论文标题
随机时间里曼尼亚歧管汉密尔顿蒙特卡洛
Randomized Time Riemannian Manifold Hamiltonian Monte Carlo
论文作者
论文摘要
哈密顿蒙特卡洛（HMC）算法将哈密顿动力学的数值近似与有限的间隔结合在一起，并进行了随机清爽和大都市校正方案是流行的抽样方案，但众所周知，它们可能会在持续时间限制下遭受慢速趋同的影响。 Bou-Rabee和Sanz-Serna的最新论文（Ann。Appl。prob。，27：2159-2194，2017）表明，可以通过简单地将汉密尔顿路径的持续时间参数随机来解决。在本文中，我们使用相同的想法来提高受约束版本的HMC的采样效率，并在各种应用程序设置中具有潜在的好处。我们既证明了固定分布的保守性，也证明了该方法的终身性。我们还比较了模型问题的数值研究中各种方案的性能，包括应用高维协方差估计。
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may suffer from slow convergence in the continuous time limit. A recent paper of Bou-Rabee and Sanz-Serna (Ann. Appl. Prob., 27:2159-2194, 2017) demonstrated that this issue can be addressed by simply randomizing the duration parameter of the Hamiltonian paths. In this article, we use the same idea to enhance the sampling efficiency of a constrained version of HMC, with potential benefits in a variety of application settings. We demonstrate both the conservation of the stationary distribution and the ergodicity of the method. We also compare the performance of various schemes in numerical studies of model problems, including an application to high-dimensional covariance estimation.
