An Invitation to Statistics in Wasserstein Space
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 fundame...
Spremljeno u:
| Glavni autori: | , |
|---|---|
| Format: | Online |
| Jezik: | engleski |
| Izdano: |
Springer Nature
2021
|
| Teme: | |
| Online pristup: | ONIX_20200513_9783030384388_4 |
| Oznake: |
Bez oznaka, Budi prvi tko označuje ovaj zapis!
|
| _version_ | 1869519676323659776 |
|---|---|
| author | Panaretos, Victor M. Zemel, Yoav |
| author_browse | Panaretos, Victor M. Zemel, Yoav |
| author_facet | Panaretos, Victor M. Zemel, Yoav |
| author_sort | Panaretos, Victor M. |
| collection | Directory of Open Access Books |
| description | 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. ; 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. Open access. |
| format | Online |
| id | doab-20.500.12854ir-37237 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-372372025-03-22T20:33:55Z An Invitation to Statistics in Wasserstein Space Panaretos, Victor M. Zemel, Yoav 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics 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. ; 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. Open access. 2021-02-10T14:43:33Z 2021-02-10T14:43:33Z 2020-05-13T14:21:04Z 2020 book ONIX_20200513_9783030384388_4 OCN: 1148226628 http://library.oapen.org/handle/20.500.12657/37704 https://directory.doabooks.org/handle/20.500.12854/37237 eng SpringerBriefs in Probability and Mathematical Statistics open access image/jpeg image/jpeg image/jpeg n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/37704/1/2020_Book_AnInvitationToStatisticsInWass.pdf https://library.oapen.org/bitstream/20.500.12657/37704/1/2020_Book_AnInvitationToStatisticsInWass.pdf https://library.oapen.org/bitstream/20.500.12657/37704/1/2020_Book_AnInvitationToStatisticsInWass.pdf Springer Nature Springer 10.1007/978-3-030-38438-8 10.1007/978-3-030-38438-8 9fa3421d-f917-4153-b9ab-fc337c396b5a Springer 147 Cham open access |
| spellingShingle | 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics Panaretos, Victor M. Zemel, Yoav An Invitation to Statistics in Wasserstein Space |
| title | An Invitation to Statistics in Wasserstein Space |
| title_full | An Invitation to Statistics in Wasserstein Space |
| title_fullStr | An Invitation to Statistics in Wasserstein Space |
| title_full_unstemmed | An Invitation to Statistics in Wasserstein Space |
| title_short | An Invitation to Statistics in Wasserstein Space |
| title_sort | invitation to statistics in wasserstein space |
| topic | 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics |
| topic_facet | 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics |
| url | ONIX_20200513_9783030384388_4 |
| work_keys_str_mv | AT panaretosvictorm aninvitationtostatisticsinwassersteinspace AT zemelyoav aninvitationtostatisticsinwassersteinspace AT panaretosvictorm invitationtostatisticsinwassersteinspace AT zemelyoav invitationtostatisticsinwassersteinspace |