Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866912003901095936 |
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| author | Gu, Hyemin Birmpa, Panagiota Pantazis, Yannis Rey-Bellet, Luc Katsoulakis, Markos A. |
| author_facet | Gu, Hyemin Birmpa, Panagiota Pantazis, Yannis Rey-Bellet, Luc Katsoulakis, Markos A. |
| contents | We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based and are constructed as gradient flows of Lipschitz-regularized Kullback-Leibler or other $f$-divergences, where data from a source distribution can be stably transported as particles, towards the vicinity of the target distribution. As a highlighted result in data integration, we demonstrate that the proposed algorithms correctly transport gene expression data points with dimension exceeding 54K, while the sample size is typically only in the hundreds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17230 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data Gu, Hyemin Birmpa, Panagiota Pantazis, Yannis Rey-Bellet, Luc Katsoulakis, Markos A. Machine Learning 35Q84, 49Q22, 62B10, 65C35, 68T07, 94A17 We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based and are constructed as gradient flows of Lipschitz-regularized Kullback-Leibler or other $f$-divergences, where data from a source distribution can be stably transported as particles, towards the vicinity of the target distribution. As a highlighted result in data integration, we demonstrate that the proposed algorithms correctly transport gene expression data points with dimension exceeding 54K, while the sample size is typically only in the hundreds. |
| title | Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data |
| topic | Machine Learning 35Q84, 49Q22, 62B10, 65C35, 68T07, 94A17 |
| url | https://arxiv.org/abs/2210.17230 |