Randomized Runge-Kutta-Nyström Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910817654407168 |
|---|---|
| author | Bou-Rabee, Nawaf Kleppe, Tore Selland |
| author_facet | Bou-Rabee, Nawaf Kleppe, Tore Selland |
| contents | We introduce $5/2$- and $7/2$-order $L^2$-accurate randomized Runge-Kutta-Nyström methods, tailored for approximating Hamiltonian flows within non-reversible Markov chain Monte Carlo samplers, such as unadjusted Hamiltonian Monte Carlo and unadjusted kinetic Langevin Monte Carlo. We establish quantitative $5/2$-order $L^2$-accuracy upper bounds under gradient and Hessian Lipschitz assumptions on the potential energy function. The numerical experiments demonstrate the superior efficiency of the proposed unadjusted samplers on a variety of well-behaved, high-dimensional target distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07399 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Randomized Runge-Kutta-Nyström Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo Bou-Rabee, Nawaf Kleppe, Tore Selland Numerical Analysis Probability Computation Methodology Machine Learning 60J05 (Primary) 65C05, 65L05, 65P10 (Secondary) We introduce $5/2$- and $7/2$-order $L^2$-accurate randomized Runge-Kutta-Nyström methods, tailored for approximating Hamiltonian flows within non-reversible Markov chain Monte Carlo samplers, such as unadjusted Hamiltonian Monte Carlo and unadjusted kinetic Langevin Monte Carlo. We establish quantitative $5/2$-order $L^2$-accuracy upper bounds under gradient and Hessian Lipschitz assumptions on the potential energy function. The numerical experiments demonstrate the superior efficiency of the proposed unadjusted samplers on a variety of well-behaved, high-dimensional target distributions. |
| title | Randomized Runge-Kutta-Nyström Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo |
| topic | Numerical Analysis Probability Computation Methodology Machine Learning 60J05 (Primary) 65C05, 65L05, 65P10 (Secondary) |
| url | https://arxiv.org/abs/2310.07399 |