Sparse Inverse Covariance Selection with Non-Convex Regularizations

Resource type
Thesis type
(Thesis) M.Sc.
Date created
2013-10-29
Authors/Contributors
Author: Li, Xiaorui
Abstract
Sparse inverse covariance selection is a powerful tool for estimating sparse graphs in statistical learning, whose mathematical model is to maximize the regularized log-likelihood function. In this thesis, we consider introducing some non-convex regularizers to this problem. In particular, we first propose several non-convex regularized maximum likelihood estimation models. Using the specific structure of those regularizers, we then develop a DC programming approach for solving these models. We show that each subproblem of this approach is a weighted graphical lasso problem, and we propose a warm-started alternating direction method of multipliers to solve each subproblem. In addition, we propose a decomposition scheme by extending the exact covariance thresholding technique for graphical lasso to our general non-convex model, which enables us to solve large-scale problems efficiently. Finally, we compare the performance of our approach with some existing approaches on both randomly generated and real-life instances, and report some promising computational results.
Document
Identifier
etd8077
Copyright statement
Copyright is held by the author.
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The author granted permission for the file to be printed, but not for the text to be copied and pasted.
Scholarly level
Supervisor or Senior Supervisor
Thesis advisor: Lu, Zhaosong
Member of collection
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