# SwISS: A Scalable Markov chain Monte Carlo Divide-and-Conquer Strategy

arXiv: https://arxiv.org/abs/2208.04080 · HTML: https://mlsanity.com/paper/2208.04080/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 8 Aug 2022.

## Builds on (most cited first, 9 of 9)

- [Stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/1907.06986/) (2019)
- [Scalable Bayes via Barycenter in Wasserstein Space](https://mlsanity.com/paper/1508.05880/) (2015)
- [Asymptotically Exact, Embarrassingly Parallel MCMC](https://mlsanity.com/paper/1311.4780/) (2013)
- [Control Variates for Stochastic Gradient MCMC](https://mlsanity.com/paper/1706.05439/) (2017)
- [Merging MCMC Subposteriors through Gaussian-Process Approximations](https://mlsanity.com/paper/1605.08576/) (2016)
- [Adaptive, delayed-acceptance MCMC for targets with expensive likelihoods](https://mlsanity.com/paper/1509.00172/) (2015)
- [Speeding Up MCMC by Delayed Acceptance and Data Subsampling](https://mlsanity.com/paper/1507.06110/) (2015)
- [Likelihood Inflating Sampling Algorithm](https://mlsanity.com/paper/1605.02113/) (2016)
- [sgmcmc: An R Package for Stochastic Gradient Markov Chain Monte Carlo](https://mlsanity.com/paper/1710.00578/) (2017)

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

- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problems](https://mlsanity.com/paper/2503.16222/) (2025)
- [Bayes Hilbert Spaces for Posterior Approximation](https://mlsanity.com/paper/2304.09053/) (2023)
- [Tempered Guided Diffusion](https://mlsanity.com/paper/2605.03712/) (2026)
- [Diffusion Generative Modelling for Divide-and-Conquer MCMC](https://mlsanity.com/paper/2406.11664/) (2024)
- [Hypergraph Generation via Structured Stochastic Diffusion](https://mlsanity.com/paper/2605.05024/) (2026)

## Abstract (arXiv)

Divide-and-conquer strategies for Monte Carlo algorithms are an increasingly popular approach to making Bayesian inference scalable to large data sets. In its simplest form, the data are partitioned across multiple computing cores and a separate Markov chain Monte Carlo algorithm on each core targets the associated partial posterior distribution, which we refer to as a sub-posterior, that is the posterior given only the data from the segment of the partition associated with that core. Divide-and-conquer techniques reduce computational, memory and disk bottle-necks, but make it difficult to recombine the sub-posterior samples. We propose SwISS: Sub-posteriors with Inflation, Scaling and Shifting; a new approach for recombining the sub-posterior samples which is simple to apply, scales to high-dimensional parameter spaces and accurately approximates the original posterior distribution through affine transformations of the sub-posterior samples. We prove that our transformation is asymptotically optimal across a natural set of affine transformations and illustrate the efficacy of SwISS against competing algorithms on synthetic and real-world data sets.