Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "16101"
  #_source: array:26 [
    "id" => "16101"
    "slug" => "16101-minimax-optimality-of-deep-neural-networks-on-dependent-data-via-pac-bayes-bounds"
    "yearMonth" => "2025-12"
    "year" => "2025"
    "title" => "Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds"
    "description" => "ALQUIER, P. et KENGNE, W. (2025). Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds. <i>The Electronic Journal of Statistics</i>, 19, pp. 5895-5924."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "ALQUIER Pierre"
        "bid" => "B00809923"
        "slug" => "alquier-pierre"
      ]
      1 => array:1 [
        "name" => "KENGNE William"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:4 [
      0 => "Deep neural networks"
      1 => "minimax optimality"
      2 => "Bayesian neural network"
      3 => "PAC Bayes bounds  oracle inequality"
    ]
    "updatedAt" => "2025-12-10 16:32:58"
    "publicationUrl" => "https://doi.org/10.1214/25-EJS2475"
    "publicationInfo" => array:3 [
      "pages" => "5895-5924"
      "volume" => "19"
      "number" => ""
    ]
    "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" => "In a groundbreaking work, [58] proved the minimax optimality of deep neural networks with ReLU activation for least-squares regression estimation over a large class of functions defined by composition. In this paper, we extend these results in many directions. First, we remove the i.i.d. assumption on the observations, to allow some time dependence. The observations are assumed to be a Markov chain with a non-null pseudo-spectral gap. Then, we study a more general class of machine learning problems, which includes least-squares and logistic regression as special cases. Leveraging on PAC-Bayes oracle inequalities and a version of Bernstein inequality due to [53], we derive upper bounds on the estimation risk for a generalized Bayesian estimator. In the case of least-squares regression, this bound matches (up to a logarithmic factor) the lower bound in [58]. We establish a similar lower bound for classification with the logistic loss, and prove that the proposed DNN estimator is optimal in the minimax sense."
      "en" => "In a groundbreaking work, [58] proved the minimax optimality of deep neural networks with ReLU activation for least-squares regression estimation over a large class of functions defined by composition. In this paper, we extend these results in many directions. First, we remove the i.i.d. assumption on the observations, to allow some time dependence. The observations are assumed to be a Markov chain with a non-null pseudo-spectral gap. Then, we study a more general class of machine learning problems, which includes least-squares and logistic regression as special cases. Leveraging on PAC-Bayes oracle inequalities and a version of Bernstein inequality due to [53], we derive upper bounds on the estimation risk for a generalized Bayesian estimator. In the case of least-squares regression, this bound matches (up to a logarithmic factor) the lower bound in [58]. We establish a similar lower bound for classification with the logistic loss, and prove that the proposed DNN estimator is optimal in the minimax sense."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2025-12-15T11:21:45.000Z"
    "docTitle" => "Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/alquier-pierre">ALQUIER Pierre</a>, KENGNE William"
    "docDescription" => "<span class="document-property-authors">ALQUIER Pierre, KENGNE William</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2025</span>"
    "keywordList" => "<a href="#">Deep neural networks</a>, <a href="#">minimax optimality</a>, <a href="#">Bayesian neural network</a>, <a href="#">PAC Bayes bounds  oracle inequality</a>"
    "docPreview" => "<b>Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds</b><br><span>2025-12 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1214/25-EJS2475" target="_blank">Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds</a>"
  ]
  +lang: "en"
  +"_score": 8.777956
  +"_ignored": array:2 [
    0 => "abstract.en.keyword"
    1 => "abstract.fr.keyword"
  ]
  +"parent": null
}