Some contributions to high dimensional statistical learning
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Huang, Hanwen. Some Contributions to High Dimensional Statistical Learning. Chapel Hill, NC: University of North Carolina at Chapel Hill, 2011. https://doi.org/10.17615/d016-1035APA
Huang, H. (2011). Some contributions to high dimensional statistical learning. Chapel Hill, NC: University of North Carolina at Chapel Hill. https://doi.org/10.17615/d016-1035Chicago
Huang, Hanwen. 2011. Some Contributions to High Dimensional Statistical Learning. Chapel Hill, NC: University of North Carolina at Chapel Hill. https://doi.org/10.17615/d016-1035- Last Modified
- March 21, 2019
- Creator
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Huang, Hanwen
- Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
- Abstract
- This dissertation consists of two major contributions to high dimensional statistical learning. The focus is on classification which is one of the central research topics in the field of statistical learning. This research is on both binary and multiclass learning. For binary classification, we propose the Bi-Directional Discrimination (BDD) method which generalizes linear classifiers from one hyperplane to two or more hyperplanes. BDD combines the strengths of linear and general nonlinear methods. Linear classifiers are very popular, but can suffer some serious limitations when the classes have distinct subpopulations. General nonlinear classifiers can give improved classification error rates, but do not give clear interpretation of the results and present great challenges in terms of overfitting in high dimensions. BDD gives much of the flexibility of a general nonlinear classifier while maintaining the interpretability, and less tendency towards overfitting, of linear classifiers. While the idea is generally applicable, we focus our discussion on the generalization of the Support Vector Machine (SVM) and Distance Weighted Discrimination (DWD) methods. The performance and usefulness of the proposed method are assessed using asymptotics, and demonstrated through analysis of simulated and real data. For multiclass learning, the DWD method is generalized from the binary case to the multiclass case. DWD is a powerful tool for solving binary classification problems which has been shown to improve upon SVM in high dimensional situations. We extend the binary DWD to the multiclass DWD. In addition to some well known extensions which simply combine several binary DWD classifiers, we propose a global multiclass DWD (MDWD) which finds a single classifier that simultaneously considers all classes. Our theoretical results show that MDWD is Fisher consistent, even in the particularly challenging case when there is no dominating class (i.e., maximal class conditional probability is less than 1/2). The performances of different multiclass DWD methods are assessed through simulation and real data studies.
- Date of publication
- December 2011
- DOI
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- Rights statement
- In Copyright
- Note
- "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Statistics and Operations Research (Statistics)."
- Advisor
- Marron, James Stephen
- Language
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- Place of publication
- Chapel Hill, NC
- Access right
- Open access
- Date uploaded
- March 18, 2013
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