{"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/scaling-gaussian-process-regression-with","title":"Scaling Gaussian Process Regression with Derivatives","arxiv_id":"1810.12283","date":"2018-10-29","proceeding":"NeurIPS 2018 12","authors":["David Eriksson","Kun Dong","Eric Hans Lee","David Bindel","Andrew Gordon Wilson"],"abstract":"Gaussian processes (GPs) with derivatives are useful in many applications,\nincluding Bayesian optimization, implicit surface reconstruction, and terrain\nreconstruction. Fitting a GP to function values and derivatives at $n$ points\nin $d$ dimensions requires linear solves and log determinants with an ${n(d+1)\n\\times n(d+1)}$ positive definite matrix -- leading to prohibitive\n$\\mathcal{O}(n^3d^3)$ computations for standard direct methods. We propose\niterative solvers using fast $\\mathcal{O}(nd)$ matrix-vector multiplications\n(MVMs), together with pivoted Cholesky preconditioning that cuts the iterations\nto convergence by several orders of magnitude, allowing for fast kernel\nlearning and prediction. Our approaches, together with dimensionality\nreduction, enables Bayesian optimization with derivatives to scale to\nhigh-dimensional problems and large evaluation budgets.","url_abs":"http://arxiv.org/abs/1810.12283v1","url_pdf":"http://arxiv.org/pdf/1810.12283v1.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":"scaling-gaussian-process-regression-with","repo_url":"https://github.com/ericlee0803/GP_Derivatives","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"surface-reconstruction","task_name":"Surface Reconstruction"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1810.12283","atlas_url":"https://app.syntology.ai/?focus=1810.12283","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}