A Difference of Convex Functions Algorithm for Switched Linear Regression
Identifieur interne : 000162 ( Hal/Curation ); précédent : 000161; suivant : 000163A Difference of Convex Functions Algorithm for Switched Linear Regression
Auteurs : Tao Pham Dinh [France] ; Hoai Minh Le [France] ; Hoai An Le Thi [France] ; Fabien Lauer [France]Source :
- IEEE Transactions on Automatic Control [ 0018-9286 ] ; 2014.
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Abstract
This paper deals with switched linear system identification and more particularly aims at solving switched linear regression problems in a large-scale setting with both numerous data and many parameters to learn. We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The paper proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.
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DOI: 10.1109/TAC.2014.2301575
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We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The paper proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">A Difference of Convex Functions Algorithm for Switched Linear Regression</title><author role="aut"><persName><forename type="first">Tao</forename><surname>Pham Dinh</surname></persName><email></email><idno type="halauthor">310301</idno><affiliation ref="#struct-90"></affiliation></author><author role="aut"><persName><forename type="first">Hoai Minh</forename><surname>Le</surname></persName><email></email><idno type="halauthor">970693</idno><affiliation ref="#struct-402694"></affiliation></author><author role="aut"><persName><forename type="first">Hoai An</forename><surname>Le Thi</surname></persName><email></email><idno type="halauthor">970694</idno><affiliation ref="#struct-402694"></affiliation></author><author role="aut"><persName><forename type="first">Fabien</forename><surname>Lauer</surname></persName><email>fabien.lauer@loria.fr</email><ptr type="url" target="http://www.loria.fr/~lauer/"></ptr><idno type="idhal">fabien-lauer</idno><idno type="halauthor">1091620</idno><affiliation ref="#struct-206035"></affiliation></author><editor role="depositor"><persName><forename>Fabien</forename><surname>Lauer</surname></persName><email>fabien.lauer@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2014-01-15 09:58:28</date><date type="whenModified">2016-02-09 20:19:02</date><date type="whenReleased">2014-01-16 14:54:35</date><date type="whenProduced">2014</date><date type="whenEndEmbargoed">2014-01-15</date><ref type="file" target="https://hal.archives-ouvertes.fr/hal-00931206/document"><date notBefore="2014-01-15"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.archives-ouvertes.fr/hal-00931206/file/PhamLeLeThiLauerTAC14.pdf"><date notBefore="2014-01-15"></date></ref></edition><respStmt><resp>contributor</resp><name key="108844"><persName><forename>Fabien</forename><surname>Lauer</surname></persName><email>fabien.lauer@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-00931206</idno><idno type="halUri">https://hal.archives-ouvertes.fr/hal-00931206</idno><idno type="halBibtex">phamdinh:hal-00931206</idno><idno type="halRefHtml">IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2014, <10.1109/TAC.2014.2301575></idno><idno type="halRef">IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2014, <10.1109/TAC.2014.2301575></idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="UNIV-METZ">Université Paul Verlaine - Metz</idno><idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="LORIA-ALGO-TEST5">LORIA-ALGO-TEST5 </idno><idno type="stamp" n="LMI-ROUEN">Laboratoire de Mathématiques de l'INSA Rouen - Normandie Université - INSA Rouen</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="en">A Difference of Convex Functions Algorithm for Switched Linear Regression</title><author role="aut"><persName><forename type="first">Tao</forename><surname>Pham Dinh</surname></persName><idno type="halAuthorId">310301</idno><affiliation ref="#struct-90"></affiliation></author><author role="aut"><persName><forename type="first">Hoai Minh</forename><surname>Le</surname></persName><idno type="halAuthorId">970693</idno><affiliation ref="#struct-402694"></affiliation></author><author role="aut"><persName><forename type="first">Hoai An</forename><surname>Le Thi</surname></persName><idno type="halAuthorId">970694</idno><affiliation ref="#struct-402694"></affiliation></author><author role="aut"><persName><forename type="first">Fabien</forename><surname>Lauer</surname></persName><email>fabien.lauer@loria.fr</email><ptr type="url" target="http://www.loria.fr/~lauer/"></ptr><idno type="idHal">fabien-lauer</idno><idno type="halAuthorId">1091620</idno><affiliation ref="#struct-206035"></affiliation></author></analytic><monogr><idno type="halJournalId" status="VALID">5358</idno><idno type="issn">0018-9286</idno><title level="j">IEEE Transactions on Automatic Control</title><imprint><publisher>Institute of Electrical and Electronics Engineers</publisher><biblScope unit="pp">to appear</biblScope><date type="datePub">2014</date></imprint></monogr><idno type="doi">10.1109/TAC.2014.2301575</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">Switched linear systems</term><term xml:lang="en">Piecewise affine systems</term><term xml:lang="en">System identification</term><term xml:lang="en">Switched regression</term><term xml:lang="en">Nonconvex optimization</term><term xml:lang="en">Nonsmooth optimization</term><term xml:lang="en">DC programming</term><term xml:lang="en">DCA</term></keywords><classCode scheme="halDomain" n="info.info-lg">Computer Science [cs]/Machine Learning [cs.LG]</classCode><classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode><classCode scheme="halDomain" n="spi.auto">Engineering Sciences [physics]/Automatic</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><abstract xml:lang="en">This paper deals with switched linear system identification and more particularly aims at solving switched linear regression problems in a large-scale setting with both numerous data and many parameters to learn. We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The paper proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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