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Degree

Doctor of Philosophy, Ohio State University, Statistics, 2005.

Abstract

Margin-based classifiers defined by functional margins are generally believed to yield high performance in classification. In this thesis, a general theory that quantifies the size of generalization error of a margin classifier is presented. The trade-off between geometric margins and training errors is captured, in addition to the complexity of a classification problem. The theory permits an investigation of the generalization ability of convex and nonconvex margin classifiers, including support vector machines (SVM), kernel logistic regression (KLR), and ψ-learning. Our theory indicates that the generalization ability of a certain class of nonconvex losses may be substantially faster than those for convex losses. Illustrative examples for both linear and nonlinear classification are provided.

Subject Headings

Statistics

Keywords

Bayes risk; classification; consistency; convex; nonconvex

Advisor

Xiaotong Shen

Pages

ix, 63 p.:ill

Document number: osu1124282485
Permalink: http://rave.ohiolink.edu/etdc/view?acc_num=osu1124282485

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