1h6QSyH

Recommendations

Info

8 Tree-Based Methods In this chapter, we describe tree-based methods for regression and classification. These involve stratifying or segmenting the predictor space into a number of simple regions. In order to make a prediction for a given observation, we typically use the mean or the mode of the training observations in the region to which it belongs. Since the set of splitting rules used to segment the predictor space can be summarized in a tree, these types of approaches are known as decision tree methods. Tree-based methods are simple and useful for interpretation. However, they typically are not competitive with the best supervised learning approaches, such as those seen in Chapters 6 and 7, in terms of prediction accuracy. Hence in this chapter we also introduce bagging, random forests, and boosting. Each of these approaches involves producing multiple trees which are then combined to yield a single consensus prediction. We will see that combining a large number of trees can often result in dramatic improvements in prediction accuracy, at the expense of some loss in interpretation. decision tree 8.1 The Basics of Decision Trees Decision trees can be applied to both regression and classification problems. We first consider regression problems, and then move on to classification. G. James et al., An Introduction to Statistical Learning: with Applications in R, Springer Texts in Statistics 103, DOI 10.1007/978-1-4614-7138-7 8, © Springer Science+Business Media New York 2013 303
304 8. Tree-Based Methods Years < 4.5 | 5.11 Hits < 117.5 6.00 6.74 FIGURE 8.1. For the Hitters data, a regression tree for predicting the log salary of a baseball player, based on the number of years that he has played in the major leagues and the number of hits that he made in the previous year. At a given internal node, the label (of the form X j
Page 1 and 2:
Springer Texts in Statistics Gareth
Page 4 and 5:
Gareth James • Daniela Witten •
Page 6:
To our parents: Alison and Michael
Page 9 and 10:
viii Preface disciplines who wish t
Page 11 and 12:
x Contents 3 Linear Regression 59 3
Page 13 and 14:
xii Contents 6.6 Lab 2: Ridge Regre
Page 15 and 16:
xiv Contents 10.5 Lab 2: Clustering
Page 17 and 18:
2 1. Introduction Wage 50 100 200 3
Page 19 and 20:
4 1. Introduction Predicted Probabi
Page 21 and 22:
6 1. Introduction of least squares,
Page 23 and 24:
8 1. Introduction in order to contr
Page 25 and 26:
10 1. Introduction In general, we w
Page 27 and 28:
12 1. Introduction of A and B is de
Page 29 and 30:
14 1. Introduction Name Auto Boston
Page 31 and 32:
16 2. Statistical Learning Sales 5
Page 33 and 34:
18 2. Statistical Learning Income Y
Page 35 and 36:
20 2. Statistical Learning In this
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
26 2. Statistical Learning additive
Page 43 and 44:
28 2. Statistical Learning tistical
Page 45 and 46:
30 2. Statistical Learning where ˆ
Page 47 and 48:
32 2. Statistical Learning We now m
Page 49 and 50:
34 2. Statistical Learning Y −10
Page 51 and 52:
36 2. Statistical Learning 0.0 0.5
Page 53 and 54:
38 2. Statistical Learning o o o o
Page 55 and 56:
40 2. Statistical Learning o o o o
Page 57 and 58:
42 2. Statistical Learning Error Ra
Page 59 and 60:
44 2. Statistical Learning The matr
Page 61 and 62:
46 2. Statistical Learning We will
Page 63 and 64:
48 2. Statistical Learning [3,] 3 7
Page 65 and 66:
50 2. Statistical Learning > plot(c
Page 67 and 68:
52 2. Statistical Learning 2.4 Exer
Page 69 and 70:
54 2. Statistical Learning (b) What
Page 71 and 72:
56 2. Statistical Learning 9. This
Page 74 and 75:
3 Linear Regression This chapter is
Page 76 and 77:
3.1 Simple Linear Regression 3.1 Si
Page 78 and 79:
3.1 Simple Linear Regression 63 3 2
Page 80 and 81:
3.1 Simple Linear Regression 65 con
Page 82 and 83:
3.1 Simple Linear Regression 67 In
Page 84 and 85:
Quantity Value Residual standard er
Page 86 and 87:
3.2 Multiple Linear Regression 71 a
Page 88 and 89:
3.2 Multiple Linear Regression 73 Y
Page 90 and 91:
3.2 Multiple Linear Regression 75 T
Page 92 and 93:
3.2 Multiple Linear Regression 77 w
Page 94 and 95:
3.2 Multiple Linear Regression 79 i
Page 96 and 97:
3.2 Multiple Linear Regression 81 S
Page 98 and 99:
3.3 Other Considerations in the Reg
Page 100 and 101:
x i = 3.3 Other Considerations in t
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
3.4 The Marketing Plan 103 units wh
Page 120 and 121:
y x 2 y x 2 3.5 Comparison of Linea
Page 122 and 123:
3.5 Comparison of Linear Regression
Page 124 and 125:
3.6 Lab: Linear Regression 109 p=1
Page 126 and 127:
3.6 Lab: Linear Regression 111 Coef
Page 128 and 129:
3.6 Lab: Linear Regression 113 > pl
Page 130 and 131:
3.6 Lab: Linear Regression 115 > lm
Page 132 and 133:
3.6 Lab: Linear Regression 117 > lm
Page 134 and 135:
3.6 Lab: Linear Regression 119 Shel
Page 136 and 137:
3.7 Exercises 121 (b) Answer (a) us
Page 138 and 139:
3.7 Exercises 123 10. This question
Page 140 and 141:
3.7 Exercises 125 (d) Create a scat
Page 142 and 143:
4 Classification The linear regress
Page 144 and 145:
4.2 Why Not Linear Regression? 129
Page 146 and 147:
4.3 Logistic Regression 131 0 500 1
Page 148 and 149:
4.3 Logistic Regression 133 β 1 do
Page 150 and 151:
4.3 Logistic Regression 135 Coeffic
Page 152 and 153:
4.3 Logistic Regression 137 Default
Page 154 and 155:
4.4 Linear Discriminant Analysis 13
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
4.5 A Comparison of Classification
Page 168 and 169:
4.5 A Comparison of Classification
Page 170 and 171:
4.6 Lab: Logistic Regression, LDA,
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
4.7 Exercises 169 we will use obser
Page 186 and 187:
Applied 4.7 Exercises 171 10. This
Page 188:
4.7 Exercises 173 return(result) Th
Page 191 and 192:
176 5. Resampling Methods 5.1 Cross
Page 193 and 194:
178 5. Resampling Methods Mean Squa
Page 195 and 196:
180 5. Resampling Methods LOOCV 10
Page 197 and 198:
182 5. Resampling Methods Mean Squa
Page 199 and 200:
184 5. Resampling Methods has highe
Page 201 and 202:
186 5. Resampling Methods Error Rat
Page 203 and 204:
188 5. Resampling Methods Y −2
Page 205 and 206:
190 5. Resampling Methods Obs X Y Z
Page 207 and 208:
192 5. Resampling Methods > mean((m
Page 209 and 210:
194 5. Resampling Methods first is
Page 211 and 212:
196 5. Resampling Methods Next, we
Page 213 and 214:
198 5. Resampling Methods (f) When
Page 215 and 216:
200 5. Resampling Methods predict.g
Page 218 and 219:
6 Linear Model Selection and Regula
Page 220 and 221:
6.1 Subset Selection 205 6.1 Subset
Page 222 and 223:
6.1 Subset Selection 207 p = 20, th
Page 224 and 225:
6.1 Subset Selection 209 #Variables
Page 226 and 227:
6.1 Subset Selection 211 C p 10000
Page 228 and 229:
6.1 Subset Selection 213 will lead
Page 230 and 231:
6.2 Shrinkage Methods 215 obvious w
Page 232 and 233:
6.2 Shrinkage Methods 217 regressio
Page 234 and 235:
6.2 Shrinkage Methods 219 discussed
Page 236 and 237:
6.2 Shrinkage Methods 221 respectiv
Page 238 and 239:
6.2 Shrinkage Methods 223 Mean Squa
Page 240 and 241:
6.2 Shrinkage Methods 225 To simpli
Page 242 and 243:
6.2 Shrinkage Methods 227 (β j ) 0
Page 244 and 245:
6.3 Dimension Reduction Methods 229
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
6.4 Considerations in High Dimensio
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
6.5 Lab 1: Subset Selection Methods
Page 262 and 263:
Page 264 and 265:
Page 266 and 267: 6.6 Lab 2: Ridge Regression and the
Page 272 and 273: 6.7 Lab 3: PCR and PLS Regression 2
Page 274 and 275: 6.8 Exercises 259 final seven-compo
Page 276 and 277: 6.8 Exercises 261 (a) As we increas
Page 278 and 279: 6.8 Exercises 263 (d) Repeat (c), u
Page 280 and 281: 7 Moving Beyond Linearity So far in
Page 282 and 283: || 7.1 Polynomial Regression 267 De
Page 284 and 285: || 7.2 Step Functions 269 Piecewise
Page 286 and 287: 7.4 Regression Splines 271 7.4 Regr
Page 288 and 289: 7.4 Regression Splines 273 plot is
Page 290 and 291: 7.4 Regression Splines 275 Natural
Page 292 and 293: 7.5 Smoothing Splines 277 Wage 50 1
Page 294 and 295: 7.5 Smoothing Splines 279 to the nu
Page 296 and 297: 7.6 Local Regression 281 Local Regr
Page 298 and 299: 7.7 Generalized Additive Models 283
Page 300 and 301: 7.7 Generalized Additive Models 285
Page 302 and 303: 7.8 Lab: Non-linear Modeling 287 25
Page 304 and 305: 7.8 Lab: Non-linear Modeling 289 po
Page 306 and 307: 7.8 Lab: Non-linear Modeling 291 po
Page 308 and 309: 7.8.2 Splines 7.8 Lab: Non-linear M
Page 310 and 311: 7.8 Lab: Non-linear Modeling 295 In
Page 312 and 313: 7.9 Exercises 297 It is easy to see
Page 314 and 315: 7.9 Exercises 299 5. Consider two c
Page 316: 7.9 Exercises 301 (a) Generate a re
Page 321 and 322: 306 8. Tree-Based Methods have been
Page 323 and 324: 308 8. Tree-Based Methods R5 R2 t4
Page 325 and 326: 310 8. Tree-Based Methods Years < 4
Page 327 and 328: 312 8. Tree-Based Methods E =1− m
Page 329 and 330: 314 8. Tree-Based Methods Figure 8.
Page 331 and 332: 316 8. Tree-Based Methods ▼ Unfor
Page 333 and 334: 318 8. Tree-Based Methods Error 0.1
Page 335 and 336: 320 8. Tree-Based Methods 8.2.2 Ran
Page 337 and 338: 322 8. Tree-Based Methods of the ot
Page 339 and 340: 324 8. Tree-Based Methods stumps wi
Page 341 and 342: 326 8. Tree-Based Methods > tree.ca
Page 343 and 344: 328 8. Tree-Based Methods Residual
Page 345 and 346: 330 8. Tree-Based Methods The test
Page 347 and 348: 332 8. Tree-Based Methods 8.4 Exerc
Page 349 and 350: 334 8. Tree-Based Methods (e) Use r
Page 352 and 353: 9 Support Vector Machines In this c
Page 354 and 355: 9.1 Maximal Margin Classifier 339 X
Page 356 and 357: 9.1 Maximal Margin Classifier 341 h
Page 358 and 359: 9.1 Maximal Margin Classifier 343 m
Page 360 and 361: 9.2 Support Vector Classifiers 345
Page 362 and 363: 9.2 Support Vector Classifiers 347
Page 364 and 365: 9.3 Support Vector Machines 349 X2
Page 366 and 367: 9.3 Support Vector Machines 351 in
Page 368 and 369:
9.3 Support Vector Machines 353 X2
Page 370 and 371:
9.4 SVMs with More than Two Classes
Page 372 and 373:
9.5 Relationship to Logistic Regres
Page 374 and 375:
9.6 Lab: Support Vector Machines 35
Page 376 and 377:
Page 378 and 379:
Page 380 and 381:
9.6.3 ROC Curves 9.6 Lab: Support V
Page 382 and 383:
Page 384 and 385:
Obs. X 1 X 2 Y 1 3 4 Red 2 2 2 Red
Page 386 and 387:
9.7 Exercises 371 (b) Compute the c
Page 388 and 389:
10 Unsupervised Learning Most of th
Page 390 and 391:
10.2 Principal Components Analysis
Page 392 and 393:
Page 394 and 395:
Page 396 and 397:
Page 398 and 399:
Page 400 and 401:
10.2.4 Other Uses for Principal Com
Page 402 and 403:
10.3 Clustering Methods 387 K=2 K=3
Page 404 and 405:
10.3 Clustering Methods 389 Data St
Page 406 and 407:
10.3 Clustering Methods 391 X2 −2
Page 408 and 409:
10.3 Clustering Methods 393 0.0 0.5
Page 410 and 411:
Algorithm 10.2 Hierarchical Cluster
Page 412 and 413:
10.3 Clustering Methods 397 Average
Page 414 and 415:
10.3 Clustering Methods 399 0 2 4 6
Page 416 and 417:
10.4 Lab 1: Principal Components An
Page 418 and 419:
10.4 Lab 1: Principal Components An
Page 420 and 421:
10.5 Lab 2: Clustering 405 Cluster
Page 422 and 423:
10.6 Lab 3: NCI60 Data Example 407
Page 424 and 425:
Page 426 and 427:
Page 428 and 429:
10.7 Exercises 413 differ: for inst
Page 430 and 431:
10.7 Exercises 415 (b) At a certain
Page 432 and 433:
10.7 Exercises 417 10. In this prob
Page 434 and 435:
Index C p , 78, 205, 206, 210-213 R
Page 436 and 437:
Index 421 Wage, 1, 2, 9, 10, 14, 26
Page 438 and 439:
Index 423 noise, 22, 228 non-linear
Page 440 and 441:
Index 425 read.table(), 48, 49 regs
show all

1h6QSyH

Create successful ePaper yourself

Delete template?

Save as template?