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Some methods for statistical inference using high-dimensional linear models
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Ahmed, Talal. Some methods for statistical inference using high-dimensional linear models. Retrieved from https://doi.org/doi:10.7282/t3-3svf-6a28

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TitleSome methods for statistical inference using high-dimensional linear models
NameAhmed, Talal (author); Bajwa, Waheed U. (chair); Rutgers University; School of Graduate Studies
Date Created2019
Other Date2019-10 (degree)
SubjectElectrical and Computer Engineering, Statistical inference, Probabilities
Extent1 online resource (vii, 89 pages) : illustrations
DescriptionThe ordinary linear model has been the bedrock of signal processing, statistics, and machine learning for decades. The last decade, however, has witnessed a marked transformation of this model: instead of the classical low-dimensional setting in which the sample size exceeds the number of features/predictors/variables, we are increasingly having to operate in the high-dimensional setting in which the number of variables far exceeds the sample size. Although such high-dimensional settings would ordinarily lead to ill-posed problems, the inference task has been studied under the rubric of high-dimensional statistical inference, where various notions of structure have been imposed on the model parameters to obtain unique solutions to the inference problem. While there are many statistical methods that guarantee unique solutions, these methods can easily become computationally prohibitive in ultrahigh-dimensional settings, in which the number of variables can scale exponentially with the sample size. In other cases, the traditional notions of structure on model parameters can be rather restrictive, especially when the variables naturally appear in the form of a multi-way array (tensor), as in the case of neuroimaging data analysis.
The purpose of this dissertation is to study inference using high-dimensional linear models for the cases when (i) the number of variables can scale exponentially with the number of samples, and (ii) the variables naturally form a tensor structure. Specifically, for each of these respective cases, the dissertation (i) proposes an efficient inference approach, (ii) provides high-probability performance guarantees for the proposed approach, and (iii) demonstrates efficacy of the inference approach in statistical analysis of real-world datasets.
NotePh.D.
NoteIncludes bibliographical references
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-3svf-6a28
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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