Speeding Up MCMC by Efficient Data Subsampling

• 成果类型: Article
• 署名作者: Quiroz, Matias; Kohn, Robert; Villani, Mattias; Minh-Ngoc Tran
• 署名单位: University of New South Wales Sydney; Linkoping University; University of Sydney
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1448827
• 发表日期: 2019
• 页码: 831-843
• 关键词: monte-carlo; CONVERGENCE

摘要

We propose subsampling Markov chain Monte Carlo (MCMC), an MCMC framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to n and m, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small m in our applications. We demonstrate that subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature. Supplementary materials for this article are available online.