# Mini-batch Metropolis-Hastings MCMC with Reversible SGLD Proposal

arXiv: https://arxiv.org/abs/1908.02910 · HTML: https://mlsanity.com/paper/1908.02910/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2019.

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

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- [Density Regression and Uncertainty Quantification with Bayesian Deep Noise Neural Networks](https://mlsanity.com/paper/2206.05643/) (2022)
- [Centroid Approximation for Bootstrap: Improving Particle Quality at Inference](https://mlsanity.com/paper/2110.08720/) (2021)
- [The surrogate Gibbs-posterior of a corrected stochastic MALA: Towards uncertainty quantification for neural networks](https://mlsanity.com/paper/2310.09335/) (2023)

## Abstract (arXiv)

Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary distribution. We prove that the algorithm preserves the modes of the original target distribution and derive an error bound on the approximation with mild assumptions on the likelihood. To further extend the utility of the algorithm to high dimensional settings, we construct a proposal with forward and reverse moves using stochastic gradient and show that the construction leads to reasonable acceptance probabilities. We demonstrate the performance of our algorithm in both low dimensional models and high dimensional neural network applications. Particularly in the latter case, compared to popular optimization methods, our method is more robust to the choice of learning rate and improves testing accuracy.