Foundations of machine learning:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass. [u.a.]
MIT Press
2012
|
| Series: | Adaptive computation and machine learning
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 412 S. graph. Darst. 23cm |
| ISBN: | 9780262018258 |
Staff View
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| 245 | 1 | 0 | |a Foundations of machine learning |c Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar |
| 264 | 1 | |a Cambridge, Mass. [u.a.] |b MIT Press |c 2012 | |
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Record in the Search Index
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| adam_text | Titel: Foundations of machine learning
Autor: Mohri, Mehryar
Jahr: 2012
Contents
Preface xi
1 Introduction 1
1.1 Applications and problems........................ 1
1.2 Definitions and terminology....................... 3
1.3 Cross-validation.............................. 5
1.4 Learning scenarios............................ 7
1.5 Outline .................................. 8
2 The PAC Learning Framework 11
2.1 The PAC learning model......................... 11
2.2 Guarantees for finite hypothesis sets - consistent case........ 17
2.3 Guarantees for finite hypothesis sets - inconsistent case....... 21
2.4 Generalities................................ 24
2.4.1 Deterministic versus stochastic scenarios............ 24
2.4.2 Bayes error and noise ...................... 25
2.4.3 Estimation and approximation errors.............. 26
2.4.4 Model selection.......................... 27
2.5 Chapter notes............................... 28
2.6 Exercises ................................. 29
3 Rademacher Complexity and VC-Dimension 33
3.1 Rademacher complexity......................... 34
3.2 Growth function............................. 38
3.3 VC-dimension............................... 41
3.4 Lower bounds............................... 48
3.5 Chapter notes............................... 54
3.6 Exercises ................................. 55
4 Support Vector Machines 63
4.1 Linear classification............................ 63
4.2 SVMs - separable case.......................... 64
4.2.1 Primal optimization problem.................. 64
4.2.2 Support vectors.......................... 66
4.2.3 Dual optimization problem................... 67
4.2.4 Leave-one-out analysis...................... 69
4.3 SVMs - non-separable case....................... 71
4.3.1 Primal optimization problem.................. 72
4.3.2 Support vectors.......................... 73
4.3.3 Dual optimization problem................... 74
4.4 Margin theory............................... 75
4.5 Chapter notes............................... 83
4.6 Exercises ................................. 84
5 Kernel Methods 89
5.1 Introduction................................ 89
5.2 Positive definite symmetric kernels................... 92
5.2.1 Definitions ............................ 92
5.2.2 Reproducing kernel Hilbert space................ 94
5.2.3 Properties............................. 96
5.3 Kernel-based algorithms......................... 100
5.3.1 SVMs with PDS kernels..................... 100
5.3.2 Representer theorem....................... 101
5.3.3 Learning guarantees....................... 102
5.4 Negative definite symmetric kernels................... 103
5.5 Sequence kernels............................. 106
5.5.1 Weighted transducers ...................... 106
5.5.2 Rational kernels ......................... Ill
5.6 Chapter notes............................... 115
5.7 Exercises ................................. 116
6 Boosting 121
6.1 Introduction................................ 121
6.2 AdaBoost................................. 122
6.2.1 Bound on the empirical error.................. 124
6.2.2 Relationship with coordinate descent.............. 126
6.2.3 Relationship with logistic regression.............. 129
6.2.4 Standard use in practice..................... 129
6.3 Theoretical results............................ 130
6.3.1 VC-dimension-based analysis.................. 131
6.3.2 Margin-based analysis...................... 131
6.3.3 Margin maximization ...................... 136
6.3.4 Game-theoretic interpretation.................. 137
6.4 Discussion................................. 140
6.5 Chapter notes............................... 141
6.6 Exercises ................................. 142
7 On-Line Learning 147
7.1 Introduction................................ 147
7.2 Prediction with expert advice...................... 148
7.2.1 Mistake bounds and Halving algorithm ............ 148
7.2.2 Weighted majority algorithm.................. 150
7.2.3 Randomized weighted majority algorithm........... 152
7.2.4 Exponential weighted average algorithm............ 156
7.3 Linear classification............................ 159
7.3.1 Perceptron algorithm....................... 160
7.3.2 Winnow algorithm........................ 168
7.4 On-line to batch conversion....................... 171
7.5 Game-theoretic connection........................ 174
7.6 Chapter notes............................... 175
7.7 Exercises ................................. 176
8 Multi-Class Classification 183
8.1 Multi-class classification problem.................... 183
8.2 Generalization bounds.......................... 185
8.3 Uncombined multi-class algorithms................... 191
8.3.1 Multi-class SVMs......................... 191
8.3.2 Multi-class boosting algorithms................. 192
8.3.3 Decision trees........................... 194
8.4 Aggregated multi-class algorithms ................... 198
8.4.1 One-versus-all........................... 198
8.4.2 One-versus-one.......................... 199
8.4.3 Error-correction codes...................... 201
8.5 Structured prediction algorithms.................... 203
8.6 Chapter notes............................... 206
8.7 Exercises ................................. 207
9 Ranking 209
9.1 The problem of ranking......................... 209
9.2 Generalization bound .......................... 211
9.3 Ranking with SVMs........................... 213
9.4 RankBoost ................................ 214
9.4.1 Bound on the empirical error.................. 216
9.4.2 Relationship with coordinate descent.............. 218
9.4.3 Margin bound for ensemble methods in ranking ....... 220
9.5 Bipartite ranking............................. 221
9.5.1 Boosting in bipartite ranking.................. 222
9.5.2 Area under the ROC curve................... 224
9.6 Preference-based setting......................... 226
9.6.1 Second-stage ranking problem.................. 227
9.6.2 Deterministic algorithm..................... 229
9.6.3 Randomized algorithm...................... 230
9.6.4 Extension to other loss functions................ 231
9.7 Discussion................................. 232
9.8 Chapter notes............................... 233
9.9 Exercises ................................. 234
10 Regression 237
10.1 The problem of regression........................ 237
10.2 Generalization bounds.......................... 238
10.2.1 Finite hypothesis sets ...................... 238
10.2.2 Rademacher complexity bounds................. 239
10.2.3 Pseudo-dimension bounds.................... 241
10.3 Regression algorithms.......................... 245
10.3.1 Linear regression......................... 245
10.3.2 Kernel ridge regression...................... 247
10.3.3 Support vector regression.................... 252
10.3.4 Lasso ............................... 257
10.3.5 Group norm regression algorithms............... 260
10.3.6 On-line regression algorithms.................. 261
10.4 Chapter notes............................... 262
10.5 Exercises ................................. 263
11 Algorithmic Stability 267
11.1 Definitions................................. 267
11.2 Stability-based generalization guarantee................ 268
11.3 Stability of kernel-based regularization algorithms .......... 270
11.3.1 Application to regression algorithms: SVR and KRR..... 274
11.3.2 Application to classification algorithms: SVMs ........ 276
11.3.3 Discussion............................. 276
11.4 Chapter notes............................... 277
11.5 Exercises ................................. 277
12 Dimensionality Reduction 281
12.1 Principal Component Analysis ..................... 282
12.2 Kernel Principal Component Analysis (KPCA)............ 283
12.3 KPCA and manifold learning...................... 285
12.3.1 Isomap .............................. 285
12.3.2 Laplacian eigenmaps....................... 286
12.3.3 Locally linear embedding (LLE) ................ 287
12.4 Jolmson-Lindenstrauss lemma...................... 288
12.5 Chapter notes............................... 290
12.6 Exercises ................................. 290
13 Learning Automata and Languages 293
13.1 Introduction................................ 293
13.2 Finite automata ............................. 294
13.3 Efficient exact learning.......................... 295
13.3.1 Passive learning ......................... 296
13.3.2 Learning with queries...................... 297
13.3.3 Learning automata with queries ................ 298
13.4 Identification in the limit ........................ 303
13.4.1 Learning reversible automata.................. 304
13.5 Chapter notes............................... 309
13.6 Exercises ................................. 310
14 Reinforcement Learning 313
14.1 Learning scenario............................. 313
14.2 Markov decision process model..................... 314
14.3 Policy................................... 315
14.3.1 Definition............................. 315
14.3.2 Policy value............................ 316
14.3.3 Policy evaluation......................... 316
14.3.4 Optimal policy.......................... 318
14.4 Planning algorithms........................... 319
14.4.1 Value iteration.......................... 319
14.4.2 Policy iteration.......................... 322
14.4.3 Linear programming....................... 324
14.5 Learning algorithms........................... 325
14.5.1 Stochastic approximation.................... 326
14.5.2 TD(0) algorithm......................... 330
14.5.3 Q-learning algorithm....................... 331
14.5.4 SARSA.............................. 334
14.5.5 TD(A) algorithm......................... 335
14.5.6 Large state space......................... 336
14.6 Chapter notes............................... 337
Conclusion 339
A Linear Algebra Review 341
A.l Vectors and norms............................ 341
A.l.l Norms............................... 341
A.1.2 Dual norms............................ 342
A.2 Matrices.................................. 344
A.2.1 Matrix norms........................... 344
A.2.2 Singular value decomposition.................. 345
A.2.3 Symmetric positive semidefinite (SPSD) matrices....... 346
B Convex Optimization 349
B.l Differentiation and unconstrained optimization............ 349
B.2 Convexity................................. 350
B.3 Constrained optimization........................ 353
B.4 Chapter notes............................... 357
C Probability Review 359
C.l Probability................................ 359
C.2 Random variables............................. 359
C.3 Conditional probability and independence............... 361
C.4 Expectation, Markov s inequality, and moment-generating function . 363
C.5 Variance and Chebyshev:s inequality.................. 365
D Concentration inequalities 369
D.l Hoeffding s inequality .......................... 369
D.2 AIcDiarmid s inequality ......................... 371
D.3 Other inequalities............................. 373
D.3.1 Binomial distribution: Slud s inequality............ 374
D.3.2 Normal distribution: tail bound................. 374
D.3.3 Khintchine-Kahane inequality.................. 374
D.4 Chapter notes............................... 376
D.5 Exercises ................................. 377
E Notation 379
References 381
Index 397
r
This graduate-level textbook introduces fundamental concepts and methods in machine learning. It describes several
important modern algorithms, provides the theoretical underpinnings of these algorithms, and illustrates key aspects
for their application. The authors aim to present novel theoretical tools and concepts while giving concise proofs even
for relatively advanced topics.
Foundations of Machine Learning fills the need for a general textbook that also offers theoretical details and an
emphasis on proofs. Certain topics that are often treated with insufficient attention are discussed in more detail here;
for example, entire chapters are devoted to regression, multi-class classification, and ranking. The first three chapters
lay the theoretical foundation for what follows, but each remaining chapter is mostly self-contained. The appendix
offers a concise probability review, a short introduction to convex optimization, tools for concentration bounds, and
several basic properties of matrices and norms used in the book.
The book is intended for graduate students and researchers in machine learning, statistics, and related areas; it can
be used either as a textbook or as a reference text for a research seminar.
.
|
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| spelling | Mohri, Mehryar Verfasser (DE-588)130150134 aut Foundations of machine learning Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar Cambridge, Mass. [u.a.] MIT Press 2012 XII, 412 S. graph. Darst. 23cm txt rdacontent n rdamedia nc rdacarrier Adaptive computation and machine learning Includes bibliographical references and index Hier auch später erschienene, unveränderte Nachdrucke Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Künstliche Intelligenz (DE-588)4033447-8 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 s Künstliche Intelligenz (DE-588)4033447-8 s 1\p DE-604 DE-604 Rostamizadeh, Afshin Verfasser (DE-588)1029198446 aut Talwalkar, Ameet Verfasser (DE-588)1029198578 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025293082&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025293082&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 |
| spellingShingle | Mohri, Mehryar Rostamizadeh, Afshin Talwalkar, Ameet Foundations of machine learning Maschinelles Lernen (DE-588)4193754-5 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd |
| subject_GND | (DE-588)4193754-5 (DE-588)4033447-8 |
| title | Foundations of machine learning |
| title_auth | Foundations of machine learning |
| title_exact_search | Foundations of machine learning |
| title_full | Foundations of machine learning Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar |
| title_fullStr | Foundations of machine learning Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar |
| title_full_unstemmed | Foundations of machine learning Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar |
| title_short | Foundations of machine learning |
| title_sort | foundations of machine learning |
| topic | Maschinelles Lernen (DE-588)4193754-5 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd |
| topic_facet | Maschinelles Lernen Künstliche Intelligenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025293082&sequence=000002&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=025293082&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mohrimehryar foundationsofmachinelearning AT rostamizadehafshin foundationsofmachinelearning AT talwalkarameet foundationsofmachinelearning |