On the Variance Reduction of Hamiltonian Monte Carlo via an Approximation Scheme
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：苏中根（浙江大学）
：2023-04-10 15:00
：腾讯会议：834214030（无密码）
报告人：苏中根（浙江大学）
时 间：2023年4月10日下午15:00-16:30
地 点：腾讯会议：834214030（无密码）
内容摘要:
Metropolised Hamiltonian Monte Carlo method was introduced from molecular dynamics to sample more efficiently from a high dimensional distribution, and has become more and more popular in recent years. Let (X i, i ≥ 0) be the Markov chain induced by the Metropolised Hamiltonian algorithm. For a suitable function f on the state space, we first establish the CLT for k−1/2Sk(f), where Sk(f) =\sum_{i=1}^k f(Xi), under the drift condition developed by Durmus et al (Ann. Stat., 2020). Based on the method of variance reduction given by Mijatovic et al (Bernoulli, 2018), we then obtain a sequence of control variates k−1Sk(gn) for k−1Sk(f), with the corresponding sequence of asymptotic variances σn2 converging to zero.
个人简介：
苏中根，浙江大学教授, 博士生导师。1995年获复旦大学博士学位，主要从事概率极限理论及其应用研究，内容包括概率集中不等式，随机渗流模型，高维随机矩阵和随机增长过程等。在Probab. Theory Related Fields, Electron. J. Probab., Bernoulli, Stochastic Process. Appl.等发表论文四十余篇，编著出版的《概率极限理论基础》2021年获首届全国优秀教材（高等教育类）二等奖。
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