A primal dual active set with continuation algorithm for high-dimensional nonconvex SICA-penalized regression |
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Authors: | Yueyong Shi Zehui Zhou Yuling Jiao |
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Institution: | 1. School of Economics and Management, China University of Geosciences, Wuhan, People's Republic of China;2. Research Center of Resource and Environmental Economics, China University of Geosciences, Wuhan, People's Republic of China;3. School of Mathematics and Statistics, Wuhan University, Wuhan, People's Republic of China;4. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, People's Republic of China |
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Abstract: | The smooth integration of counting and absolute deviation (SICA) penalty has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection and parameter estimation. However, solving the nonconvex optimization problem associated with SICA penalty in high-dimensional setting remains to be enriched, mainly due to the singularity at the origin and the nonconvexity of the SICA penalty function. In this paper, we develop a fast primal dual active set (PDAS) with continuation algorithm for solving the nonconvex SICA-penalized least squares in high dimensions. Upon introducing the dual variable, the PDAS algorithm iteratively identify and update the active set in the optimization using both the primal and dual information, and then solve a low-dimensional least square problem on the active set. When combined with a continuation strategy and a high-dimensional Bayesian information criterion (BIC) selector on the tuning parameters, the proposed algorithm is very efficient and accurate. Extensive simulation studies and analysis of a high-dimensional microarray gene expression data are presented to illustrate the performance of the proposed method. |
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Keywords: | Continuation high-dimensional BIC primal dual active set SICA |
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