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Cynthia Rudin. Lee, Peter Alexander Massachusetts Institute of Technology. Operations Research Center. Massachusetts Institute of Technology. Operations Research Center Sloan School of Management 2016-10-25T19:18:00Z 2016-10-25T19:18:00Z 2016 2016 http://hdl.handle.net/1721.1/105001 960814986 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). 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. by Peter Alexander Lee. S.M. 100 pages eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Operations Research Center. Think global, act local when estimating a sparse precision matrix Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="e2d4e9e6-2c85-4a48-a0a1-3f712c300252"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Think global, act local when estimating a sparse precision matrix</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2016</PublicationDate> <Authors> <Author> <DisplayName>Lee, Peter Alexander</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Operations Research Center.</Keyword> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>