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dc.contributor.authorVaiter, Samuel*
dc.contributor.authorFadili, Jalal*
dc.contributor.authorPeyré, Gabriel*
dc.date.accessioned2014-06-13T10:05:04Z
dc.date.available2014-06-13T10:05:04Z
dc.date.issued2018
dc.identifier.issn0018-9448
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13449
dc.language.isoenen
dc.subjectconvexity
dc.subjectsparsity
dc.subjectsensitivity analysis
dc.subjectlow-rank
dc.subjectpartial smoothness
dc.subjectInverse problem
dc.subject.ddc519en
dc.titleModel Consistency of Partly Smooth Regularizers
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherGroupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC) http://www.greyc.fr CNRS : UMR6072 – Université de Caen Basse-Normandie – Ecole Nationale Supérieure d'Ingénieurs de Caen;France
dc.description.abstractenThis paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force solutions of variational problems to belong to a low-dimensional manifold (the so-called model) which is stable under small perturbations of the function. This property is crucial to make the underlying low-complexity model robust to small noise. We show that a generalized ''irrepresentable condition'' implies stable model selection under small noise perturbations in the observations and the design matrix, when the regularization parameter is tuned proportionally to the noise level. This condition is shown to be almost a necessary condition. We then show that this condition implies model consistency of the regularized estimator. That is, with a probability tending to one as the number of measurements increases, the regularized estimator belongs to the correct low-dimensional model manifold. This work unifies and generalizes several previous ones, where model consistency is known to hold for sparse, group sparse, total variation and low-rank regularizations.
dc.relation.isversionofjnlnameIEEE Transactions on Information Theory
dc.relation.isversionofjnlvol64
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2018
dc.relation.isversionofdoi10.1109/TIT.2017.2713822
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-00987293
dc.relation.isversionofjnlpublisherIEEE - Institute of Electrical and Electronics Engineers
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-07-23T13:06:34Z
hal.person.labIds*
hal.person.labIds60*
hal.person.labIds60*


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