论文标题
哈密顿辅助大都市抽样
Hamiltonian Assisted Metropolis Sampling
论文作者
论文摘要
研究了各种马尔可夫链蒙特卡洛（MCMC）方法，以改进随机行走大都市采样，以模拟复杂分布。例子包括大都市调整后的兰格文算法，汉密尔顿蒙特卡洛，以及与阻尼不足的兰格文动力学有关的其他最新算法。我们提出了一类不可逆的采样算法，称为哈密顿辅助大都市采样（HAMS），并通过适当的调整和预处理策略开发了两种特定的算法。我们的火腿算法旨在实现两种独特的特性，同时将增强的目标密度以动量作为辅助变量。一个是通用的详细平衡，这会引起对目标的不可逆转探索。另一个是无拒绝的属性，它允许我们的算法以相对较大的步进尺寸令人满意地执行。此外，我们制定了广义大都市的框架 - 吊装抽样，这不仅突出了我们在更抽象的水平上的火腿构造，而且还促进了不可逆转的MCMC算法的进一步发展。我们提出了几个数值实验，其中发现所提出的算法在现有算法中始终如一地产生较高的结果。
Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and other recent algorithms related to underdamped Langevin dynamics. We propose a broad class of irreversible sampling algorithms, called Hamiltonian assisted Metropolis sampling (HAMS), and develop two specific algorithms with appropriate tuning and preconditioning strategies. Our HAMS algorithms are designed to achieve two distinctive properties, while using an augmented target density with momentum as an auxiliary variable. One is generalized detailed balance, which induces an irreversible exploration of the target. The other is a rejection-free property, which allows our algorithms to perform satisfactorily with relatively large step sizes. Furthermore, we formulate a framework of generalized Metropolis--Hastings sampling, which not only highlights our construction of HAMS at a more abstract level, but also facilitates possible further development of irreversible MCMC algorithms. We present several numerical experiments, where the proposed algorithms are found to consistently yield superior results among existing ones.
