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An invitation to statistics in Wasse...

Panaretos, Victor M.

An invitation to statistics in Wasserstein space

Record Type:	Electronic resources : Monograph/item
Title/Author:	An invitation to statistics in Wasserstein spaceby Victor M. Panaretos, Yoav Zemel.
Author:	Panaretos, Victor M.
other author:	Zemel, Yoav.
Published:	Cham :Springer International Publishing :2020.
Description:	xiii, 147 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematical statistics.
Online resource:	https://doi.org/10.1007/978-3-030-38438-8
ISBN:	9783030384388$q(electronic bk.)

An invitation to statistics in Wasserstein space
Panaretos, Victor M.

An invitation to statistics in Wasserstein space[electronic resource] /by Victor M. Panaretos, Yoav Zemel. - Cham :Springer International Publishing :2020. - xiii, 147 p. :ill., digital ;24 cm. - SpringerBriefs in probability and mathematical statistics,2365-4333. - SpringerBriefs in probability and mathematical statistics..

Optimal transportation -- The Wasserstein space -- Frechet means in the Wasserstein space -- Phase variation and Frechet means -- Construction of Frechet means and multicouplings.

Open access.

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.

ISBN: 9783030384388$q(electronic bk.)

Standard No.: 10.1007/978-3-030-38438-8doiSubjects--Topical Terms:

181877
Mathematical statistics.

LC Class. No.: QA276 / .P363 2020

Dewey Class. No.: 519.5

An invitation to statistics in Wasserstein space
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505 0 $a Optimal transportation -- The Wasserstein space -- Frechet means in the Wasserstein space -- Phase variation and Frechet means -- Construction of Frechet means and multicouplings.
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520 $a 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.
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