Title page for ETD etd-10212012-214919

Type of Document Dissertation
Author Fang, Zaili
Author's Email Address zailifang099@gmail.com
URN etd-10212012-214919
Title Some Advanced Model Selection Topics for Nonparametric/Semiparametric Models with High-Dimensional Data
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Kim, Inyoung Committee Chair
Du, Pang Committee Member
Leman, Scotland C. Committee Member
Smith, Eric P. Committee Member
Terrell, George R. Committee Member
  • 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
  • Long Tail Prior
  • Mixture Normals
  • Model Selection
  • Multivariate Smoothing Function
  • Nonnegative Garrote
  • Nonparametric Model
Date of Defense 2012-10-19
Availability restricted
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.

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