Think global, act local when estimating a sparse precision matrix
Name
960814986-MIT.pdf
Description
Full printable version
Size
3.15 MB
Format
Adobe PDF
Checksum (MD5)
081b6b3077a6443c75cf79146838c3ad
Author(s)
Lee, Peter Alexander
Advisor(s)
Cynthia Rudin.
Date Issued
2016
Publisher
Massachusetts Institute of Technology
Abstract
Substantial progress has been made in the estimation of sparse high dimensional precision matrices from scant datasets. This is important because precision matrices underpin common tasks such as regression, discriminant analysis, and portfolio optimization. However, few good algorithms for this task exist outside the space of L1 penalized optimization approaches like GLASSO. This thesis introduces LGM, a new algorithm for the estimation of sparse high dimensional precision matrices. Using the framework of probabilistic graphical models, the algorithm performs robust covariance estimation to generate potentials for small cliques and fuses the local structures to form a sparse yet globally robust model of the entire distribution. Identification of appropriate local structures is done through stochastic discrete optimization. The algorithm is implemented in Matlab and benchmarked against competitor algorithms for an array of synthetic datasets. Simulation results suggest that LGM may outperform GLASSO when model sparsity is especially important and when variables in the dataset belong to a number of closely related (if unknown) groups.
Description
Thesis: S.M., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2016.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 99-100).
Subjects
Operations Research Center.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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