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Stochastic Gradient Markov Chain Monte Carlo

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  • Christopher Nemeth
  • Paul Fearnhead

Abstract

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.

Suggested Citation

  • Christopher Nemeth & Paul Fearnhead, 2021. "Stochastic Gradient Markov Chain Monte Carlo," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 433-450, January.
  • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:533:p:433-450
    DOI: 10.1080/01621459.2020.1847120
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    Cited by:

    1. Ruben Loaiza-Maya & Didier Nibbering & Dan Zhu, 2023. "Hybrid unadjusted Langevin methods for high-dimensional latent variable models," Papers 2306.14445, arXiv.org.
    2. Loaiza-Maya, Rubén & Nibbering, Didier & Zhu, Dan, 2024. "Hybrid unadjusted Langevin methods for high-dimensional latent variable models," Journal of Econometrics, Elsevier, vol. 241(2).
    3. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org.
    4. Xiao-Kai Meng & Yan-Bing Jia & Zhi-Heng Liu & Zhi-Qiang Yu & Pei-Jie Han & Zhu-Mao Lu & Tao Jin, 2022. "High-Voltage Cable Condition Assessment Method Based on Multi-Source Data Analysis," Energies, MDPI, vol. 15(4), pages 1-16, February.

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