Show simple item record

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLiu, Yating
hal.structure.identifier
dc.contributor.authorPagès, Gilles
HAL ID: 8458
dc.date.accessioned2020-05-12T11:20:12Z
dc.date.available2020-05-12T11:20:12Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20716
dc.language.isoenen
dc.subjectClustering performanceen
dc.subjectConvergence rate of optimal quantizationen
dc.subjectDistortion functionen
dc.subjectEmpirical measureen
dc.subjectOptimal quantizationen
dc.subject.ddc519en
dc.titleConvergence Rate of Optimal Quantization and Application to the Clustering Performance of the Empirical Measureen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe study the convergence rate of the optimal quantization for a probability measure sequence (µn) n∈N* on R^d converging in the Wasserstein distance in two aspects: the first one is the convergence rate of optimal quantizer x (n) ∈ (R d) K of µn at level K; the other one is the convergence rate of the distortion function valued at x^(n), called the "performance" of x^(n). Moreover, we also study the mean performance of the optimal quantization for the empirical measure of a distribution µ with finite second moment but possibly unbounded support. As an application, we show that the mean performance for the empirical measure of the multidimensional normal distribution N (m, Σ) and of distributions with hyper-exponential tails behave like O(log n √ n). This extends the results from [BDL08] obtained for compactly supported distribution. We also derive an upper bound which is sharper in the quantization level K but suboptimal in n by applying results in [FG15].en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages32en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02484426en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2020-02
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2020-05-12T11:17:53Z
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record