{"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/non-stationary-gaussian-process-regression","title":"Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo","arxiv_id":"1508.04319","date":"2015-08-18","proceeding":null,"authors":["Markus Heinonen","Henrik Mannerström","Juho Rousu","Samuel Kaski","Harri Lähdesmäki"],"abstract":"We present a novel approach for fully non-stationary Gaussian process\nregression (GPR), where all three key parameters -- noise variance, signal\nvariance and lengthscale -- can be simultaneously input-dependent. We develop\ngradient-based inference methods to learn the unknown function and the\nnon-stationary model parameters, without requiring any model approximations. We\npropose to infer full parameter posterior with Hamiltonian Monte Carlo (HMC),\nwhich conveniently extends the analytical gradient-based GPR learning by\nguiding the sampling with model gradients. We also learn the MAP solution from\nthe posterior by gradient ascent. In experiments on several synthetic datasets\nand in modelling of temporal gene expression, the nonstationary GPR is shown to\nbe necessary for modeling realistic input-dependent dynamics, while it performs\ncomparably to conventional stationary or previous non-stationary GPR models\notherwise.","url_abs":"http://arxiv.org/abs/1508.04319v1","url_pdf":"http://arxiv.org/pdf/1508.04319v1.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":"non-stationary-gaussian-process-regression","repo_url":"https://github.com/markusheinonen/adaptivegp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"gpr","task_name":"GPR"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1508.04319","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}