Feature Augmentation via Nonparametrics and Selection (FANS) in High-Dimensional Classification

REFERENCES

• Ackermann, M., and Strimmer, K. (2009), “A General Modular Framework for Gene Set Enrichment Analysis,” BMC Bioinformatics, 10, 1471–2105.
   Web of Science ®Google Scholar
• Antoniadis, A., Lambert-Lacroix, S., and Leblanc, F. (2003), “Effective Dimension Reduction Methods for Tumor Classification Using Gene Expression Data,” Bioinformatics, 19, 563–570.
   PubMed Web of Science ®Google Scholar
• Bair, E., Hastie, T., Paul, D., and Tibshirani, R. (2006), “Prediction by Supervised Principal Components,” Journal of American Statistical Association, 101, 119–137.
   Web of Science ®Google Scholar
• Bickel, P.J., and 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.
   Web of Science ®Google Scholar
• Boulesteix, A.-L. (2004), “PLS Dimension Reduction for Classification With Microarray Data,” Statistical Applications in Genetics and Molecular Biology
   PubMed Web of Science ®Google Scholar
• Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32.
   Web of Science ®Google Scholar
• Bühlmann, P., and van de Geer, S. (2011), Statistics for High-Dimensional Data, New York: Springer.
   Google Scholar
• Cai, T., and Liu, W. (2011), “A Direct Estimation Approach to Sparse Linear Discriminant Analysis,” Journal of American Statistical Association, 106, 1566–1577.
   Web of Science ®Google Scholar
• Clemmensen, L., Hastie, T., Witten, D., and Ersboll, B. (2011), “Sparse Discriminant Analysis,” Technometrics, 53, 406–413.
   Web of Science ®Google Scholar
• Dudoit, S., Fridlyand, J., and Speed, T.P. (2002), “Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data,” Journal of American Statistical Association, 97, 77–87.
   Web of Science ®Google Scholar
• Fan, J., and Fan, Y. (2008), “High-Dimensional Classification Using Features Annealed Independence Rules,” Annals of Statistics, 36, 2605–2637.
   PubMed Web of Science ®Google Scholar
• Fan, J., Feng, Y., and Song, R. (2011), “Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models,” Journal of American Statistical Association, 106, 544–557.
   PubMed Web of Science ®Google Scholar
• Fan, J., Feng, Y., and Tong, X. (2012), “A Road to Classification in High Dimensional Space: The Regularized Optimal Affine Discriminant,” Journal of the Royal Statistical Society, Series B, 74, 745–771.
   Google Scholar
• Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties,” Journal of American Statistical Association, 96, 1348–1360.
   Web of Science ®Google Scholar
• Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultrahigh Dimensional Feature Space” ( with discussion), Journal of the Royal Statistical Society, Series B, 70, 849–911.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., Höfling, H., and Tibshirani, R. (2007), “Pathwise Coordinate Optimization,” Annals of Applied Statistics, 1, 302–332.
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Fu, W.J., Carroll, R.J., and Wang, S. (2005), “Estimating Misclassification Error With Small Samples via Bootstrap Cross-Validation,” Bioinformatics, 21, 1979–1986.
   PubMed Web of Science ®Google Scholar
• Gordon, G.J., Jensen, R.V., Hsiao, L.-L., Gullans, S.R., Blumenstock, J.E., Ramaswamy, S., Richards, W.G., Sugarbaker, D.J., and Bueno, R. (2002), “Translation of Microarray Data Into Clinically Relevant Cancer Diagnostic Tests Using Gene Expression Ratios in Lung Cancer and Mesothelioma,” Cancer Research, 62, 4963–4967.
   PubMed Web of Science ®Google Scholar
• Guo, Y., Hastie, T., and Tibshirani, R. (2007), “Regularized Linear Discriminant Analysis and its Application in Microarrays,” Biostatistics, 8, 86–100.
   PubMed Web of Science ®Google Scholar
• Hastie, T., and Tibshirani, R. (1990), Generalized Addtive Models, London: Chapman & Hall/CRC.
   Google Scholar
• Hastie, T., Tibshirani, R., and Friedman, J.H. (2009), The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.), New York: Springer-Verlag Inc.
   Google Scholar
• Huang, P. W.X. (2003), “Linear Regression and Two-Class Classification With Gene Expression Data,” Bioinformatics, 19, 2072–2978.
   PubMed Web of Science ®Google Scholar
• Li, K.-C. (1991), “Sliced Inverse Regression for Dimension Reduction” ( with discussion), Journal of American Statistical Association, 86, 316–342
   Web of Science ®Google Scholar
• Mai, Q., Zou, H., and Yuan, M. (2012), “A Direct Approach to Sparse Discriminant Analysis in Ultra-High Dimensions,” Biometrika, 99, 29–42.
   Web of Science ®Google Scholar
• Meier, L., Geer, V., and Bühlmann, P. (2009), “High-Dimensional Additive Modeling,” Annals of Statistics, 37, 3779–3821.
   Web of Science ®Google Scholar
• Nguyen, D.V., and Rocke, D.M. (2002), “Tumor Classification by Partial Least Squares Using Microarray Gene Expression Data,” Bioinformatics, 18, 39–50.
   PubMed Web of Science ®Google Scholar
• Polonik, W. (1995), “Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass Approach,” Annals of Statistics, 23, 855–881.
   Web of Science ®Google Scholar
• Raykar, V., Duraiswami, R., and Zhao, L. (2010), “Fast Computation of Kernel Estimators,” Journal of Computational and Graphical Statistics, 19, 205–220.
   Web of Science ®Google Scholar
• Shao, J., Wang, Y., Deng, X., and Wang, S. (2011), “Sparse Linear Discriminant Analysis by Thresholding for High Dimensional Data,” Annals of Statistics, 39, 1241–1265.
   Web of Science ®Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• Tong, X. (2013), “A Plug-in Approach to Anomaly Detection,” Journal of Machine Learning Research, 14, 3011–3040.
   Web of Science ®Google Scholar
• Tsybakov, A. (2004), “Optimal Aggregation of Classifiers in Statistical Learning,” Annals of Statistics, 32, 135–166.
   Web of Science ®Google Scholar
• Geer, S. (2008), “High-Dimensional Generalized Linear Models and the Lasso,” Annals of Statistics, 36, 614–645.
   Web of Science ®Google Scholar
• Witten, D., and Tibshirani, R. (2012), “Penalized Classification Using Fisher’s Linear Discriminant,” Journal of the Royal Statistical Society, Series B, 73, 753–772.
   Google Scholar
• Wu, M.C., Zhang, L., Wang, Z., Christiani, D.C., and Lin, X. (2009), “Sparse Linear Discriminant Analysis for Simultaneous Testing for the Significance of a Gene Set/Pathway and Gene Selection,” Bioinformatics, 25, 1145–1151.
   PubMed Web of Science ®Google Scholar
• Zhang, C.-H. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” Annals of Statistics, 38, 894–942
   Web of Science ®Google Scholar
• Zhang, C.-H., and Huang, J. (2008), “The Sparsity and Bias of the LASSO Selection in High-Dimensional Linear Regression,” Annals of Statistics, 36, 1567–1594.
   Web of Science ®Google Scholar
• Zhao, P., and Yu, B. (2006), “On Model Selection Consistency of Lasso,” Journal of Machine Learning Research, 7, 2541–2563
   Web of Science ®Google Scholar
• Zou, H. (2006), “The Adaptive Lasso and its Oracle Properties,” Journal of American Statistical Association, 101, 1418–1429
   Web of Science ®Google Scholar
• Zou, H., Hastie, T., and Tibshirani, R. (2006), “Sparse Principal Component Analysis,” Journal of Computational and Graphical Statistics, 15, 265–286.
   Web of Science ®Google Scholar