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dc.contributor.advisorCaramanis, Constantine
dc.creatorYi, Xinyang
dc.date.accessioned2017-04-17T15:44:58Z
dc.date.available2017-04-17T15:44:58Z
dc.date.issued2016-12
dc.date.submittedDecember 2016
dc.identifierdoi:10.15781/T2CN6Z472
dc.identifier.urihttp://hdl.handle.net/2152/46474
dc.description.abstractNon-convex optimization based algorithms are ubiquitous in machine learning and statistical estimation, especially in dealing with complex models that are noisy, non-linear or contain latent structures. Popular techniques for non-convex problems such as alternating minimization and gradient descent, are typically easy to derive and use, but mostly lack theoretical foundations. It is difficult to obtain statistical consistency guarantees for these non-convex heuristics due to the existence of local minima in non-convex problems. From algorithmic perspective, it is even unclear whether average cases of some learning problems, which typically involve NP-hardness in the worst case, can be solved in polynomial time. This thesis seeks to tackle these challenges for a few statistical learning problems: mixed linear regression, robust principal component analysis, single index models in both standard and high-dimensional settings. We provide novel non-convex approaches for these problems via exploring theoretical understandings of several techniques favored in practice, including alternating minimization, EM, and non-convex gradient descent. We also present (optimal) statistical consistency guarantees and scalable computational complexities for the proposed algorithms. Our results suggest that in the problems we study, the aforementioned non-convex heuristics can quickly converge to global optimum (or statistically comparable solutions) when initialized within certain local regions around the underlying true parameters.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectStatistical machine learning
dc.subjectHigh dimensional statistics
dc.subjectNon-convex optimization
dc.subjectMixed linear regression
dc.titleLearning with latent structures, robustness and non-linearity : non-convex approaches
dc.typeThesis
dc.date.updated2017-04-17T15:44:59Z
dc.contributor.committeeMemberDimakis, Georgios-Alex
dc.contributor.committeeMemberPrice, Eric
dc.contributor.committeeMemberSanghavi, Sujay
dc.contributor.committeeMemberWard, Rachel
dc.description.departmentElectrical and Computer Engineering
thesis.degree.departmentElectrical and Computer Engineering
thesis.degree.disciplineElectrical and Computer engineering
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
dc.type.materialtext


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