Sampling and Integration of Logconcave Functions by Algorithmic Diffusion
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912127931908096 |
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| author | Kook, Yunbum Vempala, Santosh S. |
| author_facet | Kook, Yunbum Vempala, Santosh S. |
| contents | We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and matches the best-known complexities for the special case of uniform distributions on convex bodies. For the sampling problem, our output guarantees are significantly stronger than previously known, and lead to a streamlined analysis of statistical estimation based on dependent random samples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sampling and Integration of Logconcave Functions by Algorithmic Diffusion Kook, Yunbum Vempala, Santosh S. Data Structures and Algorithms Machine Learning Statistics Theory We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and matches the best-known complexities for the special case of uniform distributions on convex bodies. For the sampling problem, our output guarantees are significantly stronger than previously known, and lead to a streamlined analysis of statistical estimation based on dependent random samples. |
| title | Sampling and Integration of Logconcave Functions by Algorithmic Diffusion |
| topic | Data Structures and Algorithms Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2411.13462 |