High-Order Langevin Monte Carlo Algorithms
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915460955504640 |
|---|---|
| author | Dang, Thanh Gurbuzbalaban, Mert Islam, Mohammad Rafiqul Yao, Nian Zhu, Lingjiong |
| author_facet | Dang, Thanh Gurbuzbalaban, Mert Islam, Mohammad Rafiqul Yao, Nian Zhu, Lingjiong |
| contents | Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based on the discretizations of $P$-th order Langevin dynamics for any $P\geq 3$. Our design of $P$-th order Langevin Monte Carlo (LMC) algorithms is by combining splitting and accurate integration methods. We obtain Wasserstein convergence guarantees for sampling from distributions with log-concave and smooth densities. Specifically, the mixing time of the $P$-th order LMC algorithm scales as $O\left(d^{\frac{1}{R}}/ε^{\frac{1}{2R}}\right)$ for $R=4\cdot 1_{\{ P=3\}}+ (2P-1)\cdot 1_{\{ P\geq 4\}}$, which has a better dependence on the dimension $d$ and the accuracy level $ε$ as $P$ grows. Numerical experiments illustrate the efficiency of our proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Order Langevin Monte Carlo Algorithms Dang, Thanh Gurbuzbalaban, Mert Islam, Mohammad Rafiqul Yao, Nian Zhu, Lingjiong Machine Learning Probability Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based on the discretizations of $P$-th order Langevin dynamics for any $P\geq 3$. Our design of $P$-th order Langevin Monte Carlo (LMC) algorithms is by combining splitting and accurate integration methods. We obtain Wasserstein convergence guarantees for sampling from distributions with log-concave and smooth densities. Specifically, the mixing time of the $P$-th order LMC algorithm scales as $O\left(d^{\frac{1}{R}}/ε^{\frac{1}{2R}}\right)$ for $R=4\cdot 1_{\{ P=3\}}+ (2P-1)\cdot 1_{\{ P\geq 4\}}$, which has a better dependence on the dimension $d$ and the accuracy level $ε$ as $P$ grows. Numerical experiments illustrate the efficiency of our proposed algorithms. |
| title | High-Order Langevin Monte Carlo Algorithms |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2508.17545 |