{"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/consistency-of-semi-supervised-learning-1","title":"Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian","arxiv_id":"2401.07463","date":"2024-01-15","proceeding":null,"authors":["Jeff Calder","Nadejda Drenska"],"abstract":"In this paper we give a broad overview of the intersection of partial differential equations (PDEs) and graph-based semi-supervised learning. The overview is focused on a large body of recent work on PDE continuum limits of graph-based learning, which have been used to prove well-posedness of semi-supervised learning algorithms in the large data limit. We highlight some interesting research directions revolving around consistency of graph-based semi-supervised learning, and present some new results on the consistency of $p$-Laplacian semi-supervised learning using the stochastic tug-of-war game interpretation of the $p$-Laplacian. We also present the results of some numerical experiments that illustrate our results and suggest directions for future work.","url_abs":"https://arxiv.org/abs/2401.07463v2","url_pdf":"https://arxiv.org/pdf/2401.07463v2.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":"consistency-of-semi-supervised-learning-1","repo_url":"https://github.com/jwcalder/p-laplace-consistency","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}