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 corroborate that support our theoretical findings.
翻译:在本文中,我们根据从密度不一定平滑的分布区进行抽样的向前后向分割的概念,分析一种最接近的方法。特别是,我们研究了Langevin等式的欧勒-马鲁亚马分解的非非无药性特性,即前向包用于处理动态中非脉冲部分。与广泛使用的Moreu-Yoshida一型和MYULA算法相比,这一信封的一个优点是,它保持了原非脉冲分布的MAP估测器。我们还研究了一些支持我们理论结论的数字实验。