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Article: Efficient methods for estimating constrained parameters with applications to regularized (lasso) logistic regression

TitleEfficient methods for estimating constrained parameters with applications to regularized (lasso) logistic regression
Authors
Issue Date2008
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csda
Citation
Computational Statistics And Data Analysis, 2008, v. 52 n. 7, p. 3528-3542 How to Cite?
AbstractFitting logistic regression models is challenging when their parameters are restricted. In this article, we first develop a quadratic lower-bound (QLB) algorithm for optimization with box or linear inequality constraints and derive the fastest QLB algorithm corresponding to the smallest global majorization matrix. The proposed QLB algorithm is particularly suited to problems to which the EM-type algorithms are not applicable (e.g., logistic, multinomial logistic, and Cox's proportional hazards models) while it retains the same EM ascent property and thus assures the monotonic convergence. Secondly, we generalize the QLB algorithm to penalized problems in which the penalty functions may not be totally differentiable. The proposed method thus provides an alternative algorithm for estimation in lasso logistic regression, where the convergence of the existing lasso algorithm is not generally ensured. Finally, by relaxing the ascent requirement, convergence speed can be further accelerated. We introduce a pseudo-Newton method that retains the simplicity of the QLB algorithm and the fast convergence of the Newton method. Theoretical justification and numerical examples show that the pseudo-Newton method is up to 71 (in terms of CPU time) or 107 (in terms of number of iterations) times faster than the fastest QLB algorithm and thus makes bootstrap variance estimation feasible. Simulations and comparisons are performed and three real examples (Down syndrome data, kyphosis data, and colon microarray data) are analyzed to illustrate the proposed methods. © 2007 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/59856
ISSN
2015 Impact Factor: 1.179
2015 SCImago Journal Rankings: 1.283
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTian, GLen_HK
dc.contributor.authorTang, MLen_HK
dc.contributor.authorFang, HBen_HK
dc.contributor.authorTan, Men_HK
dc.date.accessioned2010-05-31T03:58:52Z-
dc.date.available2010-05-31T03:58:52Z-
dc.date.issued2008en_HK
dc.identifier.citationComputational Statistics And Data Analysis, 2008, v. 52 n. 7, p. 3528-3542en_HK
dc.identifier.issn0167-9473en_HK
dc.identifier.urihttp://hdl.handle.net/10722/59856-
dc.description.abstractFitting logistic regression models is challenging when their parameters are restricted. In this article, we first develop a quadratic lower-bound (QLB) algorithm for optimization with box or linear inequality constraints and derive the fastest QLB algorithm corresponding to the smallest global majorization matrix. The proposed QLB algorithm is particularly suited to problems to which the EM-type algorithms are not applicable (e.g., logistic, multinomial logistic, and Cox's proportional hazards models) while it retains the same EM ascent property and thus assures the monotonic convergence. Secondly, we generalize the QLB algorithm to penalized problems in which the penalty functions may not be totally differentiable. The proposed method thus provides an alternative algorithm for estimation in lasso logistic regression, where the convergence of the existing lasso algorithm is not generally ensured. Finally, by relaxing the ascent requirement, convergence speed can be further accelerated. We introduce a pseudo-Newton method that retains the simplicity of the QLB algorithm and the fast convergence of the Newton method. Theoretical justification and numerical examples show that the pseudo-Newton method is up to 71 (in terms of CPU time) or 107 (in terms of number of iterations) times faster than the fastest QLB algorithm and thus makes bootstrap variance estimation feasible. Simulations and comparisons are performed and three real examples (Down syndrome data, kyphosis data, and colon microarray data) are analyzed to illustrate the proposed methods. © 2007 Elsevier Ltd. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csdaen_HK
dc.relation.ispartofComputational Statistics and Data Analysisen_HK
dc.titleEfficient methods for estimating constrained parameters with applications to regularized (lasso) logistic regressionen_HK
dc.typeArticleen_HK
dc.identifier.emailTian, GL: gltian@hku.hken_HK
dc.identifier.authorityTian, GL=rp00789en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.csda.2007.11.007en_HK
dc.identifier.scopuseid_2-s2.0-40249087061en_HK
dc.identifier.hkuros163559en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-40249087061&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume52en_HK
dc.identifier.issue7en_HK
dc.identifier.spage3528en_HK
dc.identifier.epage3542en_HK
dc.identifier.isiWOS:000255145900018-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridTian, GL=25621549400en_HK
dc.identifier.scopusauthoridTang, ML=7401974011en_HK
dc.identifier.scopusauthoridFang, HB=7402543028en_HK
dc.identifier.scopusauthoridTan, M=7401464906en_HK

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