Normalizing constants of log-concave densities
Normalizing constants of log-concave densities
复制标题
对数凹密度的标准化常数
DOI：
10.1214/18-ejs1411
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
'. Moulines
中科院分区：
文献类型：
--
作者：
N. Brosse;Alain Durmus;'. Moulines
We derive explicit bounds for the computation of normalizing constants $Z$ for log-concave densities $\pi = \exp(-U)/Z$ with respect to the Lebesgue measure on $\mathbb{R}^d$. Our approach relies on a Gaussian annealing combined with recent and precise bounds on the Unadjusted Langevin Algorithm (High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm, A. Durmus and E. Moulines). Polynomial bounds in the dimension $d$ are obtained with an exponent that depends on the assumptions made on $U$. The algorithm also provides a theoretically grounded choice of the annealing sequence of variances. A numerical experiment supports our findings. Results of independent interest on the mean squared error of the empirical average of locally Lipschitz functions are established.
影响因子：
1.2
作者：
A. Beskos;D. Crisan;A. Jasra;N. Whiteley
通讯作者：
A. Beskos;D. Crisan;A. Jasra;N. Whiteley
使用非均匀扩散对高维归一化常数进行采样
DOI：
10.48550/arxiv.1612.07583
发表时间：
2016
期刊：
arXiv e-prints
影响因子：
--
作者：
Andrieu Christophe
通讯作者：
Andrieu Christophe