Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915505213800448 |
|---|---|
| author | Zhou, Huanjian Sugiyama, Masashi |
| author_facet | Zhou, Huanjian Sugiyama, Masashi |
| contents | Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity, namely the number of sequential rounds required for sampling algorithms. While recent works have introduced several parallelizable techniques, they often exhibit suboptimal convergence rates and remain significantly weaker than the latest lower bounds for log-concave sampling. To address this, we propose a novel parallel sampling method that improves adaptive complexity dependence on dimension $d$ reducing it from $\widetilde{\mathcal{O}}(\log^2 d)$ to $\widetilde{\mathcal{O}}(\log d)$. which is even optimal for log-concave sampling with some specific adaptive complexity. Our approach builds on parallel simulation techniques from scientific computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models Zhou, Huanjian Sugiyama, Masashi Data Structures and Algorithms Distributed, Parallel, and Cluster Computing Machine Learning Numerical Analysis Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity, namely the number of sequential rounds required for sampling algorithms. While recent works have introduced several parallelizable techniques, they often exhibit suboptimal convergence rates and remain significantly weaker than the latest lower bounds for log-concave sampling. To address this, we propose a novel parallel sampling method that improves adaptive complexity dependence on dimension $d$ reducing it from $\widetilde{\mathcal{O}}(\log^2 d)$ to $\widetilde{\mathcal{O}}(\log d)$. which is even optimal for log-concave sampling with some specific adaptive complexity. Our approach builds on parallel simulation techniques from scientific computing. |
| title | Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models |
| topic | Data Structures and Algorithms Distributed, Parallel, and Cluster Computing Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2412.07435 |