A convex optimization approach to high-dimensional sparse quadratic discriminant analysis

In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for classification error. Minimax lower bounds are established demonstrate necessity of structural assumptions such as sparsity conditions on discriminating direction differential graph possible construction consistent QDA rules. We then propose a algorithm called SDAR using constrained convex optimization under assumptions. Both minimax upper obtained rule is shown be simultaneously rate over collection parameter spaces, up logarithmic factor. Simulation studies that performs well numerically. The also illustrated through an analysis prostate cancer data colon tissue data. methodology theory developed two groups in Gaussian setting extended multigroup copula model.