<?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-03886322</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="2026-05-18T00:25:32+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Sparse Multiple Kernel Learning: Support Identification via Mirror Stratifiability</title>
            <author role="aut">
              <persName>
                <forename type="first">Guillaume</forename>
                <surname>Garrigos</surname>
              </persName>
              <email type="md5">dc5c87ab311d844d1b0858a15aefff7e</email>
              <email type="domain">gmail.com</email>
              <idno type="idhal" notation="string">guillaume-garrigos</idno>
              <idno type="idhal" notation="numeric">15633</idno>
              <idno type="halauthorid" notation="string">21706-15633</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8613-5664</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=DN0Cu0IAAAAJ&amp;hl=fr</idno>
              <idno type="IDREF">https://www.idref.fr/198633696</idno>
              <affiliation ref="#struct-1004954"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Lorenzo</forename>
                <surname>Rosasco</surname>
              </persName>
              <idno type="halauthorid">1481708-0</idno>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Silvia</forename>
                <surname>Villa</surname>
              </persName>
              <idno type="halauthorid">1759981-0</idno>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Guillaume</forename>
                <surname>Garrigos</surname>
              </persName>
              <email type="md5">c761894bd6c194d8b12afcad216bd28f</email>
              <email type="domain">lpsm.paris</email>
            </editor>
            <funder ref="#projeurop-712458"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2022-12-06 12:11:53</date>
              <date type="whenModified">2024-10-30 13:34:11</date>
              <date type="whenReleased">2022-12-21 10:54:43</date>
              <date type="whenProduced">2018-09-03</date>
              <date type="whenEndEmbargoed">2022-12-06</date>
              <ref type="file" target="https://hal.science/hal-03886322v1/document">
                <date notBefore="2022-12-06"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03886322v1/file/1803.00783.pdf" id="file-3886322-3399723">
                <date notBefore="2022-12-06"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1803.00783"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="194505">
                <persName>
                  <forename>Guillaume</forename>
                  <surname>Garrigos</surname>
                </persName>
                <email type="md5">c761894bd6c194d8b12afcad216bd28f</email>
                <email type="domain">lpsm.paris</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03886322</idno>
            <idno type="halUri">https://hal.science/hal-03886322</idno>
            <idno type="halBibtex">garrigos:hal-03886322</idno>
            <idno type="halRefHtml">&lt;i&gt;2018 26th European Signal Processing Conference (EUSIPCO)&lt;/i&gt;, Sep 2018, Rome, Italy. pp.1077-1081, &lt;a target="_blank" href="https://dx.doi.org/10.23919/EUSIPCO.2018.8553267"&gt;&amp;#x27E8;10.23919/EUSIPCO.2018.8553267&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">2018 26th European Signal Processing Conference (EUSIPCO), Sep 2018, Rome, Italy. pp.1077-1081, &amp;#x27E8;10.23919/EUSIPCO.2018.8553267&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3886322-3399723"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="OPENAIRE">OpenAIRE</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="LPSM" corresp="SORBONNE-UNIVERSITE">Laboratoire de Probabilités, Statistique et Modélisation</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SORBONNE-UNIV" corresp="SORBONNE-UNIVERSITE">Sorbonne Université 01/01/2018</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="UP-SCIENCES">Université Paris Cité - Faculté des Sciences</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="SUPRA_MATHS_INFO">Mathématiques + Informatique</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="0">No</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Sparse Multiple Kernel Learning: Support Identification via Mirror Stratifiability</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Guillaume</forename>
                    <surname>Garrigos</surname>
                  </persName>
                  <email type="md5">dc5c87ab311d844d1b0858a15aefff7e</email>
                  <email type="domain">gmail.com</email>
                  <idno type="idhal" notation="string">guillaume-garrigos</idno>
                  <idno type="idhal" notation="numeric">15633</idno>
                  <idno type="halauthorid" notation="string">21706-15633</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8613-5664</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=DN0Cu0IAAAAJ&amp;hl=fr</idno>
                  <idno type="IDREF">https://www.idref.fr/198633696</idno>
                  <affiliation ref="#struct-1004954"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Lorenzo</forename>
                    <surname>Rosasco</surname>
                  </persName>
                  <idno type="halauthorid">1481708-0</idno>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Silvia</forename>
                    <surname>Villa</surname>
                  </persName>
                  <idno type="halauthorid">1759981-0</idno>
                </author>
              </analytic>
              <monogr>
                <title level="m">2018 26th European Signal Processing Conference (EUSIPCO)</title>
                <meeting>
                  <title>2018 26th European Signal Processing Conference (EUSIPCO)</title>
                  <date type="start">2018-09-03</date>
                  <date type="end">2018-09-07</date>
                  <settlement>Rome</settlement>
                  <country key="IT">Italy</country>
                </meeting>
                <imprint>
                  <publisher>IEEE</publisher>
                  <biblScope unit="pp">1077-1081</biblScope>
                </imprint>
              </monogr>
              <idno type="arxiv">1803.00783</idno>
              <idno type="doi">10.23919/EUSIPCO.2018.8553267</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Group Sparsity</term>
                <term xml:lang="en">Support recovery</term>
                <term xml:lang="en">Feature Selection</term>
                <term xml:lang="en">Multiple Kernel Learning</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem depending on a data fit term and a suitable regularizer. In this paper we consider feature maps which are the concatenation of a fixed, possibly large, set of simpler feature maps. The penalty is a sparsity inducing one, promoting solutions depending only on a small subset of the features. The group lasso problem is a special case of this more general setting. We show that one of the most popular optimization algorithms to solve the regularized objective function, the forward-backward splitting method, allows to perform feature selection in a stable manner. In particular, we prove that the set of relevant features is identified by the algorithm after a finite number of iterations if a suitable qualification condition holds. Our analysis rely on the notions of stratification and mirror stratifiability.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1004954" status="VALID">
          <idno type="IdRef">235620025</idno>
          <idno type="RNSR">201822759P</idno>
          <idno type="ROR">https://ror.org/02vnd0e65</idno>
          <orgName>Laboratoire de Probabilités, Statistique et Modélisation</orgName>
          <orgName type="acronym">LPSM (UMR_8001)</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Campus Jussieu Tour 16-26, 1er étage 4, Place Jussieu 75005 Paris / Bâtiment Sophie Germain 5ème étage Avenue de France 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lpsm.paris</ref>
          </desc>
          <listRelation>
            <relation name="UMR_8001" active="#struct-413221" type="direct"/>
            <relation name="UMR8001" active="#struct-441569" type="direct"/>
            <relation name="UMR_8001" active="#struct-557826" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-413221" status="VALID">
          <idno type="IdRef">221333754</idno>
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Sorbonne Université</orgName>
          <orgName type="acronym">SU</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>21 rue de l’École de médecine - 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sorbonne-universite.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-557826" status="VALID">
          <idno type="IdRef">236453505</idno>
          <idno type="ISNI">0000 0004 7885 7602</idno>
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris Cité</orgName>
          <orgName type="acronym">UPCité</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>85 boulevard Saint-Germain75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-paris.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="europeanProject" xml:id="projeurop-712458" status="VALID">
          <idno type="number">724175</idno>
          <idno type="program">EXCELLENT SCIENCE - European Research Council (ERC)</idno>
          <idno type="call">ERC-2016-COG</idno>
          <orgName>NORIA</orgName>
          <desc>Numerical Optimal tRansport for ImAging</desc>
          <date type="start">2017-10-01</date>
          <date type="end">2023-09-30</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>