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The degrees of freedom of the group Lasso for a general design

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorVAITER, Samuel
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPEYRÉ, Gabriel
hal.structure.identifierEquipe Image - Laboratoire GREYC - UMR6072
dc.contributor.authorFADILI, Jalal M.
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDELEDALLE, Charles-Alban
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDOSSAL, Charles
dc.date.accessioned2024-04-04T02:20:19Z
dc.date.available2024-04-04T02:20:19Z
dc.date.issued2013
dc.date.conference2013-07
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189477
dc.description.abstractEnIn this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, from which a few are active. In such a situation, the group Lasso is an attractive method for variable selection since it promotes sparsity of the groups. We study the sensitivity of any group Lasso solution to the observations and provide its precise local parameterization. When the noise is Gaussian, this allows us to derive an unbiased estimator of the degrees of freedom of the group Lasso. This result holds true for any fixed design, no matter whether it is under- or overdetermined. Our results specialize to those of [1], [2] for blocks of size one, i.e. l1 norm. These results allow objective choice of the regularisation parameter through e.g. the SURE.
dc.language.isoen
dc.source.titleSPARS'13
dc.title.enThe degrees of freedom of the group Lasso for a general design
dc.typeCommunication dans un congrès
dc.subject.halInformatique [cs]/Traitement des images
bordeaux.page1 page
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleSPARS'13
bordeaux.countryCH
bordeaux.title.proceedingSPARS'13
bordeaux.conference.cityLausanne
bordeaux.peerReviewedoui
hal.identifierhal-00926929
hal.version1
hal.invitednon
hal.proceedingsoui
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00926929v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=SPARS'13&rft.date=2013&rft.spage=1%20page&rft.epage=1%20page&rft.au=VAITER,%20Samuel&PEYR%C3%89,%20Gabriel&FADILI,%20Jalal%20M.&DELEDALLE,%20Charles-Alban&DOSSAL,%20Charles&rft.genre=unknown


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