Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions
Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions
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DOI：
10.1007/s40072-020-00175-6
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Nawaf Bou-Rabee;A. Eberle
中科院分区：
文献类型：
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作者：
Nawaf Bou-Rabee;A. Eberle
在Hilbert空间上，导出了精确预条件哈密顿蒙特卡罗算法（pHMC）收敛到平衡的非渐近定量界。因此，pHMC的显式和无量纲边界适用于高维分布产生的过渡路径采样和路径积分分子动力学。不需要潜在势能的全局凸性。我们的结果是基于在一个精心设计的距离收缩的双尺度耦合。
We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequence, explicit and dimension-free bounds for pHMC applied to high-dimensional distributions arising in transition path sampling and path integral molecular dynamics are given. Global convexity of the underlying potential energies is not required. Our results are based on a two-scale coupling which is contractive in a carefully designed distance.