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性的任务，涉及在特定约束条件下从分布中生成样本。针对该任务存在多种算法类型，从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（具体为动能朗之万动力学）提出了一系列新型采样算法。我们的算法系列源自先进的数值方法——分裂阶方案，包括BU和BAO两类分裂方案族。其优势在于具有优越的强阶（偏差）速率和计算效率。特别地，我们提供了包括Wasserstein压缩和收敛性结果在内的若干理论见解。我们能够展示有利结果，例如相比现有非分裂方法在复杂度界上的改进。通过包含玩具示例和贝叶斯线性回归在内的多组约束模型数值实验，验证了我们的结果。