Stochastic Gradient Markov Chain Monte Carlo

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...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 116; no. 533; pp. 433 - 450
Main Authors: Nemeth, Christopher, Fearnhead, Paul
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 02.01.2021
Taylor & Francis Ltd
Subjects:
Algorithms
Bayesian analysis
Bayesian inference
Bayesian theory
Computational efficiency
Computing costs
Costs
data collection
Inference
Iterative methods
Markov analysis
Markov chain
Markov chain Monte Carlo
Markov chains
Monte Carlo simulation
Railroad transportation
Regression analysis
Scalable Monte Carlo
Statistical inference
Statistical methods
Statistics
Stochastic gradients
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary: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 datasets, 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 article, we focus on a particular class of scalable Monte Carlo algorithms, stochastic gradient Markov chain Monte Carlo (SGMCMC) which utilizes 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 .
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2020.1847120