Some Advanced Model Selection Topics for Nonparametric/Semiparametric Models with High-Dimensional Data
MetadataShow full item record
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.
- Doctoral Dissertations 
Showing items related by title, author, creator and subject.
Page, Ernest H.; Nance, Richard E. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1994), TR-94-04
STRUCTURAL EQUATION MODELS EXAMINING THE RELATIONSHIPS BETWEEN THE BIG FIVE PERSONALITY FACTORS AND THE MUSIC MODEL OF ACADEMIC MOTIVATION COMPONENTS Fink, Jonathan Rupert (Virginia Tech, 2015-12-09)Scholars have long been interested in the complex relationships between personality and motivation. However, much of their understanding has been limited to The Big Five personality factors (namely, Openness, Conscientiousness, ...
Gaertner, Evan (Virginia Tech, 2015-06-11)Floating offshore wind turbines in deep waters offer significant advantages to onshore and near-shore wind turbines. However, due to the motion of floating platforms in response to wind and wave loading, the aerodynamics ...