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

Francesca R. Crucinio; Sahani Pathiraja

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arXiv · 2506.05905

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

Francesca R. Crucinio·Sahani Pathiraja

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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 and conduct an extensive empirical study to identify when these algorithms outperforms other popular Monte Carlo algorithms.

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Francesca R. Crucinio, Sahani Pathiraja. 2025-06-06. Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows. https://arxiv.org/abs/2506.05905

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