{"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/combinatorial-optimization-of-the-coefficient","title":"Combinatorial optimization of the coefficient of determination","arxiv_id":"2410.09316","date":"2024-10-12","proceeding":null,"authors":["Marc Harary"],"abstract":"Robust correlation analysis is among the most critical challenges in statistics. Herein, we develop an efficient algorithm for selecting the $k$- subset of $n$ points in the plane with the highest coefficient of determination $\\left( R^2 \\right)$. Drawing from combinatorial geometry, we propose a method called the \\textit{quadratic sweep} that consists of two steps: (i) projectively lifting the data points into $\\mathbb R^5$ and then (ii) iterating over each linearly separable $k$-subset. Its basis is that the optimal set of outliers is separable from its complement in $\\mathbb R^2$ by a conic section, which, in $\\mathbb R^5$, can be found by a topological sweep in $\\Theta \\left( n^5 \\log n \\right)$ time. Although key proofs of quadratic separability remain underway, we develop strong mathematical intuitions for our conjectures, then experimentally demonstrate our method's optimality over several million trials up to $n=30$ without error. Implementations in Julia and fully seeded, reproducible experiments are available at https://github.com/marc-harary/QuadraticSweep.","url_abs":"https://arxiv.org/abs/2410.09316v1","url_pdf":"https://arxiv.org/pdf/2410.09316v1.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":"combinatorial-optimization-of-the-coefficient","repo_url":"https://github.com/marc-harary/quadraticsweep","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}