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dc.contributor.authorLiu, Yating
dc.contributor.authorPagès, Gilles
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 performance
dc.subjectConvergence rate of optimal quantization
dc.subjectDistortion function
dc.subjectEmpirical measure
dc.subjectOptimal quantization
dc.subject.ddc519en
dc.titleConvergence Rate of Optimal Quantization and Application to the Clustering Performance of the Empirical Measure
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].
dc.publisher.cityParisen
dc.identifier.citationpages32
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSL
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02484426
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2022-11-10T14:26:25Z


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