{"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/sparsestep-approximating-the-counting-norm","title":"SparseStep: Approximating the Counting Norm for Sparse Regularization","arxiv_id":"1701.06967","date":"2017-01-24","proceeding":null,"authors":["Gerrit J. J. van den Burg","Patrick J. F. Groenen","Andreas Alfons"],"abstract":"The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and iteratively strengthening this approximation to arrive at a sparse solution. Theoretical analysis of the penalty function shows that the estimator yields unbiased estimates of the parameter vector. An iterative majorization algorithm is derived which has a straightforward implementation reminiscent of ridge regression. In addition, the SparseStep algorithm is compared with similar methods through a rigorous simulation study which shows it often outperforms existing methods in both model fit and prediction accuracy.","url_abs":"https://arxiv.org/abs/1701.06967v1","url_pdf":"https://arxiv.org/pdf/1701.06967v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"sparsestep-approximating-the-counting-norm","repo_url":"https://github.com/GjjvdBurg/SparseStep","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}