The forward-backward envelope for sampling with the overdamped Langevin algorithm
The forward-backward envelope for sampling with the overdamped Langevin algorithm
复制标题
使用过阻尼 Langevin 算法进行采样的前向-后向包络
DOI：
10.1007/s11222-023-10254-y
复制
发表时间：
2023
影响因子：
2.2
通讯作者：
Eftekhari A
中科院分区：
文献类型：
--
作者：
Eftekhari A
在本文中，我们分析了一个近似的方法的基础上的思想，向前向后分裂的密度分布，不一定是光滑的抽样。特别是，我们研究了Langevin方程的Euler-Maruyama离散化的非渐近性质，其中前后向包络用于处理动力学的非光滑部分。与广泛使用的Moreu-Yoshida算法和MYSTARY算法相比，这种包络的优点在于它保持了原始非光滑分布的MAP估计。我们还研究了一些数值实验，支持我们的理论研究结果。
In this paper, we analyse a proximal method based on the idea of forward–backward splitting for sampling from distributions with densities that are not necessarily smooth. In particular, we study the non-asymptotic properties of the Euler–Maruyama discretization of the Langevin equation, where the forward–backward envelope is used to deal with the non-smooth part of the dynamics. An advantage of this envelope, when compared to widely-used Moreu–Yoshida one and the MYULA algorithm, is that it maintains the MAP estimator of the original non-smooth distribution. We also study a number of numerical experiments that support our theoretical findings.