{"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/bolasso-model-consistent-lasso-estimation","title":"Bolasso: model consistent Lasso estimation through the bootstrap","arxiv_id":"0804.1302","date":"2008-04-08","proceeding":null,"authors":["Francis Bach"],"abstract":"We consider the least-square linear regression problem with regularization by\nthe l1-norm, a problem usually referred to as the Lasso. In this paper, we\npresent a detailed asymptotic analysis of model consistency of the Lasso. For\nvarious decays of the regularization parameter, we compute asymptotic\nequivalents of the probability of correct model selection (i.e., variable\nselection). For a specific rate decay, we show that the Lasso selects all the\nvariables that should enter the model with probability tending to one\nexponentially fast, while it selects all other variables with strictly positive\nprobability. We show that this property implies that if we run the Lasso for\nseveral bootstrapped replications of a given sample, then intersecting the\nsupports of the Lasso bootstrap estimates leads to consistent model selection.\nThis novel variable selection algorithm, referred to as the Bolasso, is\ncompared favorably to other linear regression methods on synthetic data and\ndatasets from the UCI machine learning repository.","url_abs":"http://arxiv.org/abs/0804.1302v1","url_pdf":"http://arxiv.org/pdf/0804.1302v1.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":"bolasso-model-consistent-lasso-estimation","repo_url":"https://github.com/dmolitor/bolasso","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"bolasso-model-consistent-lasso-estimation","repo_url":"https://github.com/jameshorine/fastFeatures","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"variable-selection","task_name":"Variable Selection"},{"task_slug":"model","task_name":"model"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}