<?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-04893622v1</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="2026-05-09T05:17:01+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting</title>
            <author role="aut">
              <persName>
                <forename type="first">Constantin</forename>
                <surname>Philippenko</surname>
              </persName>
              <idno type="halauthorid">2675076-0</idno>
              <affiliation ref="#struct-25027"/>
              <affiliation ref="#struct-1176625"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Kevin</forename>
                <surname>Scaman</surname>
              </persName>
              <idno type="halauthorid">1140610-0</idno>
              <affiliation ref="#struct-25027"/>
              <affiliation ref="#struct-1176625"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Laurent</forename>
                <surname>Massoulié</surname>
              </persName>
              <email type="md5">c4d60e691b2987567e3cda0486cb54ae</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">massoulie-laurent</idno>
              <idno type="idhal" notation="numeric">1215385</idno>
              <idno type="halauthorid" notation="string">142632-1215385</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-7263-0069</idno>
              <affiliation ref="#struct-25027"/>
              <affiliation ref="#struct-1176625"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Constantin</forename>
                <surname>Philippenko</surname>
              </persName>
              <email type="md5">cc4266433fc6008d83377a137ceadab9</email>
              <email type="domain">gmail.com</email>
            </editor>
            <funder ref="#projanr-109987"/>
            <funder ref="#projanr-50388"/>
            <funder>Groupe La Poste, sponsor of the Inria Foundation, in the framework of the FedMalin Inria Challenge</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-01-17 12:14:56</date>
              <date type="whenModified">2025-07-24 03:23:02</date>
              <date type="whenReleased">2025-01-17 14:41:18</date>
              <date type="whenProduced">2025-02-25</date>
              <date type="whenEndEmbargoed">2025-01-17</date>
              <ref type="file" target="https://hal.science/hal-04893622v1/document">
                <date notBefore="2025-01-17"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04893622v1/file/2024_matrix_factorisation_AAAI.pdf" id="file-4893622-4253406">
                <date notBefore="2025-01-17"/>
              </ref>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2025-07-21 21:55:43</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1467209">
                <persName>
                  <forename>Constantin</forename>
                  <surname>Philippenko</surname>
                </persName>
                <email type="md5">cc4266433fc6008d83377a137ceadab9</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04893622</idno>
            <idno type="halUri">https://hal.science/hal-04893622</idno>
            <idno type="halBibtex">philippenko:hal-04893622</idno>
            <idno type="halRefHtml">&lt;i&gt;AAAI 2025 - 39th Annual AAAI Conference on Artificial Intelligence&lt;/i&gt;, Feb 2025, Philadelphia, United States</idno>
            <idno type="halRef">AAAI 2025 - 39th Annual AAAI Conference on Artificial Intelligence, Feb 2025, Philadelphia, United States</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0 - Attribution<ref corresp="#file-4893622-4253406"/></licence>
            </availability>
          </publicationStmt>
          <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="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Constantin</forename>
                    <surname>Philippenko</surname>
                  </persName>
                  <idno type="halauthorid">2675076-0</idno>
                  <affiliation ref="#struct-25027"/>
                  <affiliation ref="#struct-1176625"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Kevin</forename>
                    <surname>Scaman</surname>
                  </persName>
                  <idno type="halauthorid">1140610-0</idno>
                  <affiliation ref="#struct-25027"/>
                  <affiliation ref="#struct-1176625"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Laurent</forename>
                    <surname>Massoulié</surname>
                  </persName>
                  <email type="md5">c4d60e691b2987567e3cda0486cb54ae</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">massoulie-laurent</idno>
                  <idno type="idhal" notation="numeric">1215385</idno>
                  <idno type="halauthorid" notation="string">142632-1215385</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-7263-0069</idno>
                  <affiliation ref="#struct-25027"/>
                  <affiliation ref="#struct-1176625"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>AAAI 2025 - 39th Annual AAAI Conference on Artificial Intelligence</title>
                  <date type="start">2025-02-25</date>
                  <date type="end">2025-03-04</date>
                  <settlement>Philadelphia</settlement>
                  <country key="US">United States</country>
                </meeting>
                <imprint/>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Optimization</term>
                <term xml:lang="en">Federated learning</term>
                <term xml:lang="en">Matrix factorisation</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-lg">Computer Science [cs]/Machine Learning [cs.LG]</classCode>
              <classCode scheme="halDomain" n="stat.ml">Statistics [stat]/Machine Learning [stat.ML]</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>We analyze a distributed algorithm to compute a low-rank matrix factorization on $N$ clients, each holding a local dataset $\mathbf{S}^i \in \mathbb{R}^{n_i \times d}$, mathematically, we seek to solve $min_{\mathbf{U}^i \in \mathbb{R}^{n_i\times r}, \mathbf{V}\in \mathbb{R}^{d \times r} } \frac{1}{2} \sum_{i=1}^N \|\mathbf{S}^i - \mathbf{U}^i \mathbf{V}^\top\|^2_{\text{F}}$. Considering a power initialization of $\mathbf{V}$, we rewrite the previous smooth non-convex problem into a smooth strongly-convex problem that we solve using a parallel Nesterov gradient descent potentially requiring a single step of communication at the initialization step. For any client $i$ in $\{1, \dots, N\}$, we obtain a global $\mathbf{V}$ in $\mathbb{R}^{d \times r}$ common to all clients and a local variable $\mathbf{U}^i$ in $\mathbb{R}^{n_i \times r}$. We provide a linear rate of convergence of the excess loss which depends on $\sigma_{\max} / \sigma_{r}$, where $\sigma_{r}$ is the $r^{\mathrm{th}}$ singular value of the concatenation $\mathbf{S}$ of the matrices $(\mathbf{S}^i)_{i=1}^N$. This result improves the rates of convergence given in the literature, which depend on $\sigma_{\max}^2 / \sigma_{\min}^2$. We provide an upper bound on the Frobenius-norm error of reconstruction under the power initialization strategy. We complete our analysis with experiments on both synthetic and real data.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="regrouplaboratory" xml:id="struct-25027" status="VALID">
          <idno type="IdRef">148034055</idno>
          <idno type="RNSR">199812876J</idno>
          <idno type="ROR">05y6rqs46</idno>
          <orgName>Département d'informatique - ENS-PSL</orgName>
          <orgName type="acronym">DI-ENS</orgName>
          <date type="start">1999-01-01</date>
          <desc>
            <address>
              <addrLine>École normale supérieure 45 rue d'Ulm F-75230 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.di.ens.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-59704" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation active="#struct-300009" type="direct"/>
            <relation name="UMR8548" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-1176625" status="VALID">
          <idno type="RNSR">202324449E</idno>
          <idno type="ROR">https://ror.org/02jkb9r34</idno>
          <orgName>Apprentissage, graphes et optimisation distribuée</orgName>
          <orgName type="acronym">ARGO</orgName>
          <date type="start">2023-10-01</date>
          <date type="end">2027-09-30</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-25027" type="direct"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation name="UMR8548" active="#struct-441569" type="indirect"/>
            <relation active="#struct-454310" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-59704" status="VALID">
          <idno type="IdRef">031738419</idno>
          <idno type="ISNI">0000000123532622</idno>
          <idno type="ROR">https://ror.org/05a0dhs15</idno>
          <orgName>École normale supérieure - Paris</orgName>
          <orgName type="acronym">ENS-PSL</orgName>
          <date type="start">1985-07-24</date>
          <desc>
            <address>
              <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</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="laboratory" xml:id="struct-454310" status="VALID">
          <idno type="IdRef">241614864</idno>
          <idno type="RNSR">196718247G</idno>
          <idno type="ROR">https://ror.org/05eyd5d35</idno>
          <orgName>Centre Inria de Paris</orgName>
          <date type="start">2016-03-10</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-109987" status="VALID">
          <idno type="anr">ANR-23-PEIA-0005</idno>
          <orgName>REDEEM</orgName>
          <desc>Resilient, Decentralized and Privacy-Preserving Machine Learning</desc>
          <date type="start">2023</date>
        </org>
        <org type="anrProject" xml:id="projanr-50388" status="VALID">
          <idno type="anr">ANR-19-P3IA-0001</idno>
          <orgName>PRAIRIE</orgName>
          <desc>PaRis Artificial Intelligence Research InstitutE</desc>
          <date type="start">2019</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>