Keywords

Mathematical statistics

Abstract

The purpose of the present dissertation is to study model selection techniques which are specifically designed for classification of high-dimensional data with a large number of classes. To the best of our knowledge, this problem has never been studied in depth previously. We assume that the number of components p is much larger than the number of samples n, and that only few of those p components are useful for subsequent classification. In what follows, we introduce two Bayesian models which use two different approaches to the problem: one which discards components which have “almost constant” values (Model 1) and another which retains the components for which between-group variations are larger than withingroup variation (Model 2). We show that particular cases of the above two models recover familiar variance or ANOVA-based component selection. When one has only two classes and features are a priori independent, Model 2 reduces to the Feature Annealed Independence Rule (FAIR) introduced by Fan and Fan (2008) and can be viewed as a natural generalization to the case of L > 2 classes. A nontrivial result of the dissertation is that the precision of feature selection using Model 2 improves when the number of classes grows. Subsequently, we examine the rate of misclassification with and without feature selection on the basis of Model 2.

Notes

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Graduation Date

2011

Semester

Fall

Advisor

Pensky, Marianna

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0004097

URL

http://purl.fcla.edu/fcla/etd/CFE0004097

Language

English

Release Date

December 2011

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Subjects

Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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