# Extended Stochastic Gradient MCMC for Large-Scale Bayesian Variable Selection

arXiv: https://arxiv.org/abs/2002.02919 · HTML: https://mlsanity.com/paper/2002.02919/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 6 of 6)

- [Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selection](https://mlsanity.com/paper/2207.11208/) (2022)
- [Causal-StoNet: Causal Inference for High-Dimensional Complex Data](https://mlsanity.com/paper/2403.18994/) (2024)
- [Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference](https://mlsanity.com/paper/2505.19136/) (2025)
- [Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks](https://mlsanity.com/paper/2505.01995/) (2025)
- [Choosing the number of factors in factor analysis with incomplete data via a hierarchical Bayesian information criterion](https://mlsanity.com/paper/2204.09086/) (2022)
- [A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rules](https://mlsanity.com/paper/2306.13641/) (2023)

## Abstract (arXiv)

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient MCMC lgoriathm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional MCMC algorithms. The proposed algorithms have much alleviated the pain of Bayesian methods in big data computing.