Academic Journal
Wasserstein Barycenters can be Computed in Polynomial Time in Fixed Dimension.
| Τίτλος: | Wasserstein Barycenters can be Computed in Polynomial Time in Fixed Dimension. |
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| Συγγραφείς: | Altschulerá, Jason M.1 JASONALT@MIT.EDU, Boix-Adser, Enric1 EBOIX@MIT.EDU |
| Πηγή: | Journal of Machine Learning Research. 2021, Vol. 22, p1-19. 19p. |
| Θεματικοί όροι: | Computational geometry, Polynomial time algorithms, Machine learning, Computer graphics |
| Περίληψη: | Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics. However, it is unknown whether Wasserstein barycenters can be computed in polynomial time, either exactly or to high precision (i.e., with polylog(1~") runtime dependence). This paper answers these questions in the affirmative for any fixed dimension. Our approach is to solve an exponential-size linear programming formulation by efficiently implementing the corresponding separation oracle using techniques from computational geometry. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Machine Learning Research is the property of Microtome Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: Wasserstein Barycenters can be Computed in Polynomial Time in Fixed Dimension. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Altschulerá%2C+Jason+M%2E%22">Altschulerá, Jason M.</searchLink><relatesTo>1</relatesTo><i> JASONALT@MIT.EDU</i><br /><searchLink fieldCode="AR" term="%22Boix-Adser%2C+Enric%22">Boix-Adser, Enric</searchLink><relatesTo>1</relatesTo><i> EBOIX@MIT.EDU</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Machine+Learning+Research%22">Journal of Machine Learning Research</searchLink>. 2021, Vol. 22, p1-19. 19p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Computational+geometry%22">Computational geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+time+algorithms%22">Polynomial time algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+graphics%22">Computer graphics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics. However, it is unknown whether Wasserstein barycenters can be computed in polynomial time, either exactly or to high precision (i.e., with polylog(1~") runtime dependence). This paper answers these questions in the affirmative for any fixed dimension. Our approach is to solve an exponential-size linear programming formulation by efficiently implementing the corresponding separation oracle using techniques from computational geometry. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Machine Learning Research is the property of Microtome Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 1 Subjects: – SubjectFull: Computational geometry Type: general – SubjectFull: Polynomial time algorithms Type: general – SubjectFull: Machine learning Type: general – SubjectFull: Computer graphics Type: general Titles: – TitleFull: Wasserstein Barycenters can be Computed in Polynomial Time in Fixed Dimension. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Altschulerá, Jason M. – PersonEntity: Name: NameFull: Boix-Adser, Enric IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 15324435 Numbering: – Type: volume Value: 22 Titles: – TitleFull: Journal of Machine Learning Research Type: main |
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