Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows

• URL: http://arxiv.org/abs/2506.05905v1
• Date: Fri, 06 Jun 2025 09:24:46 GMT
• Title: Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows
• Authors: Francesca R. Crucinio, Sahani Pathiraja,
• Abstract summary: We consider several partial differential equations whose solution is a minimiser of the Kullback--Leibler divergence from $pi$.<n>We propose a novel algorithm to approximate the Wasserstein--Fisher--Rao flow of the Kullback--Leibler divergence.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the problem of sampling from a probability distribution $\pi$. It is well known that this can be written as an optimisation problem over the space of probability distribution in which we aim to minimise the Kullback--Leibler divergence from $\pi$. We consider several partial differential equations (PDEs) whose solution is a minimiser of the Kullback--Leibler divergence from $\pi$ and connect them to well-known Monte Carlo algorithms. We focus in particular on PDEs obtained by considering the Wasserstein--Fisher--Rao geometry over the space of probabilities and show that these lead to a natural implementation using importance sampling and sequential Monte Carlo. We propose a novel algorithm to approximate the Wasserstein--Fisher--Rao flow of the Kullback--Leibler divergence which empirically outperforms the current state-of-the-art. We study tempered versions of these PDEs obtained by replacing the target distribution with a geometric mixture of initial and target distribution and show that these do not lead to a convergence speed up.

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