Variational Formulation of Particle Flow

Yinzhuang Yi; Jorge Cortés; Nikolay Atanasov

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arXiv · 2505.04007

Variational Formulation of Particle Flow

Yinzhuang Yi·Jorge Cortés·Nikolay Atanasov

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Abstract

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.

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BibTeX RIS

Yinzhuang Yi, Jorge Cortés, Nikolay Atanasov. 2026-03-05. Variational Formulation of Particle Flow. https://arxiv.org/abs/2505.04007

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