Stochastic Gradient Markov Chain Monte Carlo
By Christopher Nemeth, Paul Fearnhead. 2019
177 citations recorded by the source corpus.
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.
Subfields: Numerical Analysis, Statistics and Probability
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In Statistics and Probability
- Muhammad Shahzad
- Cedrique Rovile Njieutcheu Tassi
- Richard Bamler
- Matthias Humt
- Mohsin Ali
- Jakob Gawlikowski
- Peter Jung
- Jianxiang Feng
Citations in the corpus
- GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning (2021, methodology): “Several studies suggested alternative, more efficient, posterior sampling techniques when the classes are imbalanced or when using sub-samples of the data (Nemeth & Fearnhead, 2020; Sachs et al., 2020; Sen et al., 2020).”
- A survey of uncertainty in deep neural networks (2021, methodology): “A more detailed review of the SG-MCMC with a focus on supporting theoretical results can be found in Nemeth and Fearnhead [82].”