{"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/auxiliary-gradient-based-sampling-algorithms","title":"Auxiliary gradient-based sampling algorithms","arxiv_id":"1610.09641","date":"2016-10-30","proceeding":null,"authors":["Michalis K. Titsias","Omiros Papaspiliopoulos"],"abstract":"We introduce a new family of MCMC samplers that combine auxiliary variables,\nGibbs sampling and Taylor expansions of the target density. Our approach\npermits the marginalisation over the auxiliary variables yielding marginal\nsamplers, or the augmentation of the auxiliary variables, yielding auxiliary\nsamplers. The well-known Metropolis-adjusted Langevin algorithm (MALA) and\npreconditioned Crank-Nicolson Langevin (pCNL) algorithm are shown to be special\ncases. We prove that marginal samplers are superior in terms of asymptotic\nvariance and demonstrate cases where they are slower in computing time compared\nto auxiliary samplers. In the context of latent Gaussian models we propose new\nauxiliary and marginal samplers whose implementation requires a single tuning\nparameter, which can be found automatically during the transient phase.\nExtensive experimentation shows that the increase in efficiency (measured as\neffective sample size per unit of computing time) relative to (optimised\nimplementations of) pCNL, elliptical slice sampling and MALA ranges from\n10-fold in binary classification problems to 25-fold in log-Gaussian Cox\nprocesses to 100-fold in Gaussian process regression, and it is on par with\nRiemann manifold Hamiltonian Monte Carlo in an example where the latter has the\nsame complexity as the aforementioned algorithms. We explain this remarkable\nimprovement in terms of the way alternative samplers try to approximate the\neigenvalues of the target. We introduce a novel MCMC sampling scheme for\nhyperparameter learning that builds upon the auxiliary samplers. The MATLAB\ncode for reproducing the experiments in the article is publicly available and a\nSupplement to this article contains additional experiments and implementation\ndetails.","url_abs":"http://arxiv.org/abs/1610.09641v3","url_pdf":"http://arxiv.org/pdf/1610.09641v3.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":"auxiliary-gradient-based-sampling-algorithms","repo_url":"https://github.com/mtitsias/aGrad","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1610.09641","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}