File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Accelerating the quadratic lower-bound algorithm via optimizing the shrinkage parameter

TitleAccelerating the quadratic lower-bound algorithm via optimizing the shrinkage parameter
Authors
KeywordsCox Proportional Hazards Model
Em-Type Algorithms
Logistic Regression
Newton-Raphson Algorithm
Optimal Qlb Algorithm
Qlb Algorithm
Issue Date2012
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csda
Citation
Computational Statistics And Data Analysis, 2012, v. 56 n. 2, p. 255-265 How to Cite?
AbstractWhen the Newton-Raphson algorithm or the Fisher scoring algorithm does not work and the EM-type algorithms are not available, the quadratic lower-bound (QLB) algorithm may be a useful optimization tool. However, like all EM-type algorithms, the QLB algorithm may also suffer from slow convergence which can be viewed as the cost for having the ascent property. This paper proposes a novel 'shrinkage parameter' approach to accelerate the QLB algorithm while maintaining its simplicity and stability (i.e., monotonic increase in log-likelihood). The strategy is first to construct a class of quadratic surrogate functions Q r(θ|θ (t)) that induces a class of QLB algorithms indexed by a 'shrinkage parameter' r (r∈R) and then to optimize r over R under some criterion of convergence. For three commonly used criteria (i.e., the smallest eigenvalue, the trace and the determinant), we derive a uniformly optimal shrinkage parameter and find an optimal QLB algorithm. Some theoretical justifications are also presented. Next, we generalize the optimal QLB algorithm to problems with penalizing function and then investigate the associated properties of convergence. The optimal QLB algorithm is applied to fit a logistic regression model and a Cox proportional hazards model. Two real datasets are analyzed to illustrate the proposed methods. © 2011 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/172485
ISSN
2015 Impact Factor: 1.179
2015 SCImago Journal Rankings: 1.283
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTian, GLen_US
dc.contributor.authorTang, MLen_US
dc.contributor.authorLiu, Cen_US
dc.date.accessioned2012-10-30T06:22:45Z-
dc.date.available2012-10-30T06:22:45Z-
dc.date.issued2012en_US
dc.identifier.citationComputational Statistics And Data Analysis, 2012, v. 56 n. 2, p. 255-265en_US
dc.identifier.issn0167-9473en_US
dc.identifier.urihttp://hdl.handle.net/10722/172485-
dc.description.abstractWhen the Newton-Raphson algorithm or the Fisher scoring algorithm does not work and the EM-type algorithms are not available, the quadratic lower-bound (QLB) algorithm may be a useful optimization tool. However, like all EM-type algorithms, the QLB algorithm may also suffer from slow convergence which can be viewed as the cost for having the ascent property. This paper proposes a novel 'shrinkage parameter' approach to accelerate the QLB algorithm while maintaining its simplicity and stability (i.e., monotonic increase in log-likelihood). The strategy is first to construct a class of quadratic surrogate functions Q r(θ|θ (t)) that induces a class of QLB algorithms indexed by a 'shrinkage parameter' r (r∈R) and then to optimize r over R under some criterion of convergence. For three commonly used criteria (i.e., the smallest eigenvalue, the trace and the determinant), we derive a uniformly optimal shrinkage parameter and find an optimal QLB algorithm. Some theoretical justifications are also presented. Next, we generalize the optimal QLB algorithm to problems with penalizing function and then investigate the associated properties of convergence. The optimal QLB algorithm is applied to fit a logistic regression model and a Cox proportional hazards model. Two real datasets are analyzed to illustrate the proposed methods. © 2011 Elsevier Inc. All rights reserved.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csdaen_US
dc.relation.ispartofComputational Statistics and Data Analysisen_US
dc.subjectCox Proportional Hazards Modelen_US
dc.subjectEm-Type Algorithmsen_US
dc.subjectLogistic Regressionen_US
dc.subjectNewton-Raphson Algorithmen_US
dc.subjectOptimal Qlb Algorithmen_US
dc.subjectQlb Algorithmen_US
dc.titleAccelerating the quadratic lower-bound algorithm via optimizing the shrinkage parameteren_US
dc.typeArticleen_US
dc.identifier.emailTian, GL: gltian@hku.hken_US
dc.identifier.authorityTian, GL=rp00789en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.csda.2011.07.013en_US
dc.identifier.scopuseid_2-s2.0-80053280614en_US
dc.identifier.hkuros225930-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80053280614&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume56en_US
dc.identifier.issue2en_US
dc.identifier.spage255en_US
dc.identifier.epage265en_US
dc.identifier.eissn1872-7352-
dc.identifier.isiWOS:000296667300003-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridTian, GL=25621549400en_US
dc.identifier.scopusauthoridTang, ML=7401974011en_US
dc.identifier.scopusauthoridLiu, C=36457166600en_US
dc.identifier.citeulike9664624-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats