{"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/nonconvex-regularized-robust-regression-with","title":"Iteratively Reweighted $\\ell_1$-Penalized Robust Regression","arxiv_id":"1907.04027","date":"2019-07-09","proceeding":null,"authors":["Xiaoou Pan","Qiang Sun","Wen-Xin Zhou"],"abstract":"This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moment, we show that iteratively reweighted $\\ell_1$-penalized adaptive Huber regression estimator satisfies exponential deviation bounds and oracle properties, including the oracle convergence rate and variable selection consistency, under a weak beta-min condition. Computationally, we need as many as $O(\\log s + \\log\\log d)$ iterations to reach such an oracle estimator, where $s$ and $d$ denote the sparsity and ambient dimension, respectively. Extension to a general class of robust loss functions is also considered. Numerical studies lend strong support to our methodology and theory.","url_abs":"https://arxiv.org/abs/1907.04027v3","url_pdf":"https://arxiv.org/pdf/1907.04027v3.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":"nonconvex-regularized-robust-regression-with","repo_url":"https://github.com/XiaoouPan/ILAMM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"nonconvex-regularized-robust-regression-with","repo_url":"https://github.com/XiaoouPan/tfHuber","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"variable-selection","task_name":"Variable Selection"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}