18 High-Dimensional Problems: p À
N 649
18.2 Diagonal Linear Discriminant Analysis
and Nearest Shrunken Centroids 651
18.3 Linear Classi¯ers with Quadratic Regularization 654
18.3.1 Regularized Discriminant Analysis 656
18.3.2 Logistic Regression
with Quadratic Regularization 657
18.3.3 The Support Vector Classi¯er 657
18.3.4 Feature Selection 658
18.3.5 Computational Shortcuts When p À
N 659
18.4 Linear Classi¯ers with L1 Regularization 661
18.4.1 Application of Lasso
to Protein Mass Spectroscopy 664
18.4.2 The Fused Lasso for Functional Data 666
18.5 Classi¯cation When Features are Unavailable 668
18.5.1 Example: String Kernels
and Protein Classi¯cation 668
18.5.2 Classi¯cation and Other Models Using
Inner-Product Kernels and Pairwise Distances 670
18.5.3 Example: Abstracts Classi¯cation 672
18.6 High-Dimensional Regression:
Supervised Principal Components 674
18.6.1 Connection to Latent-Variable Modeling 678
18.6.2 Relationship with Partial Least Squares 680
18.6.3 Pre-Conditioning for Feature Selection 681
18.7 Feature Assessment and the Multiple-Testing Problem 683
18.7.1 The False Discovery Rate 687
18.7.2 Asymmetric Cutpoints and the SAM Procedure 690
18.7.3 A Bayesian Interpretation of the FDR 692
18.8 Bibliographic Notes 693
Exercises 694
References 699
Author Index 729
Index 737

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