Speeding Up MCMC by Efficient Data Subsampling

Matias Quiroz, Robert Kohn, Mattias Villani and Minh-Ngoc Tran

Journal of the American Statistical Association, 2019, vol. 114, issue 526, 831-843

Abstract: 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.

Date: 2019
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Citations: View citations in EconPapers (14)

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Related works:
Working Paper: Speeding up MCMC by Efficient Data Subsampling (2016)
Working Paper: SPEEDING UP MCMC BY EFFICIENT DATA SUBSAMPLING (2015)
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DOI: 10.1080/01621459.2018.1448827

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