrices, and dependence and heavy-tail properties of data are among the most critical topics currently. In this paper, we derive a dimension-free upper bound on the deviation, that is, the bound does not depend explicitly on the dimension of matrices, but depends on their effective rank. Our result is a generalization of several existing studies on the deviation of the sum of matrices. Our proof is based on two techniques: (i) a variational approximation of the dual of moment generating functions, and (ii) robustification through truncation of eigenvalues of matrices. We show that our results are applicable to several problems such as covariance matrix estimation, hidden Markov models, and overparameterized linear regression models."
      "en" => "We study the deviation inequality for a sum of high-dimensional random matrices and operators with dependence and arbitrary heavy tails. There is an increase in the importance of the problem of estimating high-dimensional matrices, and dependence and heavy-tail properties of data are among the most critical topics currently. In this paper, we derive a dimension-free upper bound on the deviation, that is, the bound does not depend explicitly on the dimension of matrices, but depends on their effective rank. Our result is a generalization of several existing studies on the deviation of the sum of matrices. Our proof is based on two techniques: (i) a variational approximation of the dual of moment generating functions, and (ii) robustification through truncation of eigenvalues of matrices. We show that our results are applicable to several problems such as covariance matrix estimation, hidden Markov models, and overparameterized linear regression models."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
      "en" => "Information Systems, Decision Sciences and Statistics"
    ]
    "indexedAt" => "2024-05-08T01:21:54.000Z"
    "docTitle" => "Dimension-free bounds for sums of dependend matrices and operators with heavy-tailed distribution"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/alquier-pierre">ALQUIER Pierre</a>, NAKAKITA Shogo, IMAIZUMI Masaaki"
    "docDescription" => "<span class="document-property-authors">ALQUIER Pierre, NAKAKITA Shogo, IMAIZUMI Masaaki</span><br><span class="document-property-authors_fields">Systèmes d’Information, Sciences de la Décision et Statistiques</span> | <span class="document-property-year">2024</span>"
    "keywordList" => "<a href="#">Dependent process</a>, <a href="#">heavy-tailed distribution</a>, <a href="#">high-dimension</a>, <a href="#">random matrix</a>"
    "docPreview" => "<b>Dimension-free bounds for sums of dependend matrices and operators with heavy-tailed distribution</b><br><span>2024-02 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1214/24-EJS2224" target="_blank">Dimension-free bounds for sums of dependend matrices and operators with heavy-tailed distribution</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.669193
  +"parent": null
}