# Speeding Up MCMC by Efficient Data Subsampling

arXiv: https://arxiv.org/abs/1404.4178 · HTML: https://mlsanity.com/paper/1404.4178/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2014.

## Built on by (most cited first, 18 of 18)

- [Surrogate Likelihoods for Variational Annealed Importance Sampling](https://mlsanity.com/paper/2112.12194/) (2021)
- [Bayesian inference via sparse Hamiltonian flows](https://mlsanity.com/paper/2203.05723/) (2022)
- [Fast Bayesian Coresets via Subsampling and Quasi-Newton Refinement](https://mlsanity.com/paper/2203.09675/) (2022)
- [A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC](https://mlsanity.com/paper/2108.00490/) (2021)
- [Non-reversible Parallel Tempering for Deep Posterior Approximation](https://mlsanity.com/paper/2211.10837/) (2022)
- [Variational Inference for Bayesian Neural Networks under Model and Parameter Uncertainty](https://mlsanity.com/paper/2305.00934/) (2023)
- [Coreset Markov Chain Monte Carlo](https://mlsanity.com/paper/2310.17063/) (2023)
- [An optimal transport approach for selecting a representative subsample with application in efficient kernel density estimation](https://mlsanity.com/paper/2206.01182/) (2022)
- [Particle Mean Field Variational Bayes](https://mlsanity.com/paper/2303.13930/) (2023)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Optimality in Noisy Importance Sampling](https://mlsanity.com/paper/2201.02432/) (2022)
- [Function Space Bayesian Pseudocoreset for Bayesian Neural Networks](https://mlsanity.com/paper/2310.17852/) (2023)
- [General bounds on the quality of Bayesian coresets](https://mlsanity.com/paper/2405.11780/) (2024)
- [On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach](https://mlsanity.com/paper/2103.03321/) (2021)
- [Quantifying the mini-batching error in Bayesian inference for Adaptive Langevin dynamics](https://mlsanity.com/paper/2105.10347/) (2021)
- [Bayesian Computation in Deep Learning](https://mlsanity.com/paper/2502.18300/) (2025)
- [Efficient MCMC Sampling with Expensive-to-Compute and Irregular Likelihoods](https://mlsanity.com/paper/2505.10448/) (2025)

## Abstract (arXiv)

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to n and m, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small m in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature.