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Article: Regularized (bridge) logistic regression for variable selection based on ROC criterion

TitleRegularized (bridge) logistic regression for variable selection based on ROC criterion
Authors
KeywordsAUC
EM algorithm
Lasso regression
Logistic regression
MM algorithm
Issue Date2009
PublisherInternational Press. The Journal's web site is located at http://www.intlpress.com/SII
Citation
Statistics and its Interface, 2009, v. 2 n. 4, p. 493-502 How to Cite?
AbstractIt is well known that the bridge regression (with tuning parameter less or equal to 1) gives asymptotically unbiased estimates of the nonzero regression parameters while shrinking smaller regression parameters to zero to achieve variable selection. Despite advances in the last several decades in developing such regularized regression models, issues regarding the choice of penalty parameter and the computational methods for models fitting with parameter constraints even for bridge linear regression are still not resolved. In this article, we first propose a new criterion based on an area under the receiver operating characteristic (ROC) curve (AUC) to choose the appropriate penalty parameter as opposed to the conventional generalized cross-validation criterion. The model selected by the AUC criterion is shown to have better predictive accuracy while achieving sparsity simultaneously. We then approach the problem from a constrained parameter model and develop a fast minorization-maximization (MM) algorithm for non-linear optimization with positivity constraints for model fitting. This algorithm is further applied to bridge regression where the regression coefficients are constrained with l(p)-norm with the level of p selected by data for binary responses. Examples of prognostic factors and gene selection are presented to illustrate the proposed method.
Persistent Identifierhttp://hdl.handle.net/10722/143098
ISSN
2015 Impact Factor: 1.546
2015 SCImago Journal Rankings: 0.481

 

DC FieldValueLanguage
dc.contributor.authorTian, GL-
dc.contributor.authorFang, HB-
dc.contributor.authorLiu, Z-
dc.contributor.authorTan, MT-
dc.date.accessioned2011-10-28T03:43:58Z-
dc.date.available2011-10-28T03:43:58Z-
dc.date.issued2009-
dc.identifier.citationStatistics and its Interface, 2009, v. 2 n. 4, p. 493-502-
dc.identifier.issn1938-7989-
dc.identifier.urihttp://hdl.handle.net/10722/143098-
dc.description.abstractIt is well known that the bridge regression (with tuning parameter less or equal to 1) gives asymptotically unbiased estimates of the nonzero regression parameters while shrinking smaller regression parameters to zero to achieve variable selection. Despite advances in the last several decades in developing such regularized regression models, issues regarding the choice of penalty parameter and the computational methods for models fitting with parameter constraints even for bridge linear regression are still not resolved. In this article, we first propose a new criterion based on an area under the receiver operating characteristic (ROC) curve (AUC) to choose the appropriate penalty parameter as opposed to the conventional generalized cross-validation criterion. The model selected by the AUC criterion is shown to have better predictive accuracy while achieving sparsity simultaneously. We then approach the problem from a constrained parameter model and develop a fast minorization-maximization (MM) algorithm for non-linear optimization with positivity constraints for model fitting. This algorithm is further applied to bridge regression where the regression coefficients are constrained with l(p)-norm with the level of p selected by data for binary responses. Examples of prognostic factors and gene selection are presented to illustrate the proposed method.-
dc.languageeng-
dc.publisherInternational Press. The Journal's web site is located at http://www.intlpress.com/SII-
dc.relation.ispartofStatistics and its Interface-
dc.rightsStatistics and its Interface. Copyright © International Press.-
dc.subjectAUC-
dc.subjectEM algorithm-
dc.subjectLasso regression-
dc.subjectLogistic regression-
dc.subjectMM algorithm-
dc.titleRegularized (bridge) logistic regression for variable selection based on ROC criterionen_US
dc.typeArticleen_US
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1938-7989&volume=2&issue=4&spage=493&epage=502&date=2009&atitle=Regularized+(bridge)+logistic+regression+for+variable+selection+based+on+ROC+criterion-
dc.identifier.emailTian, GL: gltian@hku.hk-
dc.identifier.hkuros170617-
dc.identifier.volume2-
dc.identifier.issue4-
dc.identifier.spage493-
dc.identifier.epage502-

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