Wasserstein KL-divergence for Gaussian distributions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910269646569472 |
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| author | Datar, Adwait Ay, Nihat |
| author_facet | Datar, Adwait Ay, Nihat |
| contents | We introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space ${\Bbb R}^n$. In particular, we can evaluate the WKL-divergence of the Dirac measures concentrated in two points which turns out to be proportional to the squared distance between these points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wasserstein KL-divergence for Gaussian distributions Datar, Adwait Ay, Nihat Statistics Theory Machine Learning We introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space ${\Bbb R}^n$. In particular, we can evaluate the WKL-divergence of the Dirac measures concentrated in two points which turns out to be proportional to the squared distance between these points. |
| title | Wasserstein KL-divergence for Gaussian distributions |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2503.24022 |