The geometric foundations of Hamiltonian Monte Carlo
The geometric foundations of Hamiltonian Monte Carlo
复制标题
DOI：
10.3150/16-bej810
复制
发表时间：
2017-11-01
期刊：
影响因子：
1.5
通讯作者：
Girolami, Mark
中科院分区：
文献类型：
--
作者：
Betancourt, Michael;Byrne, Simon;Girolami, Mark
虽然汉密尔顿蒙特卡罗已经证明了经验的成功，缺乏严格的理论理解的算法在许多方面阻碍了原则的发展的方法和使用的算法在实践中。在本文中，我们开发的算法的正式基础，通过建设措施光滑流形，并演示了如何自然识别有效的实现理论和激励有前途的推广。
Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In this paper, we develop the formal foundations of the algorithm through the construction of measures on smooth manifolds, and demonstrate how the theory naturally identifies efficient implementations and motivates promising generalizations.