论文标题
希尔伯特空间上预处理的汉密尔顿蒙特卡洛的融合
Convergence of Preconditioned Hamiltonian Monte Carlo on Hilbert Spaces
论文作者
论文摘要
在本文中，我们考虑了直接在无限二维的希尔伯特空间上定义的预处理的汉密尔顿蒙特卡洛（PHMC）算法。在这种情况下，在使目标度量的强大对数洞穴中的结合下，我们证明了标准1-Wasserstein距离中调整后的PHMC的收敛范围。这些论点依赖于两个PHMC副本的同步耦合，该耦合通过适应Arxiv的元素来控制：1805.00452。
In this article, we consider the preconditioned Hamiltonian Monte Carlo (pHMC) algorithm defined directly on an infinite-dimensional Hilbert space. In this context, and under a condition reminiscent of strong log-concavity of the target measure, we prove convergence bounds for adjusted pHMC in the standard 1-Wasserstein distance. The arguments rely on a synchronous coupling of two copies of pHMC, which is controlled by adapting elements from arXiv:1805.00452.
