Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions |
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| Authors: | Tong Su Yafei Wang Yi Liu William G Branton Eugene Asahchop Christopher Power Bei Jiang Linglong Kong Niansheng Tang |
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| Institution: | 1.Key Lab of Statistical Modeling and Data Analysis of Yunnan Province, Yunnan University, Kunming 650091, China;2.Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada; (Y.W.); (Y.L.); (B.J.);3.Department of Medicine (Neurology), University of Alberta, Edmonton, AB T6G 2G1, Canada; (W.G.B.); (E.A.); (C.P.) |
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| Abstract: | Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study. |
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| Keywords: | high dimension multicategory classification DWD sparse group lasso L2-consistency proximal algorithm |
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