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An Invitation to Statistics in Wasserstein Space

Af: Yoav Zemel, Victor M. Panaretos Engelsk Paperback

An Invitation to Statistics in Wasserstein Space

Af: Yoav Zemel, Victor M. Panaretos Engelsk Paperback
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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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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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Produktdetaljer
Sprog: Engelsk
Sider: 147
ISBN-13: 9783030384371
Indbinding: Paperback
Udgave:
ISBN-10: 3030384373
Kategori: Stokastik
Udg. Dato: 11 mar 2020
Længde: 11mm
Bredde: 234mm
Højde: 155mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 11 mar 2020
Forfatter(e): Yoav Zemel, Victor M. Panaretos
Forfatter(e) Yoav Zemel, Victor M. Panaretos

Kategori Stokastik

ISBN-13 9783030384371

Sprog Engelsk

Indbinding Paperback

Sider 147

Udgave

Længde 11mm

Bredde 234mm

Højde 155mm

Udg. Dato 11 mar 2020

Oplagsdato 11 mar 2020

Forlag Springer Nature Switzerland AG

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