mlsanityData to 7 Oct 2026

Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget

arXiv 1304.5299 ↗First posted 19 Apr 2013cs.LG stat.MLcited by 24

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Abstract (arXiv)

Can we make Bayesian posterior MCMC sampling more efficient when faced with very large datasets? We argue that computing the likelihood for N datapoints in the Metropolis-Hastings (MH) test to reach a single binary decision is computationally inefficient. We introduce an approximate MH rule based on a sequential hypothesis test that allows us to accept or reject samples with high confidence using only a fraction of the data required for the exact MH rule. While this method introduces an asymptotic bias, we show that this bias can be controlled and is more than offset by a decrease in variance due to our ability to draw more samples per unit of time.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Apr 2013.

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Citing papers per year: 2021: 5; 2022: 4; 2023: 6; 2024: 4; 2025: 3; 2026: 2.

24 papers.

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  1. 2022Bayesian inference via sparse Hamiltonian flowscited by 12
  2. 2022Fast Bayesian Coresets via Subsampling and Quasi-Newton Refinementcited by 9
  3. 2022Non-reversible Parallel Tempering for Deep Posterior Approximationcited by 7
  4. 2023Variational Inference for Bayesian Neural Networks under Model and Parameter Uncertaintycited by 5
  5. 2023Coreset Markov Chain Monte Carlocited by 5
  6. 2023Machine Learning and the Future of Bayesian Computationcited by 4
  7. 2023Structure Learning with Adaptive Random Neighborhood Informed MCMCcited by 4
  8. 2024Nystr"om Kernel Stein Discrepancycited by 4
  9. 2021Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMCcited by 3
  10. 2021Interpolating between sampling and variational inference with infinite stochastic mixturescited by 3
  11. 2026Probabilistic Inference and Learning with Stein's Methodcited by 3
  12. 2021Asynchronous and Distributed Data Augmentation for Massive Data Settingscited by 2
12 more
  1. 2023AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimizationcited by 2
  2. 2024ISR: Invertible Symbolic Regressioncited by 2
  3. 2024Robust Approximate Sampling via Stochastic Gradient Barker Dynamicscited by 2
  4. 2024General bounds on the quality of Bayesian coresetscited by 2
  5. 2025Bayesian Data Sketching for Varying Coefficient Regression Modelscited by 2
  6. 2021Quantifying the mini-batching error in Bayesian inference for Adaptive Langevin dynamicscited by 1
  7. 2022Data Subsampling for Bayesian Neural Networkscited by 1
  8. 2025Bayesian Computation in Deep Learningcited by 1
  9. 2026Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisationcited by 1
  10. 2021How To Train Your Program: a Probabilistic Programming Pattern for Bayesian Learning From Datacited by 0
  11. 2023Minibatch training of neural network ensembles via trajectory samplingcited by 0
  12. 2025Efficient MCMC Sampling with Expensive-to-Compute and Irregular Likelihoodscited by 0