{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,7]],"date-time":"2026-11-07T13:38:50Z","timestamp":1794058730012,"version":"4.8.0"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T00:00:00Z","timestamp":1678665600000},"content-version":"vor","delay-in-days":4148,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-9971405"],"award-info":[{"award-number":["DMS-9971405"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-0906801"],"award-info":[{"award-number":["DMS-0906801"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["N01-HV-28183"],"award-info":[{"award-number":["N01-HV-28183"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,3,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have proposed \u2018SAFE\u2019 rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into the optimization. We propose strong rules that are very simple and yet screen out far more predictors than the SAFE rules. This great practical improvement comes at a price: the strong rules are not foolproof and can mistakenly discard active predictors, i.e. predictors that have non-zero coefficients in the solution. We therefore combine them with simple checks of the Karush\u2013Kuhn\u2013Tucker conditions to ensure that the exact solution to the convex problem is delivered. Of course, any (approximate) screening method can be combined with the Karush\u2013Kuhn\u2013Tucker conditions to ensure the exact solution; the strength of the strong rules lies in the fact that, in practice, they discard a very large number of the inactive predictors and almost never commit mistakes. We also derive conditions under which they are foolproof. Strong rules provide substantial savings in computational time for a variety of statistical optimization problems.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2011.01004.x","type":"journal-article","created":{"date-parts":[[2011,11,3]],"date-time":"2011-11-03T13:55:06Z","timestamp":1320328506000},"page":"245-266","source":"Crossref","is-referenced-by-count":478,"title":["Strong Rules for Discarding Predictors in Lasso-Type Problems"],"prefix":"10.1093","volume":"74","author":[{"given":"Robert","family":"Tibshirani","sequence":"first","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacob","family":"Bien","sequence":"additional","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jerome","family":"Friedman","sequence":"additional","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Trevor","family":"Hastie","sequence":"additional","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Noah","family":"Simon","sequence":"additional","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan","family":"Taylor","sequence":"additional","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ryan J.","family":"Tibshirani","sequence":"additional","affiliation":[{"name":"Stanford University , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2011,11,3]]},"reference":[{"key":"2023031400060065700_","doi-asserted-by":"crossref","first-page":"2145","DOI":"10.1214\/08-AOS653","article-title":"Near-ideal model selection by l1 minimization","volume":"37","author":"Candes","year":"2009","journal-title":"Ann. 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