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arXiv · 1404.4178

Speeding Up MCMC by Efficient Data Subsampling

Matias Quiroz·Robert Kohn·Mattias Villani·Minh-Ngoc Tran
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Abstract

We propose Subsampling MCMC, a Markov Chain Monte Carlo (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.

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Matias Quiroz, Robert Kohn, Mattias Villani, Minh-Ngoc Tran. 2014-04-16. Speeding Up MCMC by Efficient Data Subsampling. https://doi.org/10.1080/01621459.2018.1448827

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