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Article: A fast em algorithm for quadratic optimization subject to Convex constraints

TitleA fast em algorithm for quadratic optimization subject to Convex constraints
Authors
KeywordsBootstrap
Cholesky decomposition
Constrained optimization
Convergence rate
Data augmentation
EM algorithm
Latent variables
Working parameter
Issue Date2007
PublisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/
Citation
Statistica Sinica, 2007, v. 17 n. 3, p. 945-964 How to Cite?
AbstractConvex constraints (CCs) such as box constraints and linear inequality constraints appear frequently in statistical inference and in applications. The problems of quadratic optimization (QO) subject to CCs occur in isotonic regression, shape-restricted non-parametric regression, variable selection (via the lasso algorithm and bridge regression), limited dependent variables models, image reconstruction, and so on. Existing packages for QO are not generally applicable to CCs. Although EM-type algorithms may be applied to such problems (Tian, Ng and Tan (2005)), the convergence rate/speed of these algorithms is painfully slow, especially for high-dimensional data. This paper develops a fast EM algorithm for QO with CCs. We construct a class of data augmentation schemes indexed by a 'working parameter' r (r ε R), and then optimize r over R under several convergence criteria. In addition, we use Cholesky decomposition to reduce both the number of latent variables and the dimension, leading to further acceleration of the EM. Standard errors of the restricted estimators are calculated using a non-parametric bootstrapping procedure. Simulation and comparison are performed and a complex multinomial dataset is analyzed to illustrate the proposed methods.
Persistent Identifierhttp://hdl.handle.net/10722/57166
ISSN
2015 Impact Factor: 0.838
2015 SCImago Journal Rankings: 2.292
References

 

DC FieldValueLanguage
dc.contributor.authorTan, Men_HK
dc.contributor.authorTian, GLen_HK
dc.contributor.authorFang, HBen_HK
dc.contributor.authorNg, KWen_HK
dc.date.accessioned2010-04-12T01:28:00Z-
dc.date.available2010-04-12T01:28:00Z-
dc.date.issued2007en_HK
dc.identifier.citationStatistica Sinica, 2007, v. 17 n. 3, p. 945-964en_HK
dc.identifier.issn1017-0405en_HK
dc.identifier.urihttp://hdl.handle.net/10722/57166-
dc.description.abstractConvex constraints (CCs) such as box constraints and linear inequality constraints appear frequently in statistical inference and in applications. The problems of quadratic optimization (QO) subject to CCs occur in isotonic regression, shape-restricted non-parametric regression, variable selection (via the lasso algorithm and bridge regression), limited dependent variables models, image reconstruction, and so on. Existing packages for QO are not generally applicable to CCs. Although EM-type algorithms may be applied to such problems (Tian, Ng and Tan (2005)), the convergence rate/speed of these algorithms is painfully slow, especially for high-dimensional data. This paper develops a fast EM algorithm for QO with CCs. We construct a class of data augmentation schemes indexed by a 'working parameter' r (r ε R), and then optimize r over R under several convergence criteria. In addition, we use Cholesky decomposition to reduce both the number of latent variables and the dimension, leading to further acceleration of the EM. Standard errors of the restricted estimators are calculated using a non-parametric bootstrapping procedure. Simulation and comparison are performed and a complex multinomial dataset is analyzed to illustrate the proposed methods.en_HK
dc.languageengen_HK
dc.publisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/en_HK
dc.relation.ispartofStatistica Sinicaen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBootstrapen_HK
dc.subjectCholesky decompositionen_HK
dc.subjectConstrained optimizationen_HK
dc.subjectConvergence rateen_HK
dc.subjectData augmentationen_HK
dc.subjectEM algorithmen_HK
dc.subjectLatent variablesen_HK
dc.subjectWorking parameteren_HK
dc.titleA fast em algorithm for quadratic optimization subject to Convex constraintsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1017-0405&volume=17&issue=3&spage=945&epage=964&date=2007&atitle=A+fast+EM+algorithm+for+quadratic+optimization+subject+to+convex+constraintsen_HK
dc.identifier.emailTian, GL: gltian@hku.hken_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.authorityTian, GL=rp00789en_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-36249018992en_HK
dc.identifier.hkuros138171-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-36249018992&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume17en_HK
dc.identifier.issue3en_HK
dc.identifier.spage945en_HK
dc.identifier.epage964en_HK
dc.publisher.placeTaiwan, Republic of Chinaen_HK
dc.identifier.scopusauthoridTan, M=7401464681en_HK
dc.identifier.scopusauthoridTian, GL=25621549400en_HK
dc.identifier.scopusauthoridFang, HB=7402543028en_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK

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