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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.15455 |
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| _version_ | 1866915195638513664 |
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| author | Baker, Elizabeth L. Schauer, Moritz Sommer, Stefan |
| author_facet | Baker, Elizabeth L. Schauer, Moritz Sommer, Stefan |
| contents | We propose a new algorithm for learning bridged diffusion processes using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob's $h$-transform, yields a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, we learn the score term $\nabla_x \log p(t, x; T, y)$ directly, for given $t, y$, completely avoiding first learning a time-reversal. We compare the performance of our algorithm with existing methods and see that it outperforms using the (learned) time-reversals to learn the score term. The code can be found at https://github.com/libbylbaker/forward_bridge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Score matching for bridges without learning time-reversals Baker, Elizabeth L. Schauer, Moritz Sommer, Stefan Machine Learning Probability We propose a new algorithm for learning bridged diffusion processes using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob's $h$-transform, yields a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, we learn the score term $\nabla_x \log p(t, x; T, y)$ directly, for given $t, y$, completely avoiding first learning a time-reversal. We compare the performance of our algorithm with existing methods and see that it outperforms using the (learned) time-reversals to learn the score term. The code can be found at https://github.com/libbylbaker/forward_bridge. |
| title | Score matching for bridges without learning time-reversals |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2407.15455 |