# Stochastic gradient Markov chain Monte Carlo

arXiv: https://arxiv.org/abs/1907.06986 · HTML: https://mlsanity.com/paper/1907.06986/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2019.

## Built on by (most cited first, 30 of 56)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning](https://mlsanity.com/paper/2102.07868/) (2021)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Fairness through Aleatoric Uncertainty](https://mlsanity.com/paper/2304.03646/) (2023)
- [Scalable Bayesian Learning with posteriors](https://mlsanity.com/paper/2406.00104/) (2024)
- [Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics](https://mlsanity.com/paper/2410.19780/) (2024)
- [Adaptive Defense against Harmful Fine-Tuning for Large Language Models via Bayesian Data Scheduler](https://mlsanity.com/paper/2510.27172/) (2025)
- [Efficient and Generalizable Tuning Strategies for Stochastic Gradient MCMC](https://mlsanity.com/paper/2105.13059/) (2021)
- [Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls](https://mlsanity.com/paper/2212.07959/) (2022)
- [Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network](https://mlsanity.com/paper/2210.04349/) (2022)
- [Sparse Deep Learning: A New Framework Immune to Local Traps and Miscalibration](https://mlsanity.com/paper/2110.00653/) (2021)
- [Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopes](https://mlsanity.com/paper/2207.04387/) (2022)
- [SwISS: A Scalable Markov chain Monte Carlo Divide-and-Conquer Strategy](https://mlsanity.com/paper/2208.04080/) (2022)
- [Bounding Wasserstein distance with couplings](https://mlsanity.com/paper/2112.03152/) (2021)
- [Coreset Markov Chain Monte Carlo](https://mlsanity.com/paper/2310.17063/) (2023)
- [Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics](https://mlsanity.com/paper/2207.12395/) (2022)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theory](https://mlsanity.com/paper/2407.06935/) (2024)
- [Benchmarking Bayesian neural networks and evaluation metrics for regression tasks](https://mlsanity.com/paper/2206.06779/) (2022)
- [TEDL: A Two-stage Evidential Deep Learning Method for Classification Uncertainty Quantification](https://mlsanity.com/paper/2209.05522/) (2022)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Centered plug-in estimation of Wasserstein distances](https://mlsanity.com/paper/2203.11627/) (2022)
- [Robust Approximate Sampling via Stochastic Gradient Barker Dynamics](https://mlsanity.com/paper/2405.08999/) (2024)
- [General bounds on the quality of Bayesian coresets](https://mlsanity.com/paper/2405.11780/) (2024)
- [Functional Stochastic Gradient MCMC for Bayesian Neural Networks](https://mlsanity.com/paper/2409.16632/) (2024)

## Abstract (arXiv)

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.