Understanding machine learning: from theory to algorithms
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Cambrige University Press
[2014]
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027241732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | xvi, 397 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107057135 |
Internformat
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Titel: Understanding machine learning
Autor: Shalev-Shwartz, Shai
Jahr: 2014
Contents
Preface page xv
1 Introduction 1
1.1 What Is Learning? 1
1.2 When Do We Need Machine Learning? 3
1.3 Types of Learning 4
1.4 Relations to Other Fields 6
1.5 How to Read This Book 7
1.6 Notation 8
Part 1 Foundations
2 A Gentle Start 13
2.1 A Formal Model - The Statistical Learning Framework 13
2.2 Empirical Risk Minimization 15
2.3 Empirical Risk Minimization with Inductive Bias 16
2.4 Exercises 20
3 A Formal Learning Model 22
3.1 PAC Learning 22
3.2 A More General Learning Model 23
3.3 Summary 28
3.4 Bibliographic Remarks 28
3.5 Exercises 28
4 Learning via Uniform Convergence 31
4.1 Uniform Convergence Is Sufficient for Learnability 31
4.2 Finite Classes Are Agnostic PAC Learnable 32
4.3 Summary 34
4.4 Bibliographic Remarks 35
4.5 Exercises 35
vii
viiì Contents
5 The Bias-Complexity Trade-off 36
5.1 The No-Free-Lunch Theorem 37
5.2 Error Decomposition 40
5.3 Summary 41
5.4 Bibliographic Remarks 41
5.5 Exercises 41
6 The VC-Dimension 43
6.1 Infinite-Size Classes Can Be Learnable 43
6.2 The VC-Dimension 44
6.3 Examples 46
6.4 The Fundamental Theorem of PAC Learning 48
6.5 Proof of Theorem 6.7 49
6.6 Summary 53
6.7 Bibliographic Remarks 53
6.8 Exercises 54
7 Nonuniform Learnability 58
7.1 Nonuniform Learnability 58
7.2 Structural Risk Minimization 60
7.3 Minimum Description Length and Occam's Razor 63
7.4 Other Notions of Learnability - Consistency 66
7.5 Discussing the Different Notions of Learnability 67
7.6 Summary 70
7.7 Bibliographic Remarks 70
7.8 Exercises 71
8 The Runtime of Learning 73
8.1 Computational Complexity of Learning 74
8.2 Implementing the ERM Rule 76
8.3 Efficiently Learnable, but Not by a Proper ERM 80
8.4 Hardness of Learning* 81
8.5 Summary 82
8.6 Bibliographic Remarks 82
8.7 Exercises 83
Part 2 From Theory to Algorithms
9 Linear Predictors 89
9.1 Halfspaces 90
9.2 Linear Regression 94
9.3 Logistic Regression 97
9.4 Summary 99
9.5 Bibliographic Remarks 99
9.6 Exercises 99
Contents ix
10 Boosting 101
10.1 Weak Learnability 102
10.2 AdaBoost 105
10.3 Linear Combinations of Base Hypotheses 108
10.4 AdaBoost for Face Recognition 110
10.5 Summary 111
10.6 Bibliographic Remarks 111
10.7 Exercises 112
11 Model Selection and Validation 114
11.1 Model Selection Using SRM 115
11.2 Validation 116
11.3 What to Do If Learning Fails 120
11.4 Summary 123
11.5 Exercises 123
12 Convex Learning Problems 124
12.1 Convexity, Lipschitzness, and Smoothness 124
12.2 Convex Learning Problems 130
12.3 Surrogate Loss Functions 134
12.4 Summary 135
12.5 Bibliographic Remarks 136
12.6 Exercises 136
13 Regularization and Stability 137
13.1 Regularized Loss Minimization 137
13.2 Stable Rules Do Not Overfit 139
13.3 Tikhonov Regularization as a Stabilizer 140
13.4 Controlling the Fitting-Stability Trade-off 144
13.5 Summary 146
13.6 Bibliographic Remarks 146
13.7 Exercises 147
14 Stochastic Gradient Descent 150
14.1 Gradient Descent 151
14.2 Subgradients 154
14.3 Stochastic Gradient Descent (SGD) 156
14.4 Variants 159
14.5 Learning with SGD 162
14.6 Summary 165
14.7 Bibliographic Remarks 166
14.8 Exercises 166
15 Support Vector Machines 167
15.1 Margin and Hard-SVM 167
15.2 Soft-SVM and Norm Regularization 171
15.3 Optimality Conditions and "Support Vectors"* 175
X Contents
15.4 Duality* 175
15.5 Implementing Soft-SVM Using SGD 176
15.6 Summary 177
15.7 Bibliographic Remarks 177
15.8 Exercises 178
16 Kernel Methods 179
16.1 Embeddings into Feature Spaces 179
16.2 The Kernel Trick 181
16.3 Implementing Soft-SVM with Kernels 186
16.4 Summary 187
16.5 Bibliographic Remarks 188
16.6 Exercises 188
17 Multiclass, Ranking, and Complex Prediction Problems 190
17.1 One-versus-All and All-Pairs 190
17.2 Linear Multiclass Predictors 193
17.3 Structured Output Prediction 198
17.4 Ranking 201
17.5 Bipartite Ranking and Multivariate Performance Measures 206
17.6 Summary 209
17.7 Bibliographic Remarks 210
17.8 Exercises 210
18 Decision Trees 212
18.1 Sample Complexity 213
18.2 Decision Tree Algorithms 214
18.3 Random Forests 217
18.4 Summary 217
18.5 Bibliographic Remarks 218
18.6 Exercises 218
19 Nearest Neighbor 219
19.1 A: Nearest Neighbors 219
19.2 Analysis 220
19.3 Efficient Implementation* 225
19.4 Summary 225
19.5 Bibliographic Remarks 225
19.6 Exercises 225
20 Neural Networks 228
20.1 Feedforward Neural Networks 229
20.2 Learning Neural Networks 230
20.3 The Expressive Power of Neural Networks 231
20.4 The Sample Complexity of Neural Networks 234
20.5 The Runtime of Learning Neural Networks 235
20.6 SGD and Backpropagation 236
Contents xi
20.7 Summary 240
20.8 Bibliographic Remarks 240
20.9 Exercises 240
Part 3 Additional Learning Models
21 Online Learning 245
21.1 Online Classification in the Realizable Case 246
21.2 Online Classification in the Unrealizable Case 251
21.3 Online Convex Optimization 257
21.4 The Online Perceptron Algorithm 258
21.5 Summary 261
21.6 Bibliographic Remarks 261
21.7 Exercises 262
22 Clustering 264
22.1 Linkage-Based Clustering Algorithms 266
22.2 ¿-Means and Other Cost Minimization Clusterings 268
22.3 Spectral Clustering 271
22.4 Information Bottleneck* 273
22.5 A High-Level View of Clustering 274
22.6 Summary 276
22.7 Bibliographic Remarks 276
22.8 Exercises 276
23 Dimensionality Reduction 278
23.1 Principal Component Analysis (PCA) 279
23.2 Random Projections 283
23.3 Compressed Sensing 285
23.4 PCA or Compressed Sensing? 292
23.5 Summary 292
23.6 Bibliographic Remarks 292
23.7 Exercises 293
24 Generative Models 295
24.1 Maximum Likelihood Estimator 295
24.2 Naive Bayes 299
24.3 Linear Discriminant Analysis 300
24.4 Latent Variables and the EM Algorithm 301
24.5 Bayesian Reasoning 305
24.6 Summary 307
24.7 Bibliographic Remarks 307
24.8 Exercises 308
25 Feature Selection and Generation 309
25.1 Feature Selection 310
25.2 Feature Manipulation and Normalization 316
25.3 Feature Learning 319
xii Contents
25.4 Summary 321
25.5 Bibliographie Remarks 321
25.6 Exercises 322
Part 4 Advanced Theory
26 Rademacher Complexities 325
26.1 The Rademacher Complexity 325
26.2 Rademacher Complexity of Linear Classes 332
26.3 Generalization Bounds for SVM 333
26.4 Generalization Bounds for Predictors with Low l\ Norm 335
26.5 Bibliographic Remarks 336
27 Covering Numbers 337
27.1 Covering 337
27.2 From Covering to Rademacher Complexity via Chaining 338
27.3 Bibliographic Remarks 340
28 Proof of the Fundamental Theorem of Learning Theory 341
28.1 The Upper Bound for the Agnostic Case 341
28.2 The Lower Bound for the Agnostic Case 342
28.3 The Upper Bound for the Realizable Case 347
29 Multiclass Learnability 351
29.1 The Natarajan Dimension 351
29.2 The Multiclass Fundamental Theorem 352
29.3 Calculating the Natarajan Dimension 353
29.4 On Good and Bad ERMs 355
29.5 Bibliographic Remarks 357
29.6 Exercises 357
30 Compression Bounds 359
30.1 Compression Bounds 359
30.2 Examples 361
30.3 Bibliographic Remarks 363
31 PAC-Bayes 364
31.1 PAC-Bayes Bounds 364
31.2 Bibliographic Remarks 366
31.3 Exercises 366
Appendix A Technical Lemmas 369
Appendix B Measure Concentration 372
B.l Markov's Inequality 372
B.2 Chebyshev's Inequality 373
B.3 Chernoff's Bounds 373
B.4 Hoeffding's Inequality 375
Contents xiii
B.5 Bennet's and Bernstein's Inequalities 376
B.6 Slud's Inequality 378
B.7 Concentration of x2 Variables 378
Appendix C Linear Algebra 380
C.1 Basic Definitions 380
C.2 Eigenvalues and Eigenvectors 381
C.3 Positive Definite Matrices 381
C.4 Singular Value Decomposition (SVD) 381
References 385
Index 395 |
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| title | Understanding machine learning from theory to algorithms |
| title_auth | Understanding machine learning from theory to algorithms |
| title_exact_search | Understanding machine learning from theory to algorithms |
| title_full | Understanding machine learning from theory to algorithms Shai Shalev-Shwartz (The Hebrew University, Jerusalem), Shai Ben-David (University of Waterloo, Canada) |
| title_fullStr | Understanding machine learning from theory to algorithms Shai Shalev-Shwartz (The Hebrew University, Jerusalem), Shai Ben-David (University of Waterloo, Canada) |
| title_full_unstemmed | Understanding machine learning from theory to algorithms Shai Shalev-Shwartz (The Hebrew University, Jerusalem), Shai Ben-David (University of Waterloo, Canada) |
| title_short | Understanding machine learning |
| title_sort | understanding machine learning from theory to algorithms |
| title_sub | from theory to algorithms |
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| topic_facet | Maschinelles Lernen Lehrbuch |
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