Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "2158"
  #_source: array:26 [
    "id" => "2158"
    "slug" => "optimal-graphon-estimation-in-cut-distance"
    "yearMonth" => "2018-10"
    "year" => "2018"
    "title" => "Optimal Graphon Estimation in Cut Distance"
    "description" => "KLOPP, O. et VERZELEN, N. (2018). Optimal Graphon Estimation in Cut Distance. <i>Probability Theory and Related Fields</i>, 174, pp. 1033-1090."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "KLOPP Olga"
        "bid" => "B00732676"
        "slug" => "klopp-olga"
      ]
      1 => array:1 [
        "name" => "VERZELEN N."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:6 [
      0 => "Inhomogeneous random graph"
      1 => "Graphon"
      2 => "W-random graphs"
      3 => "Networks"
      4 => "Stochastic block model"
      5 => "Cut distance"
    ]
    "updatedAt" => "2021-09-24 10:33:27"
    "publicationUrl" => "https://link.springer.com/article/10.1007%2Fs00440-018-0878-1"
    "publicationInfo" => array:3 [
      "pages" => "1033-1090"
      "volume" => "174"
      "number" => null
    ]
    "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" => "Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block constant matrices and step function graphons. Surprisingly, our results imply that, from the minimax point of view, the raw data, that is, the adjacency matrix of the observed graph, is already optimal and more involved procedures cannot improve the convergence rates for this metric. This phenomenon contrasts with optimal rates of convergence with respect to other classical distances for graphons such as the l1 or l2 metrics."
      "en" => "Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block constant matrices and step function graphons. Surprisingly, our results imply that, from the minimax point of view, the raw data, that is, the adjacency matrix of the observed graph, is already optimal and more involved procedures cannot improve the convergence rates for this metric. This phenomenon contrasts with optimal rates of convergence with respect to other classical distances for graphons such as the l1 or l2 metrics."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2025-01-17T15:21:42.000Z"
    "docTitle" => "Optimal Graphon Estimation in Cut Distance"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/klopp-olga">KLOPP Olga</a>, VERZELEN N."
    "docDescription" => "<span class="document-property-authors">KLOPP Olga, VERZELEN N.</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2018</span>"
    "keywordList" => "<a href="#">Inhomogeneous random graph</a>, <a href="#">Graphon</a>, <a href="#">W-random graphs</a>, <a href="#">Networks</a>, <a href="#">Stochastic block model</a>, <a href="#">Cut distance</a>"
    "docPreview" => "<b>Optimal Graphon Estimation in Cut Distance</b><br><span>2018-10 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://link.springer.com/article/10.1007%2Fs00440-018-0878-1" target="_blank">Optimal Graphon Estimation in Cut Distance</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 7.500061
  +"parent": null
}