Publication:
An Invitation to Statistics in Wasserstein Space

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datacite.subject.fos oecd::Natural sciences::Mathematics
dc.contributor.author 2020
dc.date.accessioned 2023-06-26T08:59:04Z
dc.date.available 2023-06-26T08:59:04Z
dc.date.issued 2020
dc.description DOI: https://doi.org/10.1007/978-3-030-38438-8 License: CC BY; Publisher: Springer
dc.description.abstract 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.
dc.identifier.doi https://doi.org/10.1007/978-3-030-38438-8
dc.identifier.isbn 9783030384388
dc.identifier.uri http://repository.vlu.edu.vn:443/handle/123456789/5888
dc.language.iso en
dc.subject Optimal Transportation
dc.subject Monge-Kantorovich Problem
dc.subject Barycenter
dc.subject Multimarginal Transport
dc.subject Functional Data Analysis
dc.subject Point Processes
dc.subject Random Measures
dc.subject Manifold Statistics
dc.subject Open Access
dc.subject Geometrical statistics
dc.subject Wasserstein metric
dc.subject Fréchet mean
dc.subject Procrustes analysis
dc.subject Phase variation
dc.subject Gradient descent.
dc.title An Invitation to Statistics in Wasserstein Space
dc.type Resource Types::text::book
dspace.entity.type Publication
oairecerif.author.affiliation #PLACEHOLDER_PARENT_METADATA_VALUE#
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