Some Advanced Model Selection Topics for Nonparametric/Semiparametric Models with High-Dimensional Data

Model and variable selection have attracted considerable attention in areas of application where datasets usually contain thousands of variables. Variable selection is a critical step to reduce the dimension of high dimensional data by eliminating irrelevant variables. The general objective of variable selection is not only to obtain a set of cost-effective predictors selected but also to improve prediction and prediction variance. We have made several contributions to this issue through a range of advanced topics: providing a graphical view of Bayesian Variable Selection (BVS), recovering sparsity in multivariate nonparametric models and proposing a testing procedure for evaluating nonlinear interaction effect in a semiparametric model. To address the first topic, we propose a new Bayesian variable selection approach via the graphical model and the Ising model, which we refer to the ``Bayesian Ising Graphical Model'' (BIGM). There are several advantages of our BIGM: it is easy to (1) employ the single-site updating and cluster updating algorithm, both of which are suitable for problems with small sample sizes and a larger number of variables, (2) extend this approach to nonparametric regression models, and (3) incorporate graphical prior information. In the second topic, we propose a Nonnegative Garrote on a Kernel machine (NGK) to recover sparsity of input variables in smoothing functions. We model the smoothing function by a least squares kernel machine and construct a nonnegative garrote on the kernel model as the function of the similarity matrix. An efficient coordinate descent/backfitting algorithm is developed. The third topic involves a specific genetic pathway dataset in which the pathways interact with the environmental variables. We propose a semiparametric method to model the pathway-environment interaction. We then employ a restricted likelihood ratio test and a score test to evaluate the main pathway effect and the pathway-environment interaction.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2012

Author dc:creator

• Fang, Zaili

Chair dc:contributor.committeechair

• Kim, Inyoung

Committee members dc:contributor.committeemember

• Smith, Eric P.
• Terrell, George R.
• Du, Pang
• Leman, Scotland C.

• Variable Selection
• Smoothing Splines
• Sparsistency
• Semiparametric Model
• Pathway Analysis
• Additive Model
• Cluster Algorithm
• Gaussian Random Process
• Global-Local Shrinkage
• Graphical Model
• Ising Model
• Kernel Machine
• KM Model
• LASSO
• Long Tail Prior
• Mixture Normals
• Model Selection
• Multivariate Smoothing Function
• Nonnegative Garrote
• Nonparametric Model

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-10212012-214919

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/40090