{"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/efficient-smoothed-concomitant-lasso","title":"Efficient Smoothed Concomitant Lasso Estimation for High Dimensional Regression","arxiv_id":"1606.02702","date":"2016-06-08","proceeding":null,"authors":["Eugene Ndiaye","Olivier Fercoq","Alexandre Gramfort","Vincent Leclère","Joseph Salmon"],"abstract":"In high dimensional settings, sparse structures are crucial for efficiency,\nboth in term of memory, computation and performance. It is customary to\nconsider $\\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity\nenforcing methods, the Lasso being a canonical example, are popular candidates\nto address high dimension. For efficiency, they rely on tuning a parameter\ntrading data fitting versus sparsity. For the Lasso theory to hold this tuning\nparameter should be proportional to the noise level, yet the latter is often\nunknown in practice. A possible remedy is to jointly optimize over the\nregression parameter as well as over the noise level. This has been considered\nunder several names in the literature: Scaled-Lasso, Square-root Lasso,\nConcomitant Lasso estimation for instance, and could be of interest for\nconfidence sets or uncertainty quantification. In this work, after illustrating\nnumerical difficulties for the Smoothed Concomitant Lasso formulation, we\npropose a modification we coined Smoothed Concomitant Lasso, aimed at\nincreasing numerical stability. We propose an efficient and accurate solver\nleading to a computational cost no more expansive than the one for the Lasso.\nWe leverage on standard ingredients behind the success of fast Lasso solvers: a\ncoordinate descent algorithm, combined with safe screening rules to achieve\nspeed efficiency, by eliminating early irrelevant features.","url_abs":"http://arxiv.org/abs/1606.02702v1","url_pdf":"http://arxiv.org/pdf/1606.02702v1.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":"efficient-smoothed-concomitant-lasso","repo_url":"https://github.com/EugeneNdiaye/smoothed_concomitant_lasso","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"efficient-smoothed-concomitant-lasso","repo_url":"https://github.com/samiatto/colide","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"},{"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}