An Invitation to Statistics in Wasserstein Space (Record no. 52583)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 03373naaaa2200481uu 4500 |
| 001 - CONTROL NUMBER | |
| control field | https://directory.doabooks.org/handle/20.500.12854/37237 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220220000231.0 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 978-3-030-38438-8 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-030-38438-8 |
| Terms of availability | doi |
| 041 0# - LANGUAGE CODE | |
| Language code of text/sound track or separate title | English |
| 042 ## - AUTHENTICATION CODE | |
| Authentication code | dc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBT |
| Source | bicssc |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Panaretos, Victor M. |
| Relationship | auth |
| 245 10 - TITLE STATEMENT | |
| Title | An Invitation to Statistics in Wasserstein Space |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
| Place of publication, distribution, etc. | Cham |
| Name of publisher, distributor, etc. | Springer Nature |
| Date of publication, distribution, etc. | 2020 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 electronic resource (147 p.) |
| 506 0# - RESTRICTIONS ON ACCESS NOTE | |
| Terms governing access | Open Access |
| Source of term | star |
| Standardized terminology for access restriction | Unrestricted online access |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 540 ## - TERMS GOVERNING USE AND REPRODUCTION NOTE | |
| Terms governing use and reproduction | Creative Commons |
| Use and reproduction rights | by/4.0/ |
| Source of term | cc |
| -- | http://creativecommons.org/licenses/by/4.0/ |
| 546 ## - LANGUAGE NOTE | |
| Language note | English |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Probability & statistics |
| Source of heading or term | bicssc |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Probability Theory and Stochastic Processes |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Optimal Transportation |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Monge-Kantorovich Problem |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Barycenter |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Multimarginal Transport |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Functional Data Analysis |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Point Processes |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Random Measures |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Manifold Statistics |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Open Access |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Geometrical statistics |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Wasserstein metric |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Fréchet mean |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Procrustes analysis |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Phase variation |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Gradient descent |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Probability & statistics |
| 653 ## - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Stochastics |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Zemel, Yoav |
| Relationship | auth |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Host name | www.oapen.org |
| Uniform Resource Identifier | <a href="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</a> |
| Access status | 0 |
| Public note | DOAB: download the publication |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Host name | www.oapen.org |
| Uniform Resource Identifier | <a href="https://directory.doabooks.org/handle/20.500.12854/37237">https://directory.doabooks.org/handle/20.500.12854/37237</a> |
| Access status | 0 |
| Public note | DOAB: description of the publication |
No items available.