# Stochastic gradient Markov chain Monte Carlo

## TL;DR

This paper reviews stochastic gradient MCMC algorithms, highlighting their scalability for large datasets, discussing theoretical foundations, and comparing their efficiency to traditional MCMC methods through benchmark examples.

## Contribution

It provides an overview of popular SGMCMC algorithms, reviews theoretical results, and compares their performance with standard MCMC methods.

## Key findings

- SGMCMC algorithms are more scalable for large datasets.
- Theoretical results support the validity of SGMCMC methods.
- Benchmark comparisons show efficiency gains over traditional MCMC.

## 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 in general performing exact inference 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.