{"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/the-trimmed-lasso-sparsity-and-robustness","title":"The Trimmed Lasso: Sparsity and Robustness","arxiv_id":"1708.04527","date":"2017-08-15","proceeding":null,"authors":["Dimitris Bertsimas","Martin S. Copenhaver","Rahul Mazumder"],"abstract":"Nonconvex penalty methods for sparse modeling in linear regression have been\na topic of fervent interest in recent years. Herein, we study a family of\nnonconvex penalty functions that we call the trimmed Lasso and that offers\nexact control over the desired level of sparsity of estimators. We analyze its\nstructural properties and in doing so show the following:\n  1) Drawing parallels between robust statistics and robust optimization, we\nshow that the trimmed-Lasso-regularized least squares problem can be viewed as\na generalized form of total least squares under a specific model of\nuncertainty. In contrast, this same model of uncertainty, viewed instead\nthrough a robust optimization lens, leads to the convex SLOPE (or OWL) penalty.\n  2) Further, in relating the trimmed Lasso to commonly used sparsity-inducing\npenalty functions, we provide a succinct characterization of the connection\nbetween trimmed-Lasso- like approaches and penalty functions that are\ncoordinate-wise separable, showing that the trimmed penalties subsume existing\ncoordinate-wise separable penalties, with strict containment in general.\n  3) Finally, we describe a variety of exact and heuristic algorithms, both\nexisting and new, for trimmed Lasso regularized estimation problems. We include\na comparison between the different approaches and an accompanying\nimplementation of the algorithms.","url_abs":"http://arxiv.org/abs/1708.04527v1","url_pdf":"http://arxiv.org/pdf/1708.04527v1.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":"the-trimmed-lasso-sparsity-and-robustness","repo_url":"https://github.com/copenhaver/trimmedlasso","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"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}