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dc.contributor.advisorHedayat, Samaden_US
dc.contributor.authorYuan, Tingen_US
dc.date.accessioned2016-02-17T17:33:11Z
dc.date.available2018-02-18T10:30:11Z
dc.date.created2015-12en_US
dc.date.issued2016-02-17
dc.date.submitted2015-12en_US
dc.identifier.urihttp://hdl.handle.net/10027/20247
dc.description.abstractThis thesis mainly proposes optimization schemes regarding both types of structured matrices, as well as their applications in statistics. The first structured matrix optimization is proposed under the reduced-rank constraint, and particularly it can be applied for conducting multi-label classification and variable selection simultaneously. The proposed algorithm for optimization is computationally efficient and delivers superior numerical performance in terms of both classification and variable selection accuracy. The asymptotic consistencies are also established to support the advantages of the proposed method. The second structured matrix optimization proposes the estimation of sparse positive definite matrix generated by a generic coordinate descent (CD) algorithm, and particularly it can be applied to the estimation of the high-dimensional covariance matrix and inverse covariance or precision matrix with variable selection.en_US
dc.language.isoenen_US
dc.rightsen_US
dc.rightsCopyright 2015 Ting Yuanen_US
dc.subjectStructured matrixen_US
dc.subjectStatistical Machine Learningen_US
dc.subjectReduced-rank Modelen_US
dc.subjectMulti-label Classificationen_US
dc.subjectCoordinate Descenten_US
dc.subjectPositive Definite Matrix Estimationen_US
dc.titleOn The Structured Manifold Optimization: Reduced-rank and Positive Definite Matrix Estimationen_US
thesis.degree.departmentMathematics, Statistics, and Computer Scienceen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Illinois at Chicagoen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePhD, Doctor of Philosophyen_US
dc.type.genrethesisen_US
dc.contributor.committeeMemberWang, Junhuien_US
dc.contributor.committeeMemberYang, Jieen_US
dc.contributor.committeeMemberWang, Jingen_US
dc.contributor.committeeMemberMartin, Ryanen_US
dc.type.materialtexten_US


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