We study the problem of approximate sampling from non-log-concave
distributions, e.g., Gaussian mixtures, which is often challenging even in low
dimensions due to their multimodality. We focus on performing this task via
Markov chain Monte Carlo (MCMC) methods derived from discretizations of the
overdamped Langevin diffusions, which are commonly known as Langevin Monte
Carlo algorithms. Furthermore, we are also interested in two nonsmooth cases
for which a large class of proximal MCMC methods have been developed: (i) a
nonsmooth prior is considered with a Gaussian mixture likelihood; (ii) a
Laplacian mixture distribution. Such nonsmooth and non-log-concave sampling
tasks arise from a wide range of applications to Bayesian inference and imaging
inverse problems such as image deconvolution. We perform numerical simulations
to compare the performance of most commonly used Langevin Monte Carlo
algorithms.

该论文研究了近似采样的问题，特别是非对数凹分布的问题，提出了基于 Langevin Monte Carlo 算法的马尔可夫链蒙特卡洛方法，并在两种非光滑分布的情况下进行了数字模拟来比较算法的性能。