A direct approach to sparse discriminant analysis in ultra-high dimensions

Biometrika

Volumn 99, Issue 1, 2012, Pages 29-42

  Mai, Qing ^a   Zou, Hui ^a   Yuan, Ming ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

Discriminant analysis; Features annealed independence rule; Lasso; Nearest shrunken centroids classifier; Nonpolynomial dimension asymptotics

Indexed keywords

EID: 84857556385     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asr066     Document Type: Article

References (30)

1. ALON, U., BARKAI, N., NOTTERMAN, D. A., GISH, K., MACK, S. & LEVINE, A. J. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Nat. Acad. Sci. 96, 6745-50. (Pubitemid 29274954)
2. BICKEL, P. J. & LEVINA, E. (2004). Some theory for Fisher's linear discriminant function, 'naive Bayes', and some alternatives when there are many more variables than observations. Bernoulli 10, 989-1010. (Pubitemid 44242745)
3. BICKEL, P. J. & LEVINA, E. (2008). Regularized estimation of large covariance matrices. Ann. Statist. 36, 199-227.
4. CAI, T., ZHANG, C. H. & ZHOU, H. (2010). Optimal rates of convergence for covariancematrix estimation. Ann. Statist. 38, 2118-44.
5. DETTLING, M. (2004). Bagboosting for tumor classification with gene expression data. Bioinformatics 20, 3583-93. (Pubitemid 40136794)
6. EFRON, B. (2010). Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing and Prediction. Cambridge: Cambridge University Press.
7. EFRON, B., HASTIE, T. J., JOHNSTONE, I. M. & TIBSHIRANI, R. J. (2004). Least angle regression. Ann. Statist. 32, 407-99. (Pubitemid 41250302)
8. FAN, J. & FAN, Y. (2008). High dimensional classification using features annealed independence rules. Ann. Statist. 36, 2605-37.
9. FAN, J. & LI, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Statist. Assoc. 96, 1348-60. (Pubitemid 33695585)
10. FRIEDMAN, J. H., HASTIE, T. J. & TIBSHIRANI, R. J. (2010). Regularization paths for generalized linear models via coordinate descent. J. Statist. Software 33, 1-22.
11. HALL, P.,MARRON, J. S. & NEEMAN, A. (2005). Geometric representation of high dimension, low sample size data. J. R. Statist. Soc. B 67, 427-44. (Pubitemid 40855293)
12. HAND, D. J. (2006). Classifier technology and the illusion of progress. Statist. Sci. 21, 1-14. (Pubitemid 44046906)
13. HASTIE, T. J., TIBSHIRANI, R. J. & FRIEDMAN, J. H. (2008). Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Berlin: Springer.
14. LEVINA, E., ROTHMAN, A. J. & ZHU, J. (2008). Sparse estimation of large covariance matrices via a nested lasso penalty. Ann. Appl. Statist. 2, 245-63.
15. MEINSHAUSEN, N. & B̈UHLMANN, P. (2006). High dimensional graphs and variable selection with the lasso. Ann. Statist. 34, 1436-62. (Pubitemid 44231168)
16. MICHIE, D., SPIEGELHALTER, D. J. & TAYLOR, C. C. (1994). Machine Learning, Neural and Statistical Classification, Chichester: Ellis Horwood.
17. ROTHMAN, A. J., BICKEL, P., LEVINA, E. & ZHU, J. (2008). Sparse permutation invariant covariance estimation. Electron. J. Statist. 2, 494-515.
18. SINGH, D., FEBBO, P. G., ROSS, K., JACKSON, D. G.,MANOLA, J., LADD, C., TAMAYO, P., RENSHAW, A. A.,D'AMICO, A. V., RICHIE, J. P., ET AL. (2002). Gene expression correlates of clinical prostate cancer behavior. Cancer Cell 1, 203-9. (Pubitemid 41039166)
19. TIBSHIRANI, R. J. (1996). Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B 58, 267-88.
20. TIBSHIRANI, R. J.,HASTIE, T. J.,NARASIMHAN, B. & CHU, G. (2002). Diagnosis of multiple cancer types by shrunken centroids of gene expression. Proc. Nat. Acad. Sci. 99, 6567-72. (Pubitemid 34526173)
21. TIBSHIRANI, R. J., SAUNDERS, M., ROSSET, S., ZHU, J. & KEITH, K. (2005). Sparsity and smoothness via the fused lasso. J. R. Statist. Soc. B 67, 91-108. (Pubitemid 40167043)
22. TRENDAFILOV, N. T. & JOLLIFFE, I. T. (2007). DALASS: Variable selection in discriminant analysis via the lasso. Comp. Statist. Data Anal. 51, 3718-36. (Pubitemid 46497496)
23. WAINWRIGHT, M. J. (2009). Sharp thresholds for noisy and high-dimensional recovery of sparsity using 1-constrained quadratic programming (lasso). IEEE Trans. Info. Theory 55, 2183-202.
24. WITTEN, D. M. & TIBSHIRANI, R. J. (2011). Penalized classification using Fisher's linear discriminant. J. R. Statist. Soc. B 73, 753-72.
25. WU, M. C., ZHANG, L., WANG, Z., CHRISTIANI, D. C. & LIN, X. (2009). Sparse linear discriminant analysis for simultaneous testing for the significance of a gene set/pathway and gene selection. Bioinformatics 25, 1145-51.
26. YUAN, M. & LIN, Y. (2006). Model selection and estimation in regression with grouped variables. J. R. Statist. Soc. B 68, 49-67. (Pubitemid 43415335)
27. ZHANG, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. Ann. Statist. 38, 894-942.
28. ZHAO, P. & YU, B. (2006). On model selection consistency of lasso. J.Mach. Learn. Res. 7, 2541-63. (Pubitemid 44866738)
29. ZOU, H. (2006). The adaptive lasso and its oracle properties. J. Am. Statist. Assoc. 101, 1418-29.
30. ZOU, H. & HASTIE, T. J. (2005). Regularization and variable selection via the elastic net. J. R. Statist. Soc. B 67, 301-20. (Pubitemid 40465877)