416
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Model selection with distributed SCAD penalty

, &
Pages 1938-1955 | Received 01 Feb 2017, Accepted 29 Oct 2017, Published online: 16 Nov 2017

References

  • H. Akaike, Information theory and an extension of the maximum likelihood principle, in Second International Symposium on Information Theory, B.N. Petrov, F. Caki, eds., Akademiai Kiado, Budapest, 1973, pp. 267–281.
  • D. Bertsekas, and J. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, 2nd ed., Athena Scientific, Belmont, MA, 1997.
  • E. Candes, and T. Tao, The Dantzig selector: Statistical estimation when p is much larger than n, Ann. Stat. 35 (2005), pp. 1300–1308.
  • E.J. Candes, and T. Tao, Near-optimal signal recovery from random projections: Universal encoding strategies, IEEE Trans. Inf. Theory 52 (2006), pp. 5406–5425. doi: 10.1109/TIT.2006.885507
  • S.S. Chen, M.A. Saunders, and D.L. Donoho, Atomic decomposition by basis pursuit, Siam Rev. 43 (2001), pp. 129 –159 . doi: 10.1137/S003614450037906X
  • D.L. Donoho, Compressed sensing, IEEE Trans. Inf. Theory 52 (2006), pp. 1289–1306. doi: 10.1109/TIT.2006.871582
  • D. Donoho, and M. Elad, Maximal sparsity representation via L1 minimization, Proc. Nat. Acad. Sci. 100 (2002), pp. 2197–2202. doi: 10.1073/pnas.0437847100
  • D.L. Donoho, and X. Huo, Uncertainty principles and ideal atomic decomposition, IEEE Trans. Inf. Theory 47 (2001), pp. 2845–2862. doi: 10.1109/18.959265
  • J. Eckstein, Splitting methods for monotone operators with applications to parallel optimization, Ph.D thesis, Operations Research Center, MIT, 1989.
  • J. Eckstein, and D.P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm or maximal monotone operators, Math. Program. 55 (1992), pp. 293–318. doi: 10.1007/BF01581204
  • J. Fan, and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Am. Stat. Assoc. 96 (2001), pp. 1348–1360 . doi: 10.1198/016214501753382273
  • J. Fan, and H. Peng, Nonconcave penalized likelihood with a diverging number of parameters, Ann. Stat. 32 (2004), pp. 928–961. doi: 10.1214/009053604000000256
  • J. Fan, Y. Feng, and Y. Wu, Network exploration via the adaptive LASSO and SCAD penalties, Ann. Appl. Statist. 3 (2009), pp. 521–541. doi: 10.1214/08-AOAS215
  • J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, Pathwise coordinate optimization, Ann. Appl. Statist. 1 (2007), pp. 302–332. doi: 10.1214/07-AOAS131
  • D. Gabay, and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Comput. Math. Appl. 2 (1976), pp. 17–40. doi: 10.1016/0898-1221(76)90003-1
  • R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer series in computational physics. Springer-Verlag, New York, USA, 1984.
  • R. Glowinski, and A. Marrocco, Sur l'approximation parelements nis d'ordre un, et lan resolution par penalisation-dualite, d'une classe de problemes de Dirichlet non lineaires, ESAIM Math. Model. Numer. Anal. 2 (1975), pp. 41–76.
  • J. Kalbfleisch, R. Prentice, The Statistical Analysis of Failure Time Data, 2nd ed., John Wiley & Sons, Inc., Hoboken, NJ, USA, 2002.
  • Y. Kim, H. Choi, and H. -S. Oh, Smoothly clipped absolute deviation on high dimensions, J. Am. Stat. Assoc. 103 (2008), pp. 1665–1673. doi: 10.1198/016214508000001066
  • G. Mateos, J. Bazerque, and G.B. Giannakis, Distributed sparse linear regression, IEEE. Trans. Signal. Process. 58 (2010), pp. 5262–5276. doi: 10.1109/TSP.2010.2055862
  • G. Schwarz, Estimating the dimension of a model, Ann. Stat. 6 (1978), pp. 15–18. doi: 10.1214/aos/1176344136
  • R. Tibshirani, Regression shrinkage and selection via the LASSO, J. R. Stat. Soc. 58 (1996), pp. 267–288.
  • P. Tseng, Convergence of a block coordinate descent method for nondifferentiable minimization[J], J. Optim. Theory Appl. 109 (2001), pp. 475–494. doi: 10.1023/A:1017501703105
  • Y. Wang, W. Yin, and J. Zeng, Global Convergence of ADMM in Nonconvex Nonsmooth Optimization, preprint (2015), Available at arXiv:1511.06324.
  • Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, L1/2 regularization, Sci. China Inf. Sci. 53 (2010), pp. 1159–1169. doi: 10.1007/s11432-010-0090-0
  • C. -H. Zhang, Nearly unbiased variable selection under minimax concave penalty, Ann. Stat. 38 (2010), pp. 894–942. doi: 10.1214/09-AOS729
  • H. Zhang, Y. Liang, Z. Xu, and X. Chang, Compressive sensing with noise based on SCAD penalty, Acta Math. Sinica 56 (2013), pp. 767–775.
  • H. Zou, The adaptive Lasso and its oracle properties, J. Am. Stat. Assoc. 101 (2006), pp. 1418–1429. doi: 10.1198/016214506000000735

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.