{"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/control-variates-for-stochastic-gradient-mcmc","title":"Control Variates for Stochastic Gradient MCMC","arxiv_id":"1706.05439","date":"2017-06-16","proceeding":null,"authors":["Jack Baker","Paul Fearnhead","Emily B. Fox","Christopher Nemeth"],"abstract":"It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly\nwith dataset size. A popular class of methods for solving this issue is\nstochastic gradient MCMC. These methods use a noisy estimate of the gradient of\nthe log posterior, which reduces the per iteration computational cost of the\nalgorithm. Despite this, there are a number of results suggesting that\nstochastic gradient Langevin dynamics (SGLD), probably the most popular of\nthese methods, still has computational cost proportional to the dataset size.\nWe suggest an alternative log posterior gradient estimate for stochastic\ngradient MCMC, which uses control variates to reduce the variance. We analyse\nSGLD using this gradient estimate, and show that, under log-concavity\nassumptions on the target distribution, the computational cost required for a\ngiven level of accuracy is independent of the dataset size. Next we show that a\ndifferent control variate technique, known as zero variance control variates\ncan be applied to SGMCMC algorithms for free. This post-processing step\nimproves the inference of the algorithm by reducing the variance of the MCMC\noutput. Zero variance control variates rely on the gradient of the log\nposterior; we explore how the variance reduction is affected by replacing this\nwith the noisy gradient estimate calculated by SGMCMC.","url_abs":"http://arxiv.org/abs/1706.05439v2","url_pdf":"http://arxiv.org/pdf/1706.05439v2.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":"abstracts"},"code_links":[{"paper_slug":"control-variates-for-stochastic-gradient-mcmc","repo_url":"https://github.com/msabvid/MLMC-MIMC-SGD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.05439","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}