{"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/convex-hull-approximation-of-nearly-optimal","title":"Convex Hull Approximation of Nearly Optimal Lasso Solutions","arxiv_id":"1810.05992","date":"2018-10-14","proceeding":null,"authors":["Satoshi Hara","Takanori Maehara"],"abstract":"In an ordinary feature selection procedure, a set of important features is\nobtained by solving an optimization problem such as the Lasso regression\nproblem, and we expect that the obtained features explain the data well. In\nthis study, instead of the single optimal solution, we consider finding a set\nof diverse yet nearly optimal solutions. To this end, we formulate the problem\nas finding a small number of solutions such that the convex hull of these\nsolutions approximates the set of nearly optimal solutions. The proposed\nalgorithm consists of two steps: First, we randomly sample the extreme points\nof the set of nearly optimal solutions. Then, we select a small number of\npoints using a greedy algorithm. The experimental results indicate that the\nproposed algorithm can approximate the solution set well. The results also\nindicate that we can obtain Lasso solutions with a large diversity.","url_abs":"http://arxiv.org/abs/1810.05992v1","url_pdf":"http://arxiv.org/pdf/1810.05992v1.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":"convex-hull-approximation-of-nearly-optimal","repo_url":"https://github.com/sato9hara/LassoHull","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"diversity","task_name":"Diversity"},{"task_slug":"feature-selection","task_name":"feature selection"}],"methods":[],"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}