[2505.04007] Variational Formulation of Particle Flow

Statistics > Machine Learning arXiv:2505.04007 (stat) [Submitted on 6 May 2025 (v1), last revised 5 Mar 2026 (this version, v2)] Title:Variational Formulation of Particle Flow Authors:Yinzhuang Yi, Jorge Cortés, Nikolay Atanasov View a PDF of the paper titled Variational Formulation of Particle Flow, by Yinzhuang Yi and 2 other authors View PDF HTML (experimental) 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 illu...