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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBacry, Emmanuel
HAL ID: 735850
ORCID: 0000-0001-5997-1942
hal.structure.identifierCriteo AI Lab
dc.contributor.authorBompaire, Martin
hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
hal.structure.identifierLaboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
dc.contributor.authorGaïffas, Stéphane
hal.structure.identifierSciences pour l'environnement [SPE]
dc.contributor.authorMuzy, Jean-François
HAL ID: 8572
dc.date.accessioned2020-10-26T11:48:41Z
dc.date.available2020-10-26T11:48:41Z
dc.date.issued2020
dc.identifier.issn1532-4435
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21167
dc.language.isoenen
dc.subjectHawkes processesen
dc.subjectSparsityen
dc.subjectLow-Ranken
dc.subjectRandom matricesen
dc.subjectData-driven concentrationen
dc.subject.ddc519en
dc.titleSparse and low-rank multivariate Hawkes processesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the problem of unveiling the implicit network structure of node interactions (such as user interactions in a social network), based only on high-frequency timestamps. Our inference is based on the minimization of the least-squares loss associated with a multivariate Hawkes model, penalized by L1 and trace norm of the interaction tensor. We provide a first theoretical analysis for this problem, that includes sparsity and low-rank inducing penalizations. This result involves a new data-driven concentration inequality for matrix martingales in continuous time with observable variance, which is a result of independent interest and a broad range of possible applications since it extends to matrix martingales former results restricted to the scalar case. A consequence of our analysis is the construction of sharply tuned L1 and trace-norm penalizations, that leads to a data-driven scaling of the variability of information available for each users. Numerical experiments illustrate the significant improvements achieved by the use of such data-driven penalizations.en
dc.relation.isversionofjnlnameJournal of Machine Learning Research
dc.relation.isversionofjnlvol21en
dc.relation.isversionofjnlissue50en
dc.relation.isversionofjnldate2020
dc.relation.isversionofjnlpages1 - 32en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02735273en
dc.relation.isversionofjnlpublisherMIT Pressen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2020-10-26T11:41:54Z
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