Large dimensional analysis of general margin based classification methods

Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of are available, one natural question is which type should be used given particular task. We answer this by investigating the asymptotic performance family large-margin under two component mixture models situations where data dimension $p$ sample $n$ large. This covers broad range including support vector machine, distance weighted discrimination, penalized logistic regression, unified as special cases. The results described set nonlinear equations we observe close match them with Monte Carlo simulation on finite samples. Our analytical studies shed new light how to select best classifier among various methods well choose optimal tuning parameters method.