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