statlearn - Notes on Statistical Learning John I. Marden...

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Unformatted text preview: Notes on Statistical Learning John I. Marden Copyright 2006 2 Contents 1 Introduction 5 2 Linear models 7 2.1 Good predictions: Squared error loss and in-sample error . . . . . . . . . . . 8 2.2 Matrices and least-squares estimates . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Mean vectors and covariance matrices . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Prediction using least-squares . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Subset selection and Mallows’ C p . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5.1 Estimating the in-sample errors . . . . . . . . . . . . . . . . . . . . . 15 2.5.2 Finding the best subset . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5.3 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.6 Regularization: Ridge regression . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.6.1 Estimating the in-sample errors . . . . . . . . . . . . . . . . . . . . . 24 2.6.2 Finding the best λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6.3 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.7 Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.7.1 Estimating the in-sample errors . . . . . . . . . . . . . . . . . . . . . 33 2.7.2 Finding the best λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.7.3 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 Linear Predictors of Non-linear Functions 39 3.1 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.1 Leave-one-out cross-validation . . . . . . . . . . . . . . . . . . . . . . 48 3.1.2 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.1.3 The cross-validation estimate . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Sines and cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.2.1 Estimating σ 2 e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2.2 Cross-validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.3 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3 Local fitting: Regression splines . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.3.1 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.4 Smoothing splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3 4 CONTENTS 3.4.1 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.4.2 An interesting result . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.5 A glimpse of wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.5.1 Haar wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.5.2 An example of another set of wavelets . . . . . . . . . . . . . . . . . 91 3.5.3 Example Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Example Using R ....
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This note was uploaded on 02/27/2012 for the course STATS 315A taught by Professor Tibshirani,r during the Spring '10 term at Stanford.

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statlearn - Notes on Statistical Learning John I. Marden...

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