无限维预条件Hamilton Monte Carlo的双尺度耦合
Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions
摘要：
在希尔伯特空间上，给出了精确预条件Hamilton Monte Carlo算法（pHMC）收敛到平衡点的非渐近定量界.因此，明确和无量纲的界限pHMC适用于高维分布中出现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。我们的研究结果是基于一个双尺度耦合，这是在一个精心设计的距离收缩。
英文摘要：
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.
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