{"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/disentangling-derivatives-uncertainty-and","title":"Disentangling Derivatives, Uncertainty and Error in Gaussian Process Models","arxiv_id":"2012.04947","date":"2020-12-09","proceeding":null,"authors":["Juan Emmanuel Johnson","Valero Laparra","Gustau Camps-Valls"],"abstract":"Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually available. In this paper, we showcase how the derivative of a GP model can be used to provide an analytical error propagation formulation and we analyze the predictive variance and the propagated error terms in a temperature prediction problem from infrared sounding data.","url_abs":"https://arxiv.org/abs/2012.04947v1","url_pdf":"https://arxiv.org/pdf/2012.04947v1.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":"disentangling-derivatives-uncertainty-and","repo_url":"https://github.com/jejjohnson/uncertain_gps","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[{"task_slug":"earth-observation","task_name":"Earth Observation"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"retrieval","task_name":"Retrieval"}],"methods":[{"method_slug":"gps","method_name":"GPS"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}