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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.04007 |
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| _version_ | 1866918370352300032 |
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| author | Yi, Yinzhuang Cortés, Jorge Atanasov, Nikolay |
| author_facet | Yi, Yinzhuang Cortés, Jorge Atanasov, Nikolay |
| contents | This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao gradient flow in the space of probability densities. The Fisher-Rao gradient flow is obtained as a continuous-time algorithm for variational inference, minimizing the Kullback-Leibler divergence between a variational density and the true posterior density. When considering a parametric family of variational densities, the function space Fisher-Rao gradient flow simplifies to the natural gradient flow of the variational density parameters. By adopting a Gaussian variational density, we derive a Gaussian approximated Fisher-Rao particle flow and show that, under linear Gaussian assumptions, it reduces to the Exact Daum and Huang particle flow. Additionally, we introduce a Gaussian mixture approximated Fisher-Rao particle flow to enhance the expressive power of our model through a multi-modal variational density. Simulations on low- and high-dimensional estimation problems illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Formulation of Particle Flow Yi, Yinzhuang Cortés, Jorge Atanasov, Nikolay Machine Learning This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao gradient flow in the space of probability densities. The Fisher-Rao gradient flow is obtained as a continuous-time algorithm for variational inference, minimizing the Kullback-Leibler divergence between a variational density and the true posterior density. When considering a parametric family of variational densities, the function space Fisher-Rao gradient flow simplifies to the natural gradient flow of the variational density parameters. By adopting a Gaussian variational density, we derive a Gaussian approximated Fisher-Rao particle flow and show that, under linear Gaussian assumptions, it reduces to the Exact Daum and Huang particle flow. Additionally, we introduce a Gaussian mixture approximated Fisher-Rao particle flow to enhance the expressive power of our model through a multi-modal variational density. Simulations on low- and high-dimensional estimation problems illustrate our results. |
| title | Variational Formulation of Particle Flow |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.04007 |