{"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/model-selection-with-lasso-zero-adding-straw","title":"Model selection with lasso-zero: adding straw to the haystack to better find needles","arxiv_id":"1805.05133","date":"2018-05-14","proceeding":null,"authors":["Pascaline Descloux","Sylvain Sardy"],"abstract":"The high-dimensional linear model $y = X \\beta^0 + \\epsilon$ is considered\nand the focus is put on the problem of recovering the support $S^0$ of the\nsparse vector $\\beta^0.$ We introduce Lasso-Zero, a new $\\ell_1$-based\nestimator whose novelty resides in an \"overfit, then threshold\" paradigm and\nthe use of noise dictionaries concatenated to $X$ for overfitting the response.\nTo select the threshold, we employ the quantile universal threshold based on a\npivotal statistic that requires neither knowledge nor preliminary estimation of\nthe noise level. Numerical simulations show that Lasso-Zero performs well in\nterms of support recovery and provides an excellent trade-off between high true\npositive rate and low false discovery rate compared to competitors. Our\nmethodology is supported by theoretical results showing that when no noise\ndictionary is used, Lasso-Zero recovers the signs of $\\beta^0$ under weaker\nconditions on $X$ and $S^0$ than the Lasso and achieves sign consistency for\ncorrelated Gaussian designs. The use of noise dictionary improves the procedure\nfor low signals.","url_abs":"http://arxiv.org/abs/1805.05133v2","url_pdf":"http://arxiv.org/pdf/1805.05133v2.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":"model-selection-with-lasso-zero-adding-straw","repo_url":"https://github.com/pascalinedescloux/lasso-zero","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}