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dc.contributor.authorVaiter, Samuel
HAL ID: 1995
ORCID: 0000-0002-4077-708X
*
hal.structure.identifier
dc.contributor.authorDeledalle, Charles-Alban*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorFadili, Jalal
HAL ID: 15510
*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
*
hal.structure.identifier
dc.contributor.authorDossal, Charles*
dc.date.accessioned2014-04-28T14:36:40Z
dc.date.available2014-04-28T14:36:40Z
dc.date.issued2016
dc.identifier.issn0020-3157
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13154
dc.language.isoenen
dc.subjectTotal variation
dc.subjectDegrees of freedom
dc.subjectSparsity
dc.subjectPartial smoothness
dc.subjectModel selection
dc.subjectGroup Lasso
dc.subjectSemi-algebraic sets
dc.subjecto-minimal structures
dc.subject.ddc519en
dc.titleThe Degrees of Freedom of Partly Smooth Regularizers
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherInstitut de Mathématiques de Bordeaux (IMB) http://www.math.u-bordeaux.fr/IMB/ CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II;France
dc.description.abstractenWe study regularized regression problems where the regularizer is a proper, lower-semicontinuous, convex and partly smooth function relative to a Riemannian submanifold. This encompasses several popular examples including the Lasso, the group Lasso, the max and nuclear norms, as well as their composition with linear operators (e.g., total variation or fused Lasso). Our main sensitivity analysis result shows that the predictor moves locally stably along the same active submanifold as the observations undergo small perturbations. This plays a pivotal role in getting a closed-form expression for the divergence of the predictor w.r.t. observations. We also show that, for many regularizers, including polyhedral ones or the analysis group Lasso, this divergence formula holds Lebesgue a.e. When the perturbation is random (with an appropriate continuous distribution), this allows us to derive an unbiased estimator of the degrees of freedom and the prediction risk. Our results unify and go beyond those already known in the literature
dc.publisher.cityParisen
dc.relation.isversionofjnlnameAnnals of the Institute of Statistical Mathematics
dc.relation.isversionofjnlvol69
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages791-832
dc.relation.isversionofdoi10.1007/s10463-016-0563-z
dc.identifier.urlsitehttps://arxiv.org/abs/1404.5557v4
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.submittednonen
dc.description.ssrncandidatenon
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-07-21T13:29:59Z
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