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An Invitation to Statistics in Wasserstein Space / / by Victor M. Panaretos, Yoav Zemel



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Autore: Panaretos Victor M Visualizza persona
Titolo: An Invitation to Statistics in Wasserstein Space / / by Victor M. Panaretos, Yoav Zemel Visualizza cluster
Pubblicazione: Cham, : Springer Nature, 2020
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
Edizione: 1st ed. 2020.
Descrizione fisica: 1 online resource (XIII, 147 p. 30 illus., 24 illus. in color.)
Disciplina: 519.2
519.5
Soggetto topico: Probabilities
Probability Theory and Stochastic Processes
Soggetto non controllato: Probability Theory and Stochastic Processes
Optimal Transportation
Monge-Kantorovich Problem
Barycenter
Multimarginal Transport
Functional Data Analysis
Point Processes
Random Measures
Manifold Statistics
Open Access
Geometrical statistics
Wasserstein metric
Fréchet mean
Procrustes analysis
Phase variation
Gradient descent
Probability & statistics
Stochastics
Persona (resp. second.): ZemelYoav
Nota di contenuto: Optimal transportation -- The Wasserstein space -- Fréchet means in the Wasserstein space -- Phase variation and Fréchet means -- Construction of Fréchet means and multicouplings.
Sommario/riassunto: This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.
Titolo autorizzato: An Invitation to Statistics in Wasserstein Space  Visualizza cluster
ISBN: 3-030-38438-1
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910404119803321
Lo trovi qui: Univ. Federico II
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Serie: SpringerBriefs in Probability and Mathematical Statistics, . 2365-4333