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.

Level thesis:degree_level

Doctoral

Department dc:contributor.department

Industrial and Systems Engineering

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Ngueyep Tzoumpe, Rodrigue

Advisor dc:contributor.advisor

• Serban, Nicoleta

Committee members dc:contributor.committeemember

• Xie, Yao
• Vandekerkhove, Pierre
• Goldsman, David M.
• Vengazhiyil, Roshan

• Variable selection
• High dimensional statistics
• Regularization

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1853/53551

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/53551