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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/2411.08993 |
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| _version_ | 1866915019344576512 |
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| author | Boserup, Nicklas Yang, Gefan Severinsen, Michael Lind Hipsley, Christy Anna Sommer, Stefan |
| author_facet | Boserup, Nicklas Yang, Gefan Severinsen, Michael Lind Hipsley, Christy Anna Sommer, Stefan |
| contents | We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including ancestral state reconstruction. Estimation is performed by utilising score matching to approximate diffusion bridges, which are subsequently used in an importance sampler to estimate log-likelihoods. The entire setup is differentiable, allowing gradient ascent on approximated log-likelihoods. This allows both parameter inference and diffusion mean estimation. This novel, numerically stable, score matching-based parameter inference framework is presented and demonstrated on biological two- and three-dimensional morphometry data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameter Inference via Differentiable Diffusion Bridge Importance Sampling Boserup, Nicklas Yang, Gefan Severinsen, Michael Lind Hipsley, Christy Anna Sommer, Stefan Machine Learning We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including ancestral state reconstruction. Estimation is performed by utilising score matching to approximate diffusion bridges, which are subsequently used in an importance sampler to estimate log-likelihoods. The entire setup is differentiable, allowing gradient ascent on approximated log-likelihoods. This allows both parameter inference and diffusion mean estimation. This novel, numerically stable, score matching-based parameter inference framework is presented and demonstrated on biological two- and three-dimensional morphometry data. |
| title | Parameter Inference via Differentiable Diffusion Bridge Importance Sampling |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2411.08993 |