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Statistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling

hal.structure.identifierParcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio [PANAMA]
hal.structure.identifierDynamic Networks : Temporal and Structural Capture Approach [DANTE]
dc.contributor.authorGRIBONVAL, Rémi
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
hal.structure.identifierUnderstanding the Shape of Data [DATASHAPE]
dc.contributor.authorBLANCHARD, Gilles
hal.structure.identifierGIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes [GIPSA-GAIA]
dc.contributor.authorKERIVEN, Nicolas
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTRAONMILIN, Yann
dc.date.accessioned2024-04-04T02:45:59Z
dc.date.available2024-04-04T02:45:59Z
dc.date.issued2021-08-21
dc.identifier.issn2520-2316
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191510
dc.description.abstractEnWe provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The principle of compressive statistical learning is to compress a training collection, in one pass, into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task. We explicitly describe and analyze random feature functions which empirical averages preserve the needed information for compressive clustering and compressive Gaussian mixture modeling with fixed known variance, and establish sufficient sketch sizes given the problem dimensions.
dc.description.sponsorshipApproches statistiquement et computationnellement efficicaces pour l'intelligence artificielle - ANR-19-CHIA-0021
dc.description.sponsorshipAlgorithmes, Approximations, Parcimonie et Plongements pour l'IA - ANR-19-CHIA-0009
dc.language.isoen
dc.publisherEMS Publishing House
dc.subject.enrandom moments
dc.subject.enrandom features
dc.subject.enclustering
dc.subject.enmixture modeling
dc.subject.enprincipal component analysis.
dc.subject.enprincipal component analysis
dc.subject.endimension reduction
dc.subject.enunsupervised learning
dc.subject.enkernel mean embedding
dc.subject.enstatistical learning
dc.title.enStatistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling
dc.typeArticle de revue
dc.identifier.doi10.4171/msl/21
dc.subject.halMathématiques [math]/Statistiques [math.ST]
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
dc.subject.halInformatique [cs]/Apprentissage [cs.LG]
dc.identifier.arxiv2004.08085
dc.description.sponsorshipEuropePLEASE: Projections, Learning, and Sparsity for Efficient data-processing
bordeaux.journalMathematical Statistics and Learning
bordeaux.page165–257
bordeaux.volume3
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02536818
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02536818v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Statistics%20and%20Learning&rft.date=2021-08-21&rft.volume=3&rft.issue=2&rft.spage=165%E2%80%93257&rft.epage=165%E2%80%93257&rft.eissn=2520-2316&rft.issn=2520-2316&rft.au=GRIBONVAL,%20R%C3%A9mi&BLANCHARD,%20Gilles&KERIVEN,%20Nicolas&TRAONMILIN,%20Yann&rft.genre=article


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