A link-free sparse group variable selection method for single-index model

References

• U. Alon, N. Barkai, D.A. Notterman, K. Gish, S. Ybarra, D. Mack, and J. Levine, Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays, PNAS 96 (1999), pp. 6745–6750. doi: 10.1073/pnas.96.12.6745
   PubMed Web of Science ®Google Scholar
• S. Bakin, Adaptive regression and model selection in data mining problems, Ph.D. thesis, Australian National University, 1999.
   Google Scholar
• H.D. Bondell and L. Li, Shrinkage inverse regression estimation for model-free variable selection, J. R. Stat. Soc. Ser. B 71 (2009), pp. 287–299. doi: 10.1111/j.1467-9868.2008.00686.x
   Google Scholar
• S. Chatterjee, K. Steinhaeuser, A. Banerjee, S. Chatterjee, and A. Ganguly, Sparse group lasso: Consistency and climate applications, Proceedings of the 2012 SIAM International Conference on Data Mining (2012), pp. 47–58.
   Google Scholar
• R.D. Cook, Regression Graphics, Wiley, New York, NY, 1998.
   Google Scholar
• R.D. Cook and S. Weisberg, Discussion of ‘Sliced inverse regression for dimension reduction’ by Li, J. Amer. Stat. Assoc. 86 (1991), pp. 328–332.
   Web of Science ®Google Scholar
• M.C.P. de Souto, I.G. Costa, D.S.A. de Araujo, T.B. Ludermir, and A. Schliep, Clustering cancer gene expression data: A comparative study, BMC Bioinform. 9 (2008), pp. 497. doi: 10.1186/1471-2105-9-497
   PubMed Web of Science ®Google Scholar
• S. Dudoit, J. Fridyland, and T.P. Speed, Comparison of discrimination methods for the classification of tumors using gene expression data, J. Amer. Stat. Assoc. 97 (2002), pp. 77–87. doi: 10.1198/016214502753479248
   Web of Science ®Google Scholar
• Z. Feng and L.X. Zhu, An alternating determination–optimization approach for an additive multi-index model, Comput. Stat. Data Anal. 56 (2012), pp. 1981–1993. doi: 10.1016/j.csda.2011.12.004
   Web of Science ®Google Scholar
• J. Friedman, T. Hastie, and R. Tibshirani, A note on the group lasso and a sparse group lasso, Tech. Rep., Statistics Department, Stanford University, 2010.
   Google Scholar
• P. Hall and K.C. Li, On almost linearity of low dimensional projections from high dimensional data, Ann. Stat. 21 (1993), pp. 867–889. doi: 10.1214/aos/1176349155
   Web of Science ®Google Scholar
• W. Hardle, P. Hall, and H. Ichimura, Optimal smoothing in single-index models, Ann. Stat. 21 (1993), pp. 157–178. doi: 10.1214/aos/1176349020
   Web of Science ®Google Scholar
• A. Hoerl and R. Kennard, Ridge regression, Encyclopedia Stat. Sci. 8 (1988), pp. 129–136.
   Google Scholar
• S. Horvath, B. Zhang, M. Carlson, K.V. Lu, S. Zhu, R.M. Felciano, M.F. Laurance, W. Zhao, S. Qi, Z. Chen, Y. Lee, A.C. Scheck, L.M. Liau, H. Wu, D.H. Geschwind, P.G. Febbo, H.I. Kornblum, T.F. Cloughesy, S.F. Nelson, and P.S. Mischel, Analysis of oncogenic signaling networks in glioblastoma identifies ASPM as a molecular target, PNAS 103 (2006), pp. 17402–17407. doi: 10.1073/pnas.0608396103
   PubMed Web of Science ®Google Scholar
• J. Huang, S. Ma, H. Xie, and C.-H. Zhang, A group bridge approach for variable selection, Biometrika 96 (2009), pp. 339–355. doi: 10.1093/biomet/asp020
   PubMed Web of Science ®Google Scholar
• R.A. Irizarry, B. Hobbs, F. Collin, Y.D. Beazer-Barclay, K.J. Antonellis, U. Scherf, and T.P. Speed, Exploration, normalization, and summaries of high density oligonucleotide array probe level data, Biostatistics 4 (2003), pp. 249–264. doi: 10.1093/biostatistics/4.2.249
   PubMed Web of Science ®Google Scholar
• P.D. Karp, C.A. Ouzounis, C. Moore-Kochlacs, L. Goldovsky, P. Kaipa, D. Ahrén, S. Tsoka, N. Darzentas, V. Kunin, and N. López-Bigas, Expansion of the BioCyc collection of pathway/genome databases to 160 genomes, Nucleic Acids Res. 19 (2005), pp. 6083–6089. doi: 10.1093/nar/gki892
   Web of Science ®Google Scholar
• C. Li and H. Li, Network-constrained regularization and variable selection for analysis of genomic data, Bioinformatics 24 (2008), pp. 1175–1182. doi: 10.1093/bioinformatics/btn081
   PubMed Web of Science ®Google Scholar
• K.C. Li, Sliced inverse regression for dimension reduction, J. Amer. Stat. Assoc. 86 (1991), pp. 316–327. doi: 10.1080/01621459.1991.10475035
   Web of Science ®Google Scholar
• L. Li, Sparse sufficient dimension reduction, Biometrika 94 (2007), pp. 603–613. doi: 10.1093/biomet/asm044
   Web of Science ®Google Scholar
• L. Li, R.D. Cook, and C.J. Nachtsheim, Model free variable selection, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67 (2005), pp. 285–299. doi: 10.1111/j.1467-9868.2005.00502.x
   Web of Science ®Google Scholar
• L. Li, B. Li, and L.X. Zhu, Groupwise dimension reduction, J. Amer. Stat. Assoc. 105 (2010), pp. 1188–1201. doi: 10.1198/jasa.2010.tm09643
   Web of Science ®Google Scholar
• L. Li and C.J. Nachtsheim, Sparse sliced inverse regression, Technometrics 48 (2006), pp. 503–510. doi: 10.1198/004017006000000129
   Web of Science ®Google Scholar
• L. Li and X. Yin, Sliced inverse regression with regularizations, Biometrics 64 (2008), pp. 124–131. doi: 10.1111/j.1541-0420.2007.00836.x
   PubMed Web of Science ®Google Scholar
• J. Liu, S. Ji, and J. Ye, SLEP: Sparse learning with efficient projections, Arizona State Univ. 6 (2009). Available at http://www.public.asu.edu/jye02/Software/SLEP.
   Google Scholar
• S. Ma and M.R. Kosorok, Identification of differential gene pathways with principal component analysis, Bioinformatics 25 (2009), pp. 882–889. doi: 10.1093/bioinformatics/btp085
   PubMed Web of Science ®Google Scholar
• J. MacQueen, Some methods for classification and analysis of multivariate observations, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, Berkeley, CA, University of California Press, 1967, pp. 281–297.
   Google Scholar
• T. Manoli, N. Gretz, H.-J. Grone, M. Kenzelmann, R. Eils, and B. Brors, Group testing for pathway analysis improves comparability of different microarray datasets, Bioinformatics 22 (2006), pp. 2500–2506. doi: 10.1093/bioinformatics/btl424
   PubMed Web of Science ®Google Scholar
• L. Matthews, G. Gopinath, M. Gillesphie, M. Caudy, D. Croft, B. de Bono, P. Garapati, J. Hemish, H. Hermjakob, B. Jassal, A. Kanapin, S. Lewis, S. Mahajan, B. May, E. Schmidt, I. Vastrik, G. Wu, E. Birney, L. Stein, and P. D'Eustachio, Reactome knowledge bases of biological pathways and processes, Nucleic Acids Res. 37 (2008), pp. 619–622. doi: 10.1093/nar/gkn863
   Web of Science ®Google Scholar
• L. Meier, S. van de Geer, and P. Bühlmann, The group lasso for logistic regression, J. R. Stat. Soc. Ser. B 70 (2008), pp. 53–71. doi: 10.1111/j.1467-9868.2007.00627.x
   Google Scholar
• NguyenD.V. and D.M. Rocke, Partial least squares proportional hazard regression for application to DNA microarray survival data, Bioinformatics 18 (2002), pp. 1625–1632. doi: 10.1093/bioinformatics/18.12.1625
   PubMed Web of Science ®Google Scholar
• L. Ni, R.D. Cook, and TsaiC.-L., A note on shrinkage sliced inverse regression, Biometrika 92 (2005), pp. 242–247. doi: 10.1093/biomet/92.1.242
   Web of Science ®Google Scholar
• H. Ogata, S. Goto, K. Sato, W. Fujibuchi, H. Bono, and M. Kanehisa, KEGG: Kyoto encyclopedia of genes and genomes, Nucleic Acids Res. 27 (1999), pp. 29–34. doi: 10.1093/nar/27.1.29
   PubMed Web of Science ®Google Scholar
• W. Pan, B. Xie, and X. Shen, Incorporating predictor network in penalized regression with application to microarray data, Biometrics 66 (2010), pp. 474–484. doi: 10.1111/j.1541-0420.2009.01296.x
   PubMed Web of Science ®Google Scholar
• A. Rosenwald, G. Wright, A. Wiestner, W.C. Chan, J.M. Connors, E. Campo, R.D. Gascoyne, T.M. Grogan, H.K. Muller-Hermelink, E.B. Smeland, M. Chiorazzi, J.M. Giltnane, E.M. Hurt, H. Zhao, L. Averett, S. Henrickson, L. Yang, J. Powell, W.H. Wilson, E.S. Jaffe, R. Simon, R.D. Klausner, E. Montserrat, F. Bosch, T.C. Greiner, D.D. Weisenburger, W.G. Sanger, B.J. Dave, J.C. Lynch, J. Vose, J.O. Armitage, R.I. Fisher, T.P. Miller, M. LeBlanc, G. Ott, S. Kvaloy, H. Holte, J. Delabie, and L.M. Staudt, The proliferation gene expression signature is a quantitative integrator of oncogenic events that predicts survival in mantle cell lymphoma, Cancer Cell 3 (2003), pp. 185–197. doi: 10.1016/S1535-6108(03)00028-X
   PubMed Web of Science ®Google Scholar
• N. Simon, J. Friedman, T. Hastie, and R. Tibshirani, The sparse group lasso, J. Comput. Graph. Stat. 22 (2013), pp. 231–245. doi: 10.1080/10618600.2012.681250
   Web of Science ®Google Scholar
• X. Sun, L. Zhang, H. Tan, J. Bao, C. Strouthos, and X. Zhou, Multi-scale agent-based brain cancer modeling and prediction of TKI treatment response: Incorporating EGFR signaling pathway and angiogenesis, BMC Bioinform. 13 (2012), pp. 218. doi: 10.1186/1471-2105-13-218
   PubMed Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B 58 (1996), pp. 267–288.
   Google Scholar
• K. Wang, M. Li, and M. Bucan, Pathway-based approaches for analysis of genomewide association studies, Amer. J. Hum. Genet. 81 (2007), pp. 1278–1283. doi: 10.1086/522374
   PubMed Web of Science ®Google Scholar
• T. Wang, P.-R. Xiu, and L.-X. Zhu, Non-convex penalized estimation in high-dimensional models with single-index structure, J. Multivariate Anal. 109 (2012), pp. 221–235. doi: 10.1016/j.jmva.2012.03.009
   Web of Science ®Google Scholar
• P. Wei and W. Pan, Incorporating gene networks into statistical tests for genomic data via a spatially correlated mixture model, Bioinformatics 24 (2008), pp. 404–411. doi: 10.1093/bioinformatics/btm612
   PubMed Web of Science ®Google Scholar
• X. Wen and R.D. Cook, Optimal sufficient dimension reduction in regressions with categorical predictors, J. Stat. Plan. Inference 137 (2007), pp. 1961–1978. doi: 10.1016/j.jspi.2006.05.008
   Web of Science ®Google Scholar
• X. Yin, B. Li, and R.D. Cook, Successive direction extraction for estimating the central subspace in a multiple-index regression, J. Multivariate Anal. 99 (2008), pp. 1733–1757. doi: 10.1016/j.jmva.2008.01.006
   Web of Science ®Google Scholar
• M. Yuan and Y. Lin, Model selection and estimation in regression with grouped variables, J. R. Stat. Soc. Ser. B 68 (2006), pp. 49–67. doi: 10.1111/j.1467-9868.2005.00532.x
   Google Scholar
• H. Zhu and L. Li, Biological pathway selection through nonlinear dimension reduction, Biostatistics 12 (2011), pp. 429–444. doi: 10.1093/biostatistics/kxq081
   PubMed Web of Science ®Google Scholar
• H. Zou and T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67 (2005), pp. 301–320. doi: 10.1111/j.1467-9868.2005.00503.x
   Web of Science ®Google Scholar