论文标题
非可逆的指导大都市内核
Non-reversible guided Metropolis kernel
论文作者
论文摘要
我们构建了一类非可逆大都市内核，作为Gustafson 1998提出的指导步行内核的多元扩展。我们方法的主要思想是将状态空间映射到完全有序的群体中。通过使用HAAR测量，我们构建了一种新颖的Markov内核，称为Haar-Mixture内核，该内核本身就是感兴趣的。这是通过诱导完全有序组的拓扑结构来实现的。我们提出的方法，即三角洲引导的大都市 - 黑核，是通过使用Haar-Mixture内核作为建议内核来构建的。所提出的非可逆核至少比随机步行大都市内核和汉密尔顿蒙特卡洛核的10倍，用于逻辑回归，并且根据每秒有效样本量的有效样本量，而随机观察到了随机过程。
We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson 1998. The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed Haar-mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the Delta-guided Metropolis--Haar kernel, is constructed by using the Haar-mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.
