An introduction to statistical learning: with applications in R
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2013
|
| Series: | Springer texts in statistics
103 |
| Subjects: | |
| Online Access: | Volltext Volltext Inhaltsverzeichnis Klappentext |
| Physical Description: | XIV, 426 S. graph. Darst. |
| ISBN: | 9781461471370 1461471370 9781461471387 |
| DOI: | 10.25334/Q4HT55 |
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| 245 | 1 | 0 | |a An introduction to statistical learning |b with applications in R |c Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani |
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Contents
Preface
vii
1
Introduction
1
2
Statistical Learning
15
2.1
What Is Statistical Learning?
. 15
2.1.1
Why Estimate
ƒ?. 17
2.1.2
How Do We Estimate
ƒ? . 21
2.1.3
The Trade-Off Between Prediction Accuracy
and Model Interpretabilitv
. 24
2.1.4
Supervised Versus Unsupervised Learning
. 26
2.1.5
Regression Versus Classification Problems
. 28
2.2
Assessing Model Accuracy
. 29
2.2.1
Measuring the Quality of Fit
. 29
2.2.2
The Bias-Variance Trade-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
IX
Contents
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 the Model
. 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 Linear Model
. 86
3.3.3
Potential Problems
. 92
3.4
The Marketing Plan
. 102
3.5
Comparison of Linear Regression with /"("-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
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 Logistic Model
. 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
ρ
= 1. 139
4.4.3
Linear Discriminant Analysis for
ρ >1
. 142
4.4.4
Quadratic Discriminant Analysis
. 149
4.5
A Comparison of Classification Methods
. 151
4.6
Lab: Logistic Regression, LDA. QDA. and KNN
. 154
4.6.1
The Stock Market Data
. 154
4.6.2
Logistic Regression
. 156
4.6.3
Linear Discriminant Analysis
. 161
Contents xi
4.6.4
Quadratic Discriminant Analysis
. 162
4.6.5
/C-Nearest Neighbors
. 163
4.6.6
An Application to Caravan Insurance Data
. 164
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-Validation
. 178
5.1.3
Äľ-Fold
Cross-Validation
. 181
5.1.4
Bias-Variance Trade-Off for ¿--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 Bootstrap
. 190
5.3.1
The Validation Set Approach
. 191
5.3.2
Leave-Onc-Out Cross-
Validat
ion
. 192
5.3.3
¿--Fold Cross-Validation
. 193
5.3.4
The Bootstrap
. 194
5.4
Exercises
. 197
6
Linear Model Selection and
Regularizat
io
n
203
6.1
Subset Selection
. 205
6.1.1
Best Subset Selection
. 205
6.1.2
Stepwise Selection
. 207
6.1.3
Choosing the Optimal Model
. 210
6.2
Shrinkage Methods
. 214
6.2.1
Ridge Regression
. 215
6.2.2
The Lasso
. 219
6.2.3
Selecting the Tuning Parameter
. 227
6.3
Dimension Reduction Methods
. 228
6.3.1
Principal Components Regression
. 230
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
xii Contents
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
Regression. 256
6.7.2
Partial Least
Squares . 258
6.8
Exercises .
259
7
Moving Beyond Linearity
265
7.1
Polynomial Regression
. 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 Representation
. 273
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 A
. 278
7.6
Local Regression
. 280
7.7
Generalized Additive Models
. 282
7.7.1
GAMs for Regression Problems
. 283
7.7.2
GAMs for Classification Problems
. 286
7.8
Lab: Non-linear Modeling
. 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 Linear Models
. 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 Regression Trees
. 327
Contents xiii
8.3.3
Bagging and Random Forests
. 328
8.3.4
Boosting
. 330
8.4
Exercises
. 332
9
Support Vector Machines
337
9.1
Maximal Margin Classifier
. 338
9.1.1
What
Isa
Hyperplane?
. 338
9.1.2
Classification Using a Separating Hyperplane
. 339
9.1.3
The Maximal Margin 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
. 3 15
9.3
Support Vector Machines
. 349
9.3.1
Classification with Non-linear Decision
Boundaries
. 319
9.3.2
The Support Vector Machine
. 350
9.3.3
An Application to the Heart Disease Data
. 354
9.4
SVMs with More than Two Classes
. 355
9.4.1
One-Versus-Om1 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
SVM with Multiple 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 Learning
. 373
10.2
Principal Components Analysis
. 374
10.2.1
W
hat 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
Clustering Methods
. 385
10.3.1
A'-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
xiv Contents
10.5 Lab 2:
Clustering.
404
10.5.1
tf
-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
Springer
Texts in Statistics
Gareth James
·
Daniela
Witten
·
Trevor
Hastie
■
Robert Tibshirani
An Introduction to Statistical Learning
with Applications in
R
An Introduction to Statistical Learning provides an accessible overview of the field
of statistical learning, an essential toolset for making sense of the vast and complex
data sets that have emerged in fields ranging from biology to finance to marketing to
astrophysics in the past twenty years. This book presents some of the most important
modeling and prediction techniques, along with relevant applications. Topics include
linear regression» classification, resampling methods, shrinkage approaches, tree-based
methods, support vector machines, clustering, and more. Color graphics and real-world
examples are used to illustrate the methods presented. Since the goal of this textbook
is to facilitate the use of these statistical learning techniques by practitioners in sci¬
ence, industry, and other fields, each chapter contains a tutorial on implementing the
analyses and methods presented in R, an extremely popular open source statistical
software platform.
Two of the authors co-wrote The Elements of Statistical Learning
(Hastie,
Tibshirani
and Friedman,
2nd
edition
2009),
a popular reference book for statistics and machine
learning researchers. An Introduction to Statistical Learning covers many of the same
topics, but at a level accessible to a much broader audience. This book is targeted at
statisticians and non-statisticians alike who wish to use cutting-edge statistical learn¬
ing techniques to analyze their data. The text assumes only a previous course in linear
regression and no knowledge of matrix algebra.
Gareth James is a professor of statistics at University of Southern California. He has
published an extensive body of methodological work in the domain of statistical learn
ing with particular emphasis on high-dimensional and functional data. The conceptual
framework for this book grew out of his MBA elective courses in this area.
Daniela
Witten
is an assistant professor of biostatistics at University of Washington. Her
research focuses largely on high-dimensional statistical machine learning. She has
contributed to the translation of statistical learning techniques to the field of genomics,
through collaborations and as a member of the Institute of Medicine committee that
led to the report Evolution ofTranslational Omics.
Trevor
Hastie
and Robert Tibshirani are professors of statistics at Stanford University, and
are co-authors of the successful textbook Elements of Statistical Learning.
Hastie
and
Tibshirani developed generalized additive models and wrote a popular book of that
title.
Hastie
co-developed much of the statistical modeling software and environment
in R/S-PLUS and invented principal curves and surfaces. Tibshirani proposed the lasso
and is co-author of the very successful An Introduction to the Bootstrap. |
| any_adam_object | 1 |
| author | James, Gareth Witten, Daniela Hastie, Trevor 1953- Tibshirani, Robert 1956- |
| author_GND | (DE-588)1038457327 (DE-588)108120849X (DE-588)172128242 (DE-588)172417740 |
| author_facet | James, Gareth Witten, Daniela Hastie, Trevor 1953- Tibshirani, Robert 1956- |
| author_role | aut aut aut aut |
| author_sort | James, Gareth |
| author_variant | g j gj d w dw t h th r t rt |
| building | Verbundindex |
| bvnumber | BV040957415 |
| classification_rvk | MR 2100 QH 740 SK 830 SK 840 |
| classification_tum | DAT 307f MAT 620f |
| collection | ebook |
| ctrlnum | (OCoLC)859368384 (DE-599)BVBBV040957415 |
| discipline | Informatik Soziologie Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.25334/Q4HT55 |
| format | Book |
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV040957415 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T06:22:20Z |
| institution | BVB |
| isbn | 9781461471370 1461471370 9781461471387 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025935833 |
| oclc_num | 859368384 |
| open_access_boolean | 1 |
| owner | DE-91 DE-BY-TUM DE-521 DE-29 DE-20 DE-384 DE-11 DE-M49 DE-BY-TUM DE-945 DE-1051 DE-355 DE-BY-UBR DE-2070s DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-521 DE-29 DE-20 DE-384 DE-11 DE-M49 DE-BY-TUM DE-945 DE-1051 DE-355 DE-BY-UBR DE-2070s DE-188 |
| physical | XIV, 426 S. graph. Darst. |
| psigel | ebook |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Springer texts in statistics |
| series2 | Springer texts in statistics |
| spelling | James, Gareth Verfasser (DE-588)1038457327 aut An introduction to statistical learning with applications in R Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani New York [u.a.] Springer 2013 XIV, 426 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics 103 R Programm (DE-588)4705956-4 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s R Programm (DE-588)4705956-4 s DE-604 Maschinelles Lernen (DE-588)4193754-5 s 2\p DE-604 Witten, Daniela Verfasser (DE-588)108120849X aut Hastie, Trevor 1953- Verfasser (DE-588)172128242 aut Tibshirani, Robert 1956- Verfasser (DE-588)172417740 aut Erscheint auch als Online-Ausgabe 10.25334/Q4HT55 Springer texts in statistics 103 (DE-604)BV041299084 103 https://doi.org/10.25334/Q4HT55 Verlag kostenfrei Volltext https://qubeshub.org/publications/847/serve/1/2569?el=3&download=1 Verlag kostenfrei Volltext Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025935833&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025935833&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | James, Gareth Witten, Daniela Hastie, Trevor 1953- Tibshirani, Robert 1956- An introduction to statistical learning with applications in R Springer texts in statistics R Programm (DE-588)4705956-4 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4193754-5 (DE-588)4056995-0 (DE-588)4151278-9 |
| title | An introduction to statistical learning with applications in R |
| title_auth | An introduction to statistical learning with applications in R |
| title_exact_search | An introduction to statistical learning with applications in R |
| title_full | An introduction to statistical learning with applications in R Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani |
| title_fullStr | An introduction to statistical learning with applications in R Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani |
| title_full_unstemmed | An introduction to statistical learning with applications in R Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani |
| title_short | An introduction to statistical learning |
| title_sort | an introduction to statistical learning with applications in r |
| title_sub | with applications in R |
| topic | R Programm (DE-588)4705956-4 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | R Programm Maschinelles Lernen Statistik Einführung |
| url | https://doi.org/10.25334/Q4HT55 https://qubeshub.org/publications/847/serve/1/2569?el=3&download=1 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025935833&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025935833&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV041299084 |
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