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Nonconvex matrix and tensor recovery with applications in machine learning
Descriptive
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Title
Nonconvex matrix and tensor recovery with applications in machine learning
Name
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Ghassemi
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Mohsen
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Mohsen Ghassemi
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author
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Sarwate
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Anand D
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Anand D Sarwate
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chair
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Waheed U
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Waheed U Bajwa
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Gurbuzbalaban
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Mert
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Mert Gurbuzbalaban
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internal member
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Zhang
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Cunhui
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Cunhui Zhang
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Advisory Committee
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Rutgers University
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School of Graduate Studies
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theses
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ETD doctoral
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2021
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2021-01
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English
Abstract
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This thesis focuses on some fundamental problems in machine learning that are posed as nonconvex matrix factorizations. More specifically we investigate theoretical and algorithmic aspects of the following problems: i) inductive matrix completion (IMC), ii) structured dictionary learning (DL) from tensor data, iii) tensor linear regression and iv) principal component analysis (PCA). The theoretical contributions of this thesis include providing recovery guarantees for IMC and structured DL by characterizing the local minima and other geometric properties of these problems. The recovery results are stated in terms of upper bounds on the number of observations required to recover the true matrix (dictionary in the case of DL) underlying the data. Another major theoretical contribution of this work is providing fundamental limits on the performance of tensor linear regression solvers by deriving a lower bound on the worst case mean squared error of any estimator. On the algorithmic side, this thesis proposes novel online and batch algorithms for solving structured dictionary learning problem as well as a novel multi-stage accelerated stochastic PCA algorithm that achieves near optimal results.
Subject
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Topic
Nonconvex optimization
Subject
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Topic
Machine learning
Subject
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Topic
Electrical and Computer Engineering
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Rutgers University Electronic Theses and Dissertations
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1 online resource (x, 144 pages) : illustrations
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Ph.D.
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Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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Identifier
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doi:10.7282/t3-16aw-j286
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Rights
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The author owns the copyright to this work.
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Name
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Ghassemi
GivenName
Mohsen
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Permission or license
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2021-01-05 13:05:47
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Mohsen Ghassemi
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Rutgers University. School of Graduate Studies
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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