Statistical data analysis in the Wasserstein space*

This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on the use of Wasserstein distances and tools from optimal trans...

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Main Author:	Bigot Jérémie
Format:	Article
Language:	English
Published:	EDP Sciences 2020-01-01
Series:	ESAIM: Proceedings and Surveys
Online Access:	https://www.esaim-proc.org/articles/proc/pdf/2020/02/proc206801.pdf

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spelling	doaj-4a1701de652442a4b3a0e429ae6b9cef2021-08-11T12:31:43ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592020-01-016811910.1051/proc/202068001proc206801Statistical data analysis in the Wasserstein space*Bigot Jérémie0Institut de Mathématiques de Bordeaux et CNRS (UMR 5251), Université de BordeauxThis paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on the use of Wasserstein distances and tools from optimal transport to analyse such data. In particular, we highlight the benefits of using the notions of barycenter and geodesic PCA in the Wasserstein space for the purpose of learning the principal modes of geometric variation in a dataset. In this setting, we discuss existing works and we present some research perspectives related to the emerging field of statistical optimal transport.https://www.esaim-proc.org/articles/proc/pdf/2020/02/proc206801.pdf
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bigot Jérémie
spellingShingle	Bigot Jérémie Statistical data analysis in the Wasserstein space* ESAIM: Proceedings and Surveys
author_facet	Bigot Jérémie
author_sort	Bigot Jérémie
title	Statistical data analysis in the Wasserstein space*
title_short	Statistical data analysis in the Wasserstein space*
title_full	Statistical data analysis in the Wasserstein space*
title_fullStr	Statistical data analysis in the Wasserstein space*
title_full_unstemmed	Statistical data analysis in the Wasserstein space*
title_sort	statistical data analysis in the wasserstein space*
publisher	EDP Sciences
series	ESAIM: Proceedings and Surveys
issn	2267-3059
publishDate	2020-01-01
description	This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on the use of Wasserstein distances and tools from optimal transport to analyse such data. In particular, we highlight the benefits of using the notions of barycenter and geodesic PCA in the Wasserstein space for the purpose of learning the principal modes of geometric variation in a dataset. In this setting, we discuss existing works and we present some research perspectives related to the emerging field of statistical optimal transport.
url	https://www.esaim-proc.org/articles/proc/pdf/2020/02/proc206801.pdf
work_keys_str_mv	AT bigotjeremie statisticaldataanalysisinthewassersteinspace
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Statistical data analysis in the Wasserstein space*

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