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Quadratic Discriminant Analysis Revisited, Wenbo Cao

Dissertations, Theses, and Capstone Projects

In this thesis, we revisit quadratic discriminant analysis (QDA), a standard classification method. Specifically, we investigate the parameter estimation and dimension reduction problems for QDA.

Traditionally, the parameters of QDA are estimated generatively; that is the parameters are estimated by maximizing the joint likelihood of observations and their labels. In practice, classical QDA, though computationally efficient, often underperforms discriminative classifiers, such as SVM, Boosting methods, and logistic regression. Motivated by recent research on hybrid generative/discriminative learning, we propose to estimate the parameters of QDA by minimizing a convex combination of negative joint log-likelihood and negative conditional log-likelihood of observations and …