{"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/high-dimensional-classification-through-ell_0","title":"High Dimensional Classification through $\\ell_0$-Penalized Empirical Risk Minimization","arxiv_id":"1811.09540","date":"2018-11-23","proceeding":null,"authors":["Le-Yu Chen","Sokbae Lee"],"abstract":"We consider a high dimensional binary classification problem and construct a\nclassification procedure by minimizing the empirical misclassification risk\nwith a penalty on the number of selected features. We derive non-asymptotic\nprobability bounds on the estimated sparsity as well as on the excess\nmisclassification risk. In particular, we show that our method yields a sparse\nsolution whose l0-norm can be arbitrarily close to true sparsity with high\nprobability and obtain the rates of convergence for the excess\nmisclassification risk. The proposed procedure is implemented via the method of\nmixed integer linear programming. Its numerical performance is illustrated in\nMonte Carlo experiments.","url_abs":"http://arxiv.org/abs/1811.09540v1","url_pdf":"http://arxiv.org/pdf/1811.09540v1.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":"high-dimensional-classification-through-ell_0","repo_url":"https://github.com/LeyuChen/L0-ERM","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}