Complexity of zigzag sampling algorithm for strongly log-concave distributions
Complexity of zigzag sampling algorithm for strongly log-concave distributions
复制标题
强对数凹分布的锯齿形采样算法的复杂性
DOI：
10.1007/s11222-022-10109-y
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发表时间：
2022
影响因子：
2.2
通讯作者：
Wang, Lihan
中科院分区：
文献类型：
--
作者：
Lu, Jianfeng;Wang, Lihan
We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieveserror in chi-square divergence with a computational cost equivalent to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\bigl (\kappa ^2 d^\frac{1}{2}(\log \frac{1}{\varepsilon })^{\frac{3}{2}}\bigr )$$\end{document} gradient evaluations in the regimeunder a warm start assumption, whereis the condition number anddis the dimension.
We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieveserror in chi-square divergence with a computational cost equivalent to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\bigl (\kappa ^2 d^\frac{1}{2}(\log \frac{1}{\varepsilon })^{\frac{3}{2}}\bigr )$$\end{document} gradient evaluations in the regimeunder a warm start assumption, whereis the condition number anddis the dimension.
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DOI：
10.1214/20-aap1653
发表时间：
2018-08
期刊：
The Annals of Applied Probability
影响因子：
--
作者：
C. Andrieu;Alain Durmus;Nikolas Nusken;Julien Roussel
通讯作者：
C. Andrieu;Alain Durmus;Nikolas Nusken;Julien Roussel
影响因子：
1.5
作者：
Durmus, Alain;Moulines, Eric
通讯作者：
Moulines, Eric
DOI：
10.4230/lipics.approx-random.2019.64
发表时间：
2019-05
期刊：
Theory Comput.
影响因子：
--
作者：
Zongchen Chen;S. Vempala
通讯作者：
Zongchen Chen;S. Vempala
DOI：
--
发表时间：
2019
期刊：
The Annals of Applied Probability
影响因子：
--
作者：
J. Bierkens;P. Nyquist;Mikola C. Schlottke
通讯作者：
Mikola C. Schlottke
DOI：
--
发表时间：
2020-10
期刊：
ArXiv
影响因子：
--
作者：
Zhiyan Ding;Qin Li;Jianfeng Lu;Stephen J. Wright
通讯作者：
Zhiyan Ding;Qin Li;Jianfeng Lu;Stephen J. Wright