The algebraic degree of the Wasserstein distance
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914649316786176 |
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| author | Meroni, Chiara Reinke, Bernhard Wang, Kexin |
| author_facet | Meroni, Chiara Reinke, Bernhard Wang, Kexin |
| contents | Given two rational univariate polynomials, the Wasserstein distance of their associated measures is an algebraic number. We determine the algebraic degree of the squared Wasserstein distance, serving as a measure of algebraic complexity of the corresponding optimization problem. The computation relies on the structure of a subpolytope of the Birkhoff polytope, invariant under a transformation induced by complex conjugation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The algebraic degree of the Wasserstein distance Meroni, Chiara Reinke, Bernhard Wang, Kexin Algebraic Geometry Group Theory Given two rational univariate polynomials, the Wasserstein distance of their associated measures is an algebraic number. We determine the algebraic degree of the squared Wasserstein distance, serving as a measure of algebraic complexity of the corresponding optimization problem. The computation relies on the structure of a subpolytope of the Birkhoff polytope, invariant under a transformation induced by complex conjugation. |
| title | The algebraic degree of the Wasserstein distance |
| topic | Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2401.12735 |