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Model selection and estimation in high dimensional settings

Several statistical problems can be described as estimation problem, where the goal is to learn a set of parameters, from some data, by maximizing a criterion. These type of problems are typically encountered in a supervised learning setting, where we want to relate an output (or many outputs) to multiple inputs. The relationship between these outputs and these inputs can be complex, and this complexity can be attributed to the high dimensionality of the space containing the inputs and the outputs; the existence of a structural prior knowledge within the inputs or the outputs that if ignored may lead to inefficient estimates of the parameters; and the presence of a non-trivial noise structure in the data. In this thesis we propose new statistical methods to achieve model selection and estimation when there are more predictors than observations. We also design a new set of algorithms to efficiently solve the proposed statistical models. We apply the implemented methods to genetic data sets of cancer patients and to some economics data.

Identiferoai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/53551
Date08 June 2015
CreatorsNgueyep Tzoumpe, Rodrigue
ContributorsSerban, Nicoleta
PublisherGeorgia Institute of Technology
Source SetsGeorgia Tech Electronic Thesis and Dissertation Archive
Languageen_US
Detected LanguageEnglish
TypeDissertation
Formatapplication/pdf

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