论文标题
采样受约束的连续概率分布：审查
Sampling Constrained Continuous Probability Distributions: A Review
论文作者
论文摘要
在许多机器/统计学习模型中经常出现采样约束连续分布的问题。许多Monte Carlo Markov链（MCMC）采样方法已被调整以处理随机变量的不同类型的约束。在这些方法中，与其他对应物相比，汉密尔顿蒙特卡洛（HMC）和相关方法在计算效率方面具有显着优势。在本文中，我们首先回顾了HMC和一些扩展的抽样方法，然后具体解释了三种受约束的基于HMC的采样方法，反射，重新制定和球形HMC。为了进行说明，我们将这些方法应用于解决三个众所周知的约束采样问题，截断的多元正常分布，贝叶斯正规化回归和非参数密度估计。在这篇综述中，我们还将受限的采样与受约束设计空间的实验的统计设计中的另一个类似问题联系起来。
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of constraints on the random variables. Among these methods, Hamilton Monte Carlo (HMC) and the related approaches have shown significant advantages in terms of computational efficiency compared to other counterparts. In this article, we first review HMC and some extended sampling methods, and then we concretely explain three constrained HMC-based sampling methods, reflection, reformulation, and spherical HMC. For illustration, we apply these methods to solve three well-known constrained sampling problems, truncated multivariate normal distributions, Bayesian regularized regression, and nonparametric density estimation. In this review, we also connect constrained sampling with another similar problem in the statistical design of experiments of constrained design space.
