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Articles

Group screening for ultra-high-dimensional feature under linear model

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Pages 43-54 | Received 18 Jul 2018, Accepted 17 Jun 2019, Published online: 04 Jul 2019

References

  • Alon, U., Barkai, N., Notterman, D. A., Gish, K., Ybarra, S., Mack, D., & Levine, A. J. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proceedings of the National Academy of Sciences, 96(12), 6745–6750. doi: 10.1073/pnas.96.12.6745
  • Bakin, S. (1999). Adaptive regression and model selection in data mining problems (Ph.D. thesis). Australian National University, Canberra.
  • Breheny, P., & Huang, J. (2009). Penalized methods for bi-level variable selection. Statistics and its Interface, 2(3), 369. doi: 10.4310/SII.2009.v2.n3.a10
  • Breheny, P., & Huang, J. (2015). Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors. Statistics and Computing, 25(2), 173–187. doi: 10.1007/s11222-013-9424-2
  • Fan, J., Feng, Y., & Song, R. (2011). Nonparametric independence screening in sparse ultra-high-dimensional additive models. Journal of the American Statistical Association, 106(494), 544–557. doi: 10.1198/jasa.2011.tm09779
  • Fan, J., & Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature space (with discussion). Journal of the Royal Statistical Society, Series B: Statistical Methodology, 70(5), 849–911. doi: 10.1111/j.1467-9868.2008.00674.x
  • Fan, J., Samworth, R., & Wu, Y. (2009). Ultrahigh dimensional variable selection: Beyond the linear model. Journal of Machine Learning Research, 10, 1829–1853.
  • Fan, J., & Song, R. (2010). Sure independence screening in generalized linear models with NP-dimensionality. Annals of Statistics, 38(6), 3567–3604. doi: 10.1214/10-AOS798
  • He, X., Wang, L., & Hong, H. G. (2013). Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data. Annals of Statistics, 41(1), 342–369. doi: 10.1214/13-AOS1087
  • Huang, J., Ma, S., Xie, H., & Zhang, C. H. (2009). A group bridge approach for variable selection. Biometrika, 96(2), 339–355. doi: 10.1093/biomet/asp020
  • Li, R., Zhong, W., & Zhu, L. (2012). Feature screening via distance correlation learning. Journal of the American Statistical Association, 107(499), 1129–1139. doi: 10.1080/01621459.2012.695654
  • Shao, X., & Zhang, J. (2014). Martingale difference correlation and its use in high-dimensional variable screening. The American Statistical Association, 109(507), 1302–1318. doi: 10.1080/01621459.2014.887012
  • Van der Vaart, A. W., & Wellner, J. A. (1996). Weak convergence and empirical processes. New York: Springer.
  • Wang, H. (2009). Forward regression for ultra-high dimensional variable screening. Journal of the American Statistical Association, 104(488), 1512–1524. doi: 10.1198/jasa.2008.tm08516
  • Wei, F., & Huang, J. (2010). Consistent group selection in high-dimensional linear regression. Bernoulli, 16(4), 1369–1384. doi: 10.3150/10-BEJ252
  • Yang, Y., & Zou, H. (2015). A fast unified algorithm for solving group-lasso penalize learning problems. Statistics and Computing, 2015(6), 1129–1141. doi: 10.1007/s11222-014-9498-5
  • Yuan, M., & Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 68(1), 49–67. doi: 10.1111/j.1467-9868.2005.00532.x
  • Zhang, C. H., & Huang, J. (2008). The sparsity and bias of the lasso selection in high-dimensional linear regression. The Annals of Statistics, 36(4), 1567–1594. doi: 10.1214/07-AOS520
  • Zhao, S. D., & Li, Y. (2012). Principled sure independence screening for Cox models with ultra-high-dimensional covariates. Journal of Multivariate Analysis, 105(1), 397–411. doi: 10.1016/j.jmva.2011.08.002
  • Zhao, P., Rocha, G., & Yu, B. (2009). The composite absolute penalties family for grouped and hierarchical variable selection. Annals of Statistics, 37(6A), 3468–3497. doi: 10.1214/07-AOS584
  • Zhong, W., & Zhu, L.-P. (2015). An iterative approach to distance correlation-based sure independence screening. Journal of Statistical Computation and Simulation, 85(11), 2331–2345. doi: 10.1080/00949655.2014.928820

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