Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "16081"
  #_source: array:26 [
    "id" => "16081"
    "slug" => "16081-generalized-multi-view-model-adaptive-density-estimation-under-low-rank-constraints"
    "yearMonth" => "2025-11"
    "year" => "2025"
    "title" => "Generalized multi-view model: Adaptive density estimation under low-rank constraints"
    "description" => "CHHOR, J., KLOPP, O. et TSYBAKOV, A. (2025). Generalized multi-view model: Adaptive density estimation under low-rank constraints. <i>Journal of Machine Learning Research</i>, In press, pp. 1-52."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "KLOPP Olga"
        "bid" => "B00732676"
        "slug" => "klopp-olga"
      ]
      1 => array:1 [
        "name" => "CHHOR Julien"
      ]
      2 => array:1 [
        "name" => "TSYBAKOV Alexandre"
      ]
    ]
    "ouvrage" => ""
    "keywords" => []
    "updatedAt" => "2025-11-24 09:34:18"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => "1-52"
      "volume" => "In press"
      "number" => ""
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => "États-Unis"
      "en" => "United States of America"
    ]
    "abstract" => array:2 [
      "fr" => "We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints. For discrete distributions, we assume that the two-dimensional array to estimate is a lowrank probability matrix. In the continuous case, we assume that the density with respect to the Lebesgue measure satisfies a generalized multi-view model, meaning that it is β-H¨older and can be decomposed as a sum of K components, each of which is a product of one-dimensional functions. In both settings, we propose estimators that achieve, up to logarithmic factors, the minimax optimal convergence rates under such low-rank constraints. In the discrete case, the proposed estimator is adaptive to the rank K. In the continuous case, our estimator converges with the L1 rate min((K/n)β/(2β+1),n−β/(2β+2)) up to logarithmic factors, and it is adaptive to the unknown support as well as to the smoothness β and to the unknown number of separable components K. We present efficient algorithms for computing our estimators."
      "en" => "We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints. For discrete distributions, we assume that the two-dimensional array to estimate is a lowrank probability matrix. In the continuous case, we assume that the density with respect to the Lebesgue measure satisfies a generalized multi-view model, meaning that it is β-H¨older and can be decomposed as a sum of K components, each of which is a product of one-dimensional functions. In both settings, we propose estimators that achieve, up to logarithmic factors, the minimax optimal convergence rates under such low-rank constraints. In the discrete case, the proposed estimator is adaptive to the rank K. In the continuous case, our estimator converges with the L1 rate min((K/n)β/(2β+1),n−β/(2β+2)) up to logarithmic factors, and it is adaptive to the unknown support as well as to the smoothness β and to the unknown number of separable components K. We present efficient algorithms for computing our estimators."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2025-12-06T05:21:43.000Z"
    "docTitle" => "Generalized multi-view model: Adaptive density estimation under low-rank constraints"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/klopp-olga">KLOPP Olga</a>, CHHOR Julien, TSYBAKOV Alexandre"
    "docDescription" => "<span class="document-property-authors">KLOPP Olga, CHHOR Julien, TSYBAKOV Alexandre</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2025</span>"
    "keywordList" => ""
    "docPreview" => "<b>Generalized multi-view model: Adaptive density estimation under low-rank constraints</b><br><span>2025-11 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">Generalized multi-view model: Adaptive density estimation under low-rank constraints</a>"
  ]
  +lang: "en"
  +"_score": 8.714403
  +"_ignored": array:2 [
    0 => "abstract.en.keyword"
    1 => "abstract.fr.keyword"
  ]
  +"parent": null
}