An Alternating Direction Method of Multipliers for MCP-penalized Regression with High-dimensional Data
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The minimax concave penalty (MCP) has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers (ADMM) with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush–Kuhn–Tucker (KKT) optimality conditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.
KeywordsAlternating direction method of multipliers coordinate descent continuation high-dimensional BIC minimax concave penalty penalized least squares
MR(2010) Subject Classification62J05 62J07 62J99
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The authors sincerely thank the associate editor and the referees for their valuable comments and suggestions that have led to significant improvement of this article.
- Huang, J., Jiao, Y., Liu, Y., et al.: A constructive approach to sparse linear regression in high-dimensions, arXiv preprint arXiv:1701.05128v1, 2017Google Scholar
- Jiao, Y., Jin, B., Lu, X., et al.: A primal dual active set algorithm for a class of nonconvex sparsity optimization, arXiv preprint arXiv:1310.1147v3, 2016Google Scholar
- Song, C., Yoon, S., Pavlovic, V.: Fast ADMM algorithm for distributed optimization with adaptive penalty. Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence and the Twenty-Eighth Innovative Applications of Artificial Intelligence Conference, 2016Google Scholar
- Wang, Y., Yin, W., Zeng, J.: Global convergence of ADMM in nonconvex nonsmooth optimization. arXiv preprint, arXiv:1511.06324v5, 2017Google Scholar
- Xu, Z., Figueiredo, M. A. T., Goldstein, T.: Adaptive ADMM with spectral penalty parameter selection. arXiv preprint, arXiv:1605.07246v5, 2017Google Scholar
- Yu, L., Lin, N., Wang, L.: A parallel algorithm for large-scale nonconvex penalized quantile regression. J. Comput. Graph. Statist., DOI:10.1080/10618600.2017.1328366, 2017 (just-accepted)Google Scholar