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Nonconvex matrix and tensor recovery with applications in machine learning
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Ghassemi, Mohsen. Nonconvex matrix and tensor recovery with applications in machine learning. Retrieved from https://doi.org/doi:10.7282/t3-16aw-j286

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TitleNonconvex matrix and tensor recovery with applications in machine learning
NameGhassemi, Mohsen (author); Sarwate, Anand D (chair); Bajwa, Waheed U (internal member); Gurbuzbalaban, Mert (internal member); Zhang, Cunhui (outside member); Rutgers University; School of Graduate Studies
Date Created2021
Other Date2021-01 (degree)
SubjectNonconvex optimization, Machine learning, Electrical and Computer Engineering
Extent1 online resource (x, 144 pages) : illustrations
DescriptionThis 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.
NotePh.D.
NoteIncludes bibliographical references
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-16aw-j286
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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