Most Likely Optimal Subsampled Markov Chain Monte Carlo  

作　　者：HU Guanyu WANG Haiying 

机构地区：[1]University of Missouri-Columbia,USA [2]University of Connecticut,USA

出　　处：《Journal of Systems Science & Complexity》2021年第3期1121-1134,共14页系统科学与复杂性学报（英文版）

基　　金：supported by US National Science Fundation under Grant No. 1812013。

摘　　要：Markov Chain Monte Carlo(MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. This paper proposes to approximate the log-likelihood with subsamples taken according to nonuniform subsampling probabilities, and derives the most likely optimal(MLO) subsampling probabilities for better approximation. Compared with existing subsampled MCMC algorithm with equal subsampling probabilities,the MLO subsampled MCMC has a higher estimation efficiency with the same subsampling ratio. The authors also derive a formula using the asymptotic distribution of the subsampled log-likelihood to determine the required subsample size in each MCMC iteration for a given level of precision. This formula is used to develop an adaptive version of the MLO subsampled MCMC algorithm. Numerical experiments demonstrate that the proposed method outperforms the uniform subsampled MCMC.

关 键 词：Big data MCMC metropolis-hasting algorithm nonuniform subsampling 

分 类 号：O211.62[理学—概率论与数理统计]