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Stochastic gradient Markov chain Monte Carlo

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>30/03/2021
<mark>Journal</mark>Journal of the American Statistical Association
Issue number533
Number of pages18
Pages (from-to) 433-450
Publication StatusPublished
Early online date4/01/21
<mark>Original language</mark>English


Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that performing exact inference generally requires all of the data to be processed at each iteration of the algorithm. For large data sets, the computational cost of MCMC can be prohibitive, which has led to recent developments in scalable Monte Carlo algorithms that have a significantly lower computational cost than standard MCMC. In this paper, we focus on a particular class of scalable Monte Carlo algorithms, stochastic gradient Markov chain Monte Carlo (SGMCMC) which utilises data subsampling techniques to reduce the per iteration cost of MCMC. We provide an introduction to some popular SGMCMC algorithms and review the supporting theoretical results, as well as comparing the efficiency of SGMCMC algorithms against MCMC on benchmark examples. The supporting R code is available online at https://github.com/chris-nemeth/sgmcmc-review-paper.

Bibliographic note

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association in March 2021, available online: https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1847120