{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-zig-zag-process-and-super-efficient","title":"The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data","arxiv_id":"1607.03188","date":"2016-07-11","proceeding":null,"authors":["Joris Bierkens","Paul Fearnhead","Gareth Roberts"],"abstract":"Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multi-dimensional version of the Zig-Zag process of (Bierkens, Roberts, 2017), a continuous time piecewise deterministic Markov process. While traditional MCMC methods are reversible by construction (a property which is known to inhibit rapid convergence) the Zig-Zag process offers a flexible non-reversible alternative which we observe to often have favourable convergence properties. We show how the Zig-Zag process can be simulated without discretisation error, and give conditions for the process to be ergodic. Most importantly, we introduce a sub-sampling version of the Zig-Zag process that is an example of an {\\em exact approximate scheme}, i.e. the resulting approximate process still has the posterior as its stationary distribution. Furthermore, if we use a control-variate idea to reduce the variance of our unbiased estimator, then the Zig-Zag process can be super-efficient: after an initial pre-processing step, essentially independent samples from the posterior distribution are obtained at a computational cost which does not depend on the size of the data.","url_abs":"http://arxiv.org/abs/1607.03188v2","url_pdf":"http://arxiv.org/pdf/1607.03188v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-zig-zag-process-and-super-efficient","repo_url":"https://github.com/jbierkens/zigzag-experiments","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"the-zig-zag-process-and-super-efficient","repo_url":"https://github.com/UnofficialJuliaMirror/PDSampler.jl-f9d848e4-75a0-5321-a43a-fbaa97166838","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"the-zig-zag-process-and-super-efficient","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/PDSampler.jl-f9d848e4-75a0-5321-a43a-fbaa97166838","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"the-zig-zag-process-and-super-efficient","repo_url":"https://github.com/alan-turing-institute/PDSampler.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"the-zig-zag-process-and-super-efficient","repo_url":"https://github.com/bernarditaried/ZigZag-Sampling-Tutorial","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"the-zig-zag-process-and-super-efficient","repo_url":"https://github.com/jbierkens/RZigZag","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1607.03188","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}