CODEDRAGON ㆍDevelopment/AI
An Introduction to Statistical Learning
http://www-bcf.usc.edu/~gareth/ISL/
http://www-bcf.usc.edu/~gareth/ISL/book.html
목차
Preface vii
1 Introduction 1
2 Statistical Learning 15
2.1 What Is Statistical Learning?. . . . . . 15
2.1.1 Why Estimate f?. . . . . . . . . 17
2.1.2 How Do We Estimate f?. . . . 21
2.1.3 The Trade-Off Between Prediction Accuracy
and Model Interpretability. . . 24
2.1.4 Supervised Versus Unsupervised Learning . . . . . . 26
2.1.5 Regression Versus Classification Problems . . . . . . 28
2.2 AssessingModel Accuracy. . . . . . . . 29
2.2.1 Measuring the Quality of Fit. . 29
2.2.2 The Bias-VarianceTrade-Off. . 33
2.2.3 The Classification Setting. . . . 37
2.3 Lab: Introduction to R. . . . . . . . . . 42
2.3.1 Basic Commands. . . . . . . . . 42
2.3.2 Graphics.. 45
2.3.3 Indexing Data. . . . . . . . . . 47
2.3.4 Loading Data. . . . . . . . . . . 48
2.3.5 Additional Graphical and Numerical Summaries . . 49
2.4 Exercises.. . . . . 52
3 Linear Regression 59
3.1 Simple Linear Regression. . . . . . . . 61
3.1.1 Estimating the Coefficients. . . 61
3.1.2 Assessing the Accuracy of the Coefficient
Estimates.. 63
3.1.3 Assessing the Accuracy of theModel . . . . . . . . . 68
3.2 Multiple Linear Regression. . . . . . . 71
3.2.1 Estimating the Regression Coefficients . . . . . . . . 72
3.2.2 Some Important Questions. . . 75
3.3 Other Considerations in the Regression Model . . . . . . . . 82
3.3.1 Qualitative Predictors. . . . . . 82
3.3.2 Extensions of the LinearModel. 86
3.3.3 Potential Problems. . . . . . . . 92
3.4 TheMarketing Plan. . . . . . . . . . . 102
3.5 Comparison of Linear Regression with K-Nearest
Neighbors.. . . . . 104
3.6 Lab: Linear Regression. . . . . . . . . . 109
3.6.1 Libraries.. . 109
3.6.2 Simple Linear Regression. . . . 110
3.6.3 Multiple Linear Regression. . . 113
3.6.4 Interaction Terms. . . . . . . . 115
3.6.5 Non-linear Transformations of the Predictors . . . . 115
3.6.6 Qualitative Predictors. . . . . . 117
3.6.7 Writing Functions. . . . . . . . 119
3.7 Exercises.. . . . . 120
4 Classification 127
4.1 An Overview of Classification. . . . . . 128
4.2 Why Not Linear Regression?. . . . . . 129
4.3 Logistic Regression.130
4.3.1 The LogisticModel. . . . . . . . 131
4.3.2 Estimating the Regression Coefficients . . . . . . . . 133
4.3.3 Making Predictions. . . . . . . . 134
4.3.4 Multiple Logistic Regression.. . 135
4.3.5 Logistic Regression for >2 Response Classes . . . . . 137
4.4 Linear Discriminant Analysis. . . . . . 138
4.4.1 Using Bayes' Theorem for Classification . . . . . . . 138
4.4.2 Linear Discriminant Analysis for p=1 . . . . . . . . 139
4.4.3 Linear Discriminant Analysis for p >1 . . . . . . . . 142
4.4.4 Quadratic Discriminant Analysis149
4.5 A Comparison of Classification Methods151
4.6 Lab: Logistic Regression, LDA, QDA, and KNN . . . . . . 154
4.6.1 The StockMarket Data. . . . . 154
4.6.2 Logistic Regression. . . . . . . . 156
4.6.3 Linear Discriminant Analysis. . 161
4.6.4 Quadratic Discriminant Analysis163
4.6.5 K-NearestNeighbors. . . . . . . 163
4.6.6 An Application to Caravan Insurance Data . . . . . 165
4.7 Exercises.. . . . . 168
5 Resampling Methods 175
5.1 Cross-Validation.. 176
5.1.1 The Validation Set Approach. . 176
5.1.2 Leave-One-Out Cross-Validation178
5.1.3 k-Fold Cross-Validation. . . . . 181
5.1.4 Bias-Variance Trade-Off for k-Fold
Cross-Validation. . . . . . . . . 183
5.1.5 Cross-Validation on Classification Problems . . . . . 184
5.2 The Bootstrap.. . 187
5.3 Lab: Cross-Validation and the Bootstrap190
5.3.1 The Validation Set Approach. . 191
5.3.2 Leave-One-Out Cross-Validation192
5.3.3 k-Fold Cross-Validation. . . . . 193
5.3.4 The Bootstrap. . . . . . . . . . 194
5.4 Exercises.. . . . . 197
6 Linear Model Selection and Regularization 203
6.1 Subset Selection.. 205
6.1.1 Best Subset Selection. . . . . . 205
6.1.2 Stepwise Selection. . . . . . . . 207
6.1.3 Choosing the OptimalModel. . 210
6.2 ShrinkageMethods.214
6.2.1 Ridge Regression. . . . . . . . . 215
6.2.2 The Lasso.. 219
6.2.3 Selecting the Tuning Parameter. 227
6.3 Dimension ReductionMethods. . . . . 228
6.3.1 Principal Components Regression230
6.3.2 Partial Least Squares. . . . . . 237
6.4 Considerations in High Dimensions. . . 238
6.4.1 High-Dimensional Data. . . . . 238
6.4.2 What Goes Wrong in High Dimensions? . . . . . . . 239
6.4.3 Regression in High Dimensions. 241
6.4.4 Interpreting Results in High Dimensions . . . . . . . 243
6.5 Lab 1: Subset Selection Methods. . . . 244
6.5.1 Best Subset Selection. . . . . . 244
6.5.2 Forward and Backward Stepwise Selection . . . . . . 247
6.5.3 Choosing Among Models Using the Validation
Set Approach and Cross-Validation . . . . . . . . . . 248
6.6 Lab 2: Ridge Regression and the Lasso. 251
6.6.1 Ridge Regression. . . . . . . . . 251
6.6.2 The Lasso.. 255
6.7 Lab 3: PCR and PLS Regression. . . . 256
6.7.1 Principal Components Regression256
6.7.2 Partial Least Squares. . . . . . 258
6.8 Exercises.. . . . . 259
7 Moving Beyond Linearity 265
7.1 PolynomialRegression. . . . . . . . . . 266
7.2 Step Functions.. . 268
7.3 Basis Functions.. . 270
7.4 Regression Splines.271
7.4.1 Piecewise Polynomials. . . . . . 271
7.4.2 Constraints and Splines. . . . . 271
7.4.3 The Spline Basis Representation273
7.4.4 Choosing the Number and Locations
of the Knots. . . . . . . . . . . 274
7.4.5 Comparison to Polynomial Regression . . . . . . . . 276
7.5 Smoothing Splines.277
7.5.1 An Overview of Smoothing Splines . . . . . . . . . . 277
7.5.2 Choosing the Smoothing Parameter λ . . . . . . . . 278
7.6 Local Regression.. 280
7.7 Generalized AdditiveModels. . . . . . 282
7.7.1 GAMs for Regression Problems. 283
7.7.2 GAMs for Classification Problems . . . . . . . . . . 286
7.8 Lab: Non-linearModeling. . . . . . . . 287
7.8.1 Polynomial Regression and Step Functions . . . . . 288
7.8.2 Splines.. . . 293
7.8.3 GAMs.. . . 294
7.9 Exercises.. . . . . 297
8 Tree-Based Methods 303
8.1 The Basics of Decision Trees. . . . . . 303
8.1.1 Regression Trees. . . . . . . . . 304
8.1.2 Classification Trees. . . . . . . . 311
8.1.3 Trees Versus LinearModels. . . 314
8.1.4 Advantages and Disadvantages of Trees . . . . . . . 315
8.2 Bagging, Random Forests, Boosting. . 316
8.2.1 Bagging.. . 316
8.2.2 Random Forests. . . . . . . . . 320
8.2.3 Boosting.. . 321
8.3 Lab: Decision Trees.324
8.3.1 Fitting Classification Trees. . . 324
8.3.2 Fitting RegressionTrees. . . . . 327
8.3.3 Bagging and Random Forests. . 328
8.3.4 Boosting.. . 330
8.4 Exercises.. . . . . 332
9 Support Vector Machines 337
9.1 MaximalMargin Classifier. . . . . . . . 338
9.1.1 What Is a Hyperplane?. . . . . 338
9.1.2 Classification Using a Separating Hyperplane . . . . 339
9.1.3 TheMaximalMargin Classifier. 341
9.1.4 Construction of the Maximal Margin Classifier . . . 342
9.1.5 The Non-separable Case. . . . . 343
9.2 Support Vector Classifiers. . . . . . . . 344
9.2.1 Overview of the Support Vector Classifier . . . . . . 344
9.2.2 Details of the Support Vector Classifier . . . . . . . 345
9.3 Support Vector Machines. . . . . . . . 349
9.3.1 Classification with Non-linear Decision
Boundaries.349
9.3.2 The Support Vector Machine. . 350
9.3.3 An Application to the Heart Disease Data . . . . . . 354
9.4 SVMs withMore than Two Classes. . . 355
9.4.1 One-Versus-One Classification.. 355
9.4.2 One-Versus-All Classification. . 356
9.5 Relationship to Logistic Regression. . . 356
9.6 Lab: Support Vector Machines. . . . . 359
9.6.1 Support Vector Classifier. . . . 359
9.6.2 Support Vector Machine. . . . . 363
9.6.3 ROC Curves. . . . . . . . . . . 365
9.6.4 SVMwithMultiple Classes. . . 366
9.6.5 Application to Gene Expression Data . . . . . . . . 366
9.7 Exercises.. . . . . 368
10 Unsupervised Learning 373
10.1 The Challenge of Unsupervised Learning373
10.2 Principal Components Analysis. . . . . 374
10.2.1 What Are Principal Components? . . . . . . . . . . 375
10.2.2 Another Interpretation of Principal Components . . 379
10.2.3 More on PCA. . . . . . . . . . . 380
10.2.4 Other Uses for Principal Components . . . . . . . . 385
10.3 ClusteringMethods.385
10.3.1 K-Means Clustering. . . . . . . 386
10.3.2 Hierarchical Clustering. . . . . . 390
10.3.3 Practical Issues in Clustering. . 399
10.4 Lab 1: Principal Components Analysis. 401
10.5 Lab 2: Clustering.. 404
10.5.1 K-Means Clustering. . . . . . . 404
10.5.2 Hierarchical Clustering. . . . . . 406
10.6 Lab 3: NCI60 Data Example. . . . . . 407
10.6.1 PCA on the NCI60 Data. . . . 408
10.6.2 Clustering the Observations of the NCI60 Data . . . 410
10.7 Exercises.. . . . . 413
Index 419
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