Overview
- Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature
- Presents an up-to-date overview of the state of the art, including some original results,and discusses open problems
- Suitable for self-study or to be used as a graduate level course text
Part of the book series: SpringerBriefs in Probability and Mathematical Statistics (SBPMS)
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Table of contents (5 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the authors
Dr. Yoav Zemel graduated with a PhD in Mathematics at the EPFL in 2017 and is currently a postdoctoral researcher in the Statistical Laboratory at the University of Cambridge. He completed his undergraduate studies in Mathematics and Economics at the Hebrew University of Jerusalem, and earned an MSc in Applied Mathematics at the EPFL. He is the recipient of the EPFL excellence scholarship, as well as the Hebrew University Amirim scholarship, Rector’s Prize and Dean’s Prize.
Bibliographic Information
Book Title: An Invitation to Statistics in Wasserstein Space
Authors: Victor M. Panaretos, Yoav Zemel
Series Title: SpringerBriefs in Probability and Mathematical Statistics
DOI: https://doi.org/10.1007/978-3-030-38438-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s) 2020
Softcover ISBN: 978-3-030-38437-1Published: 11 March 2020
eBook ISBN: 978-3-030-38438-8Published: 10 March 2020
Series ISSN: 2365-4333
Series E-ISSN: 2365-4341
Edition Number: 1
Number of Pages: XIII, 147
Number of Illustrations: 6 b/w illustrations, 24 illustrations in colour