  We propose an empirical Bayes estimator based on Dirichlet process mixture
model for estimating the sparse normalized mean difference, which could be
directly applied to the high dimensional linear classification. In theory, we
build a bridge to connect the estimation error of the mean difference and the
misclassification error, also provide sufficient conditions of sub-optimal
classifiers and optimal classifiers. In implementation, a variational Bayes
algorithm is developed to compute the posterior efficiently and could be
parallelized to deal with the ultra-high dimensional case.
