Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from general Markov chain Monte Carlo, to unadjusted Langevin methods. In this article we propose a series of new sampling algorithms based on the latter of these, specifically the kinetic Langevin dynamics. Our series of algorithms are motivated on advanced numerical methods which are splitting order schemes, which include the BU and BAO families of splitting schemes.Their advantage lies in the fact that they have favorable strong order (bias) rates and computationally efficiency. In particular we provide a number of theoretical insights which include a Wasserstein contraction and convergence results. We are able to demonstrate favorable results, such as improved complexity bounds over existing non-splitting methodologies. Our results are verified through numerical experiments on a range of models with constraints, which include a toy example and Bayesian linear regression.

翻译：约束采样是计算统计学中一项重要且具有挑战的任务，旨在在特定约束条件下从分布中生成样本。针对该任务已有多种算法，涵盖通用马尔可夫链蒙特卡洛方法到未调整的朗之万方法。本文基于后者（特别是动能朗之万动力学）提出一系列新型采样算法。该系列算法源于先进数值方法——即分裂阶格式，包括BU和BAO两类分裂格式族。其优势在于具有优越的强阶（偏差）收敛速率和计算效率。我们特别提供了若干理论洞见，包括Wasserstein压缩性与收敛性结果。相较于现有非分裂方法，我们能够证明更优的复杂度界等有利结果。通过在包含玩具算例和贝叶斯线性回归的多种约束模型上的数值实验，验证了方法的有效性。