Transport information Bregman divergences
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913778607587328 |
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| author | Li, Wuchen |
| author_facet | Li, Wuchen |
| contents | We study Bregman divergences in probability density space embedded with the $L^2$-Wasserstein metric. Several properties and dualities of transport Bregman divergences are provided. In particular, we derive the transport Kullback-Leibler (KL) divergence by a Bregman divergence of negative Boltzmann-Shannon entropy in $L^2$-Wasserstein space. We also derive analytical formulas and generalizations of transport KL divergence for one-dimensional probability densities and Gaussian families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_01162 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Transport information Bregman divergences Li, Wuchen Information Theory Artificial Intelligence Mathematical Physics Probability We study Bregman divergences in probability density space embedded with the $L^2$-Wasserstein metric. Several properties and dualities of transport Bregman divergences are provided. In particular, we derive the transport Kullback-Leibler (KL) divergence by a Bregman divergence of negative Boltzmann-Shannon entropy in $L^2$-Wasserstein space. We also derive analytical formulas and generalizations of transport KL divergence for one-dimensional probability densities and Gaussian families. |
| title | Transport information Bregman divergences |
| topic | Information Theory Artificial Intelligence Mathematical Physics Probability |
| url | https://arxiv.org/abs/2101.01162 |