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dc.contributor.authorFadili, Jalal M.
dc.contributor.authorGarrigos, Guillaume
dc.contributor.authorMalick, Jérôme
dc.contributor.authorPeyré, Gabriel
dc.date.accessioned2019-04-23T09:30:59Z
dc.date.available2019-04-23T09:30:59Z
dc.date.issued2019-04
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18738
dc.language.isoenen
dc.subjectMirror-Stratifiable Regularizersen
dc.titleModel Consistency for Learning with Mirror-Stratifiable Regularizersen
dc.typeCommunication / Conférence
dc.description.abstractenLow-complexity non-smooth convex regular-izers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised learning. Model consistency consists then in selecting the correct structure (for instance support or rank) by regularized empirical risk minimization. It is known that model consistency holds under appropriate non-degeneracy conditions. However such conditions typically fail for highly correlated designs and it is observed that regularization methods tend to select larger models. In this work, we provide the theoretical underpinning of this behavior using the notion of mirror-stratifiable regular-izers. This class of regularizers encompasses the most well-known in the literature, including the 1 or trace norms. It brings into play a pair of primal-dual models, which in turn allows one to locate the structure of the solution using a specific dual certificate. We also show how this analysis is applicable to optimal solutions of the learning problem, and also to the iterates computed by a certain class of stochastic proximal-gradient algorithms.en
dc.relation.ispartofdate172-03
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01988309en
dc.relation.conftitle22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019en
dc.relation.confdate2019-04
dc.relation.confcityNahaen
dc.relation.confcountryJapanen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2019-03-26T09:36:36Z
hal.person.labIds150
hal.person.labIds95043
hal.person.labIds24474
hal.person.labIds60


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