{"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/statistical-inference-using-the-morse-smale","title":"Statistical Inference using the Morse-Smale Complex","arxiv_id":"1506.08826","date":"2015-06-29","proceeding":null,"authors":["Yen-Chi Chen","Christopher R. Genovese","Larry Wasserman"],"abstract":"The Morse-Smale complex of a function $f$ decomposes the sample space into\ncells where $f$ is increasing or decreasing. When applied to nonparametric\ndensity estimation and regression, it provides a way to represent, visualize,\nand compare multivariate functions. In this paper, we present some statistical\nresults on estimating Morse-Smale complexes. This allows us to derive new\nresults for two existing methods: mode clustering and Morse-Smale regression.\nWe also develop two new methods based on the Morse-Smale complex: a\nvisualization technique for multivariate functions and a two-sample,\nmultivariate hypothesis test.","url_abs":"http://arxiv.org/abs/1506.08826v2","url_pdf":"http://arxiv.org/pdf/1506.08826v2.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":"statistical-inference-using-the-morse-smale","repo_url":"https://github.com/yenchic/Morse_Smale","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}