Variational Formulation of the Particle Flow Particle Filter
This work provides a theoretical foundation for particle flow particle filters, which is incremental as it reformulates an existing method using variational principles.
The paper tackles the problem of deriving the particle flow particle filter from a variational inference perspective, showing that the transient density follows a time-scaled trajectory of the Fisher-Rao gradient flow to minimize the Kullback-Leibler divergence between variational and true posterior densities.
This paper provides a formulation of the particle flow particle filter from the perspective of variational inference. We show that the transient density used to derive the particle flow particle filter 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.