High dimensional discriminant analysis under weak sparsity

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. In this work, we consider the discriminant analysis under the weak sparsity where many entries of the parameters are nearly zero. We develop a unified LASSO-typed framework to estimate the parameters for sparse discriminant analysis and derive the general non asymptotic error bound under the weak sparsity condition. As applications, we revisit the sparse linear discriminant analysis and sparse quadratic discriminant analysis. We establish the consistency of the estimators and also the misclassification error rate. These results extend the sparse discriminant analysis methods to weak sparsity setting and refine the existing theoretical results.