Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918329428475904 |
|---|---|
| author | Crucinio, Francesca R. Pathiraja, Sahani |
| author_facet | Crucinio, Francesca R. Pathiraja, Sahani |
| contents | We consider the problem of sampling from a probability distribution $π$. 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 $π$. We consider several partial differential equations (PDEs) whose solution is a minimiser of the Kullback--Leibler divergence from $π$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05905 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows Crucinio, Francesca R. Pathiraja, Sahani Methodology Numerical Analysis Computation Machine Learning 65C05, 62F15 We consider the problem of sampling from a probability distribution $π$. 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 $π$. We consider several partial differential equations (PDEs) whose solution is a minimiser of the Kullback--Leibler divergence from $π$ 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. |
| title | Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows |
| topic | Methodology Numerical Analysis Computation Machine Learning 65C05, 62F15 |
| url | https://arxiv.org/abs/2506.05905 |