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On The Structured Manifold Optimization: Reduced-rank and Positive Definite Matrix Estimation

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Title: On The Structured Manifold Optimization: Reduced-rank and Positive Definite Matrix Estimation
Author(s): Yuan, Ting
Advisor(s): Hedayat, Samad
Contributor(s): Wang, Junhui; Yang, Jie; Wang, Jing; Martin, Ryan
Department / Program: Mathematics, Statistics, and Computer Science
Graduate Major: Mathematics
Degree Granting Institution: University of Illinois at Chicago
Degree: PhD, Doctor of Philosophy
Genre: Doctoral
Subject(s): Structured matrix Statistical Machine Learning Reduced-rank Model Multi-label Classification Coordinate Descent Positive Definite Matrix Estimation
Abstract: This 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.
Issue Date: 2016-02-17
Genre: thesis
Rights Information: Copyright 2015 Ting Yuan
Date Available in INDIGO: 2018-02-18
Date Deposited: 2015-12

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