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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| Format: | Article |
| Language: | English |
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EDP Sciences
2020-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2020/02/proc206801.pdf |
| _version_ | 1797970381413285888 |
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| author | Bigot Jérémie |
| author_facet | Bigot Jérémie |
| author_sort | Bigot Jérémie |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T03:15:56Z |
| format | Article |
| id | doaj.art-4a1701de652442a4b3a0e429ae6b9cef |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T03:15:56Z |
| publishDate | 2020-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-4a1701de652442a4b3a0e429ae6b9cef2023-01-02T10:14:19ZengEDP 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 |
| spellingShingle | Bigot Jérémie Statistical data analysis in the Wasserstein space* ESAIM: Proceedings and Surveys |
| title | 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_short | Statistical data analysis in the Wasserstein space* |
| title_sort | statistical data analysis in the wasserstein space |
| url | https://www.esaim-proc.org/articles/proc/pdf/2020/02/proc206801.pdf |
| work_keys_str_mv | AT bigotjeremie statisticaldataanalysisinthewassersteinspace |