Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914109177462784 |
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| author | Vacher, Adrien Chehab, Omar Korba, Anna |
| author_facet | Vacher, Adrien Chehab, Omar Korba, Anna |
| contents | Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in the parameters governing multi-modality, assuming fixed dimension. Our sampling algorithm simulates a time-reversed diffusion process, using a self-normalized Monte Carlo estimator of the intermediate score functions. Unlike previous works, it avoids metastability, requires no prior knowledge of the mode locations, and relaxes the well-known log-smoothness assumption which excluded general Gaussian mixtures so far. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00565 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion Vacher, Adrien Chehab, Omar Korba, Anna Computation Machine Learning Statistics Theory Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in the parameters governing multi-modality, assuming fixed dimension. Our sampling algorithm simulates a time-reversed diffusion process, using a self-normalized Monte Carlo estimator of the intermediate score functions. Unlike previous works, it avoids metastability, requires no prior knowledge of the mode locations, and relaxes the well-known log-smoothness assumption which excluded general Gaussian mixtures so far. |
| title | Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion |
| topic | Computation Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2501.00565 |