<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04457385</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-02T08:43:38+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="it">Data-dependent Generalization Bounds via Variable-Size Compressibility</title>
            <author role="aut">
              <persName>
                <forename type="first">Milad</forename>
                <surname>Sefidgaran</surname>
              </persName>
              <email type="md5">b7ebc47c0ef5e376fb6e1ae02ff769f8</email>
              <email type="domain">telecom-paris.fr</email>
              <idno type="idhal" notation="numeric">1115692</idno>
              <idno type="halauthorid" notation="string">1651609-1115692</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3576-9552</idno>
              <affiliation ref="#struct-569607"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Abdellatif</forename>
                <surname>Zaidi</surname>
              </persName>
              <idno type="idhal" notation="numeric">1351659</idno>
              <idno type="halauthorid" notation="string">625600-1351659</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2023-9476</idno>
              <affiliation ref="#struct-1001627"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Abdellatif</forename>
                <surname>Zaidi</surname>
              </persName>
              <email type="md5">f9351f4658602d7505dbf0fc089635f8</email>
              <email type="domain">univ-eiffel.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-02-14 13:10:27</date>
              <date type="whenModified">2025-10-18 03:29:35</date>
              <date type="whenReleased">2024-02-14 13:10:27</date>
              <date type="whenProduced">2024</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/2303.05369"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="181068">
                <persName>
                  <forename>Abdellatif</forename>
                  <surname>Zaidi</surname>
                </persName>
                <email type="md5">f9351f4658602d7505dbf0fc089635f8</email>
                <email type="domain">univ-eiffel.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04457385</idno>
            <idno type="halUri">https://hal.science/hal-04457385</idno>
            <idno type="halBibtex">sefidgaran:hal-04457385</idno>
            <idno type="halRefHtml">&lt;i&gt;IEEE Transactions on Information Theory&lt;/i&gt;, In press, &lt;a target="_blank" href="https://dx.doi.org/10.1109/TIT.2024.3414266"&gt;&amp;#x27E8;10.1109/TIT.2024.3414266&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">IEEE Transactions on Information Theory, In press, &amp;#x27E8;10.1109/TIT.2024.3414266&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="ENPC-LIGM" corresp="ENPC">Laboratoire d'informatique Gaspard-Monge</idno>
            <idno type="stamp" n="LIGM" corresp="ENPC">Laboratoire d'informatique Gaspard-Monge</idno>
            <idno type="stamp" n="UNIV-EIFFEL">Université Gustave Eiffel</idno>
            <idno type="stamp" n="U-EIFFEL">Université Gustave Eiffel</idno>
            <idno type="stamp" n="LIGM_MMSID" corresp="LIGM">LIGM_MMSID - Méthodes et Modèles pour le Signal, l'Image et les Données</idno>
            <idno type="stamp" n="IP-PARIS-INFORMATIQUE-DONNEES-ET-IA">IP Paris Département d'Informatique, de Données et d'IA</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="it">Data-dependent Generalization Bounds via Variable-Size Compressibility</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Milad</forename>
                    <surname>Sefidgaran</surname>
                  </persName>
                  <email type="md5">b7ebc47c0ef5e376fb6e1ae02ff769f8</email>
                  <email type="domain">telecom-paris.fr</email>
                  <idno type="idhal" notation="numeric">1115692</idno>
                  <idno type="halauthorid" notation="string">1651609-1115692</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3576-9552</idno>
                  <affiliation ref="#struct-569607"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Abdellatif</forename>
                    <surname>Zaidi</surname>
                  </persName>
                  <idno type="idhal" notation="numeric">1351659</idno>
                  <idno type="halauthorid" notation="string">625600-1351659</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2023-9476</idno>
                  <affiliation ref="#struct-1001627"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">5382</idno>
                <idno type="issn">0018-9448</idno>
                <title level="j">IEEE Transactions on Information Theory</title>
                <imprint>
                  <publisher>Institute of Electrical and Electronics Engineers</publisher>
                  <date type="datePub" subtype="inPress">2024</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2303.05369</idno>
              <idno type="doi">10.1109/TIT.2024.3414266</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="stat.ml">Statistics [stat]/Machine Learning [stat.ML]</classCode>
              <classCode scheme="halDomain" n="info.info-it">Computer Science [cs]/Information Theory [cs.IT]</classCode>
              <classCode scheme="halDomain" n="info.info-lg">Computer Science [cs]/Machine Learning [cs.LG]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this paper, we establish novel data-dependent upper bounds on the generalization error through the lens of a "variable-size compressibility" framework that we introduce newly here. In this framework, the generalization error of an algorithm is linked to a variable-size 'compression rate' of its input data. This is shown to yield bounds that depend on the empirical measure of the given input data at hand, rather than its unknown distribution. Our new generalization bounds that we establish are tail bounds, tail bounds on the expectation, and in-expectations bounds. Moreover, it is shown that our framework also allows to derive general bounds on any function of the input data and output hypothesis random variables. In particular, these general bounds are shown to subsume and possibly improve over several existing PAC-Bayes and data-dependent intrinsic dimension-based bounds that are recovered as special cases, thus unveiling a unifying character of our approach. For instance, a new data-dependent intrinsic dimension-based bound is established, which connects the generalization error to the optimization trajectories and reveals various interesting connections with the rate-distortion dimension of a process, the R\'enyi information dimension of a process, and the metric mean dimension.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-569607" status="VALID">
          <orgName>Huawei Technologies France</orgName>
          <date type="start">2014-04-01</date>
          <desc>
            <address>
              <addrLine>790 avenue Dr Maurice DonatMarco Polo A06250 Mougins</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.huawei.com/fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-431513" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1001627" status="OLD">
          <idno type="IdRef">142877891</idno>
          <idno type="RNSR">200212717U</idno>
          <orgName>Laboratoire d'Informatique Gaspard-Monge</orgName>
          <orgName type="acronym">LIGM</orgName>
          <date type="start">2020-01-01</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>Université Gustave Eiffel, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://ligm.u-pem.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301545" type="direct"/>
            <relation name="UMR8049" active="#struct-441569" type="direct"/>
            <relation active="#struct-580722" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-431513" status="VALID">
          <idno type="ROR">https://ror.org/02rbzf697</idno>
          <orgName>Huawei Technologies France [Boulogne-Billancourt]</orgName>
          <desc>
            <address>
              <addrLine>Arcs de Seine18 quai du Point du JourCS 7000392100 Boulogne Billancourt</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-580722" status="VALID">
          <idno type="ROR">https://ror.org/03x42jk29</idno>
          <orgName>Université Gustave Eiffel</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Cité Descartes, 5 Boulevard Descartes • Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-gustave-eiffel.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>