{"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/false-discoveries-occur-early-on-the-lasso","title":"False Discoveries Occur Early on the Lasso Path","arxiv_id":"1511.01957","date":"2015-11-05","proceeding":null,"authors":["Weijie Su","Malgorzata Bogdan","Emmanuel Candes"],"abstract":"In regression settings where explanatory variables have very low correlations\nand there are relatively few effects, each of large magnitude, we expect the\nLasso to find the important variables with few errors, if any. This paper shows\nthat in a regime of linear sparsity---meaning that the fraction of variables\nwith a non-vanishing effect tends to a constant, however small---this cannot\nreally be the case, even when the design variables are stochastically\nindependent. We demonstrate that true features and null features are always\ninterspersed on the Lasso path, and that this phenomenon occurs no matter how\nstrong the effect sizes are. We derive a sharp asymptotic trade-off between\nfalse and true positive rates or, equivalently, between measures of type I and\ntype II errors along the Lasso path. This trade-off states that if we ever want\nto achieve a type II error (false negative rate) under a critical value, then\nanywhere on the Lasso path the type I error (false positive rate) will need to\nexceed a given threshold so that we can never have both errors at a low level\nat the same time. Our analysis uses tools from approximate message passing\n(AMP) theory as well as novel elements to deal with a possibly adaptive\nselection of the Lasso regularizing parameter.","url_abs":"http://arxiv.org/abs/1511.01957v4","url_pdf":"http://arxiv.org/pdf/1511.01957v4.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":"false-discoveries-occur-early-on-the-lasso","repo_url":"https://github.com/wjsu/fdrlasso","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"false-discoveries-occur-early-on-the-lasso","repo_url":"https://github.com/Adeikalam/Theoretical-Guidelines-for-High-Dimentional-Data-Analysis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"false-discoveries-occur-early-on-the-lasso","repo_url":"https://github.com/CedricAllainEnsae/fdrlasso","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1511.01957","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}