{"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-parametric-estimation-of-stochastic","title":"Non-parametric Estimation of Stochastic Differential Equations with Sparse Gaussian Processes","arxiv_id":"1704.04375","date":"2017-04-14","proceeding":null,"authors":["Constantino A. García","Abraham Otero","Paulo Félix","Jesús Presedo","David G. Márquez"],"abstract":"The application of Stochastic Differential Equations (SDEs) to the analysis\nof temporal data has attracted increasing attention, due to their ability to\ndescribe complex dynamics with physically interpretable equations. In this\npaper, we introduce a non-parametric method for estimating the drift and\ndiffusion terms of SDEs from a densely observed discrete time series. The use\nof Gaussian processes as priors permits working directly in a function-space\nview and thus the inference takes place directly in this space. To cope with\nthe computational complexity that requires the use of Gaussian processes, a\nsparse Gaussian process approximation is provided. This approximation permits\nthe efficient computation of predictions for the drift and diffusion terms by\nusing a distribution over a small subset of pseudo-samples. The proposed method\nhas been validated using both simulated data and real data from economy and\npaleoclimatology. The application of the method to real data demonstrates its\nability to capture the behaviour of complex systems.","url_abs":"http://arxiv.org/abs/1704.04375v2","url_pdf":"http://arxiv.org/pdf/1704.04375v2.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-parametric-estimation-of-stochastic","repo_url":"https://github.com/citiususc/voila","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1704.04375","atlas_url":"https://app.syntology.ai/?focus=1704.04375","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}