On Lq convergence of the Hamiltonian Monte Carlo
JOURNAL OF APPLIED ANALYSIS(2023)
摘要
We establish L-q convergence for Hamiltonian Monte Carlo (HMC) algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 <= q < infinity and weakly for 1 < q < 2) to the desired target distribution. In addition, we establish a general convergence rate for an L-q convergence given a convergence rate at a specific q*, and apply this result to conclude geometric convergence in the Euclidean space for HMC with uniformly strongly logarithmic concave target and auxiliary distributions. We also present the results of experiments to illustrate convergence in L-q.
更多查看译文
关键词
Convergence,L-q spaces,Hamiltonian Monte Carlo
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要