Convergence rates of generalization errors for margin-based classification

This paper develops a general approach to quantifying the size of generalization errors for margin-based classification. A trade-off between geometric margins and training errors is exhibited along with the complexity of a binary classification problem. Consequently, this results in dealing with learning theory in a broader framework, in particular, of handling both convex and non-convex margin classifiers, among which includes, support vector machines, kernel logistic regression, and ψ-learning. Examples for both linear and nonlinear classifications are provided.