Most Likely Optimal Subsampled Markov Chain Monte Carlo

• Published in: Journal of systems science and complexity Vol. 34; no. 3; pp. 1121 - 1134
• Main Authors: Hu, Guanyu, Wang, Haiying
• Format: Journal Article
• Language: English
• Published: Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.06.2021; Springer Nature B.V
• Subjects: Algorithms; Complex Systems; Control; Iterative methods; Markov analysis; Markov chains; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Statistics; Systems Theory; MCMC; Big data; nonuniform subsampling; metropolis-hasting algorithm
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-020-9335-1

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.