Foundations of machine learning:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Massachusetts ; London, England
The MIT Press
[2018]
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| Edition: | Second edition |
| Series: | Adaptive computation and machine learning series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 486 Seiten Illustrationen (teilweise farbig) |
| ISBN: | 9780262039406 |
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MARC
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Contents I 1 2 . Preface Introduction 1 1.1 1.2 1.3 1.4 1.5 1.6 1 2 3 4 6 7 2.5 2.6 4 What is machine learning? What kind of problems can be tackled using machine learning? Some standard learning tasks Learning stages Learning scenarios Generalization The PAC LearningFramework 2.1 2.2 2.3 2.4 3 xiii The PAC learning model Guarantees for finite hypothesis sets — consistent case Guarantees for finite hypothesis sets — inconsistent case Generalities 2.4.1 Deterministic versus stochastic scenarios 2.4.2 Bayes error and noise Chapter notes Exercises 9 9 15 19 21 21 22 23 23 Rademacher Complexityand VC-Dimension 29 3.1 3.2 3.3 3.4 3.5 3.6 30 34 36 43 48 50 Rademacher complexity Growth function VC-dimension Lower bounds Chapter notes Exercises Model Selection 61 4.1 4.2 4.3 61 62 64 Estimation and approximation errors Empirical risk minimization (ERM) Structural risk minimization (SRM)
4.4 4.5 4.6 4.7 4.8 4.9 Cross-validation n-Fold cross-validation Regularization-based algorithms Convex surrogate losses Chapter notes Exercises Support Vector Machines 5.1 5.2 5.3 5.4 5.5 5.6 Linear classification Separable case 5.2.1 Primal optimization problem 5.2.2 Support vectors 5.2.3 Dual optimization problem 5.2.4 Leave-one-out analysis Non-separable case 5.3.1 Primal optimization problem 5.3.2 Support vectors 5.3.3 Dual optimization problem Margin theory Chapter notes Exercises Kernel Methods 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 Introduction Positive definite symmetric kernels 6.2.1 Definitions 6.2.2 Reproducing kernel Hilbert space 6.2.3 Properties Kernel-based algorithms 6.3.1 SVMs with PDS kernels 6.3.2 Representer theorem 6.3.3 Learning guarantees Negative definite symmetric kernels Sequence kernels 6.5.1 Weighted transducers 6.5.2 Rational kernels Approximate kernel feature maps Chapter notes Exercises Boosting 7.1 7.2 Introduction AdaBoost 7.2.1 Bound on the empirical error 7.2.2 Relationship with coordinate descent 7.2.3 Practical use 68 71 72 73 77 78 79 79 80 81 83 83 85 87 88 89 90 91 100 100 105 105 108 108 110 112 116 116 117 117 119 121 122 126 130 135 137 145 145 146 149 150 154
7.3 7.4 7.5 7.6 7.7 Theoretical results 7.3.1 VC-dimension-based analysis 7.3.2 Li-geometric margin 7.3.3 Margin-based analysis 7.3.4 Margin maximization 7.3.5 Game-theoretic interpretation Li-regularization Discussion Chapter notes Exercises On-Line Learning 8.1 8.2 8.3 8.4 8.5 8.6 8.7 Introduction Prediction with expert advice 8.2.1 Mistake bounds and Halving algorithm 8.2.2 Weighted majority algorithm 8.2.3 Randomized weighted majority algorithm 8.2.4 Exponential weighted average algorithm Linear classification 8.3.1 Perceptron algorithm 8.3.2 Winnow algorithm On-line to batch conversion Game-theoretic connection Chapter notes Exercises Multi-Class Classification 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Multi-class classification problem Generalization bounds Uncombined multi-class algorithms 9.3.1 Multi-class SVMs 9.3.2 Multi-class boosting algorithms 9.3.3 Decision trees Aggregated multi-class algorithms 9.4.1 One-versus-all 9.4.2 One-versus-one 9.4.3 Error-correcting output codes Structured prediction algorithms Chapter notes Exercises Ranking 10.1 10.2 10.3 The problem of ranking Generalization bound Ranking with SVMs 154 154 155 157 161 162 165 167 168 170 177 178 178 179 181 183 186 190 190 198 201 204 205 206 213 213 215 221 221 222 224 228 229 229 231 233 235 237 239 240 241 243
10.4 10.5 10.6 10.7 10.8 10.9 RankBoost 10.4.1 Bound on the empirical error 10.4.2 Relationship with coordinate descent 10.4.3 Margin bound for ensemble methods in ranking Bipartite ranking 10.5.1 Boosting in bipartite ranking 10.5.2 Area under the ROC curve Preference-based setting 10.6.1 Second-stage ranking problem 10.6.2 Deterministic algorithm 10.6.3 Randomized algorithm 10.6.4 Extension to other loss functions Other ranking criteria Chapter notes Exercises Regression 11.1 11.2 11.3 11.4 11.5 The problem of regression Generalization bounds 11.2.1 Finite hypothesis sets 11.2.2 Rademacher complexity bounds 11.2.3 Pseudo-dimension bounds Regression algorithms 11.3.1 Linear regression 11.3.2 Kernel ridge regression 11.3.3 Support vector regression 11.3.4 Lasso 11.3.5 Group norm regression algorithms 11.3.6 On-line regression algorithms Chapter notes Exercises Maximum Entropy Models 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 Density estimation problem 12.1.1 Maximum Likelihood (ML) solution 12.1.2 Maximum a Posteriori (MAP) solution Density estimation problem augmented with features Maxent principle Maxent models Dual problem Generalization bound Coordinate descent algorithm Extensions Լշ-regularization 244 246 248 250 251 252 255 257 257 259 260 262 262 263 264 267 267 268 268 269 271 275 275 276 281 285 289 289 290 292 295 295 296 297 297 298 299 299 303 304 306 308
13 12.10 Chapter notes 12.11 Exercises 312 313 Conditional Maximum EntropyModels 315 13.1 13.2 13.3 13.4 13.5 315 316 316 317 319 320 320 321 321 325 325 325 326 328 330 331 13.6 13.7 13.8 13.9 13.10 13.11 14 Algorithmic Stability 333 14.1 14.2 14.3 333 334 336 339 341 342 342 343 14.4 14.5 15 Definitions Stability-based generalization guarantee Stability of kernel-based regularization algorithms 14.3.1 Application to regressionalgorithms: SVR and KRR 14.3.2 Application to classification algorithms: SVMs 14.3.3 Discussion Chapter notes Exercises Dimensionality Reduction 347 15.1 15.2 15.3 348 349 351 351 352 353 354 356 356 15.4 15.5 15.6 16 Learning problem Conditional Maxent principle Conditional Maxent models Dual problem Properties 13.5.1 Optimization problem 13.5.2 Feature vectors 13.5.3 Prediction Generalization bounds Logistic regression 13.7.1 Optimization problem 13.7.2 Logistic model Լշ-regularization Proof of the duality theorem Chapter notes Exercises Principal component analysis Kernel principal component analysis (KPCA) KPCA and manifold learning 15.3.1 Isomap 15.3.2 Laplacian eigenmaps 15.3.3 Locally linear embedding (LLE) Johnson-Lindenstrauss lemma Chapter notes Exercises Learning Automata and Languages 359 16.1 359 Introduction
16.2 16.3 16.4 16.5 16.6 17 Finite automata Efficient exact learning 16.3.1 Passive learning 16.3.2 Learning with queries 16.3.3 Learning automata with queries Identification in the limit 16.4.1 Learning reversible automata Chapter notes Exercises Reinforcement Learning 379 17.1 17.2 17.3 379 380 381 381 382 382 385 387 387 390 392 393 394 397 398 402 402 403 405 17.4 17.5 17.6 Learning scenario Markov decision process model Policy 17.3.1 Definition 17.3.2 Policy value 17.3.3 Optimal policies 17.3.4 Policy evaluation Planning algorithms 17.4.1 Value iteration 17.4.2 Policy iteration 17.4.3 Linear programming Learning algorithms 17.5.1 Stochastic approximation 17.5.2 TD(0) algorithm 17.5.3 Q-learning algorithm 17.5.4 SARSA 17.5.5 TD(A) algorithm 17.5.6 Large state space Chapter notes Conclusion A 360 361 362 363 364 369 370 375 376 407 Linear Algebra Review 409 A.1 409 409 410 411 411 411 412 412 A.2 Vectors and norms A.1.1 Norms A.1.2 Dual norms A.1.3 Relationship between norms Matrices A.2.1 Matrix norms A.2.2 Singular value decomposition A.2.3 Symmetric positive semidefinite (SPSD) matrices
Convex Optimization B.1 B.2 в.з В.4 В.5 В.6 Differentiation and unconstrained optimization Convexity Constrained optimization Fenchel duality B.4.1 Subgradients B.4.2 Core B.4.3 Conjugate functions Chapter notes Exercises Probability Review C.1 C.2 с.з C.4 C.5 C.6 C.7 Probability Random variables Conditional probability and independence Expectation and Markov's inequality Variance and Chebyshev’s inequality Moment-generating functions Exercises 415 415 415 419 422 422 423 423 426 427 429 429 429 431 431 432 434 435 Concentration Inequalities 437 D.1 D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9 D.10 D.11 D.12 437 438 439 440 440 441 442 443 443 444 445 445 Hoeffding’s inequality Sanov’s theorem Multiplicative Chernoff bounds Binomial distribution tails: Upper bounds Binomial distribution tails: Lower bound Azuma’s inequality McDiarmid's inequality Normal distribution tails: Lower bound Khintchine-Kahane inequality Maximal inequality Chapter notes Exercises Notions of Information Theory 449 E.1 E.2 449 450 453 453 456 457 E.3 E.4 E.5 E.6 Entropy Relative entropy Mutual information Bregman divergences Chapter notes Exercises
F Notation 459 Bibliography 461 Index 475 |
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| spelling | Mohri, Mehryar Verfasser (DE-588)130150134 aut Foundations of machine learning Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar Second edition Cambridge, Massachusetts ; London, England The MIT Press [2018] © 2018 xv, 486 Seiten Illustrationen (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Adaptive computation and machine learning series Machine learning Computer algorithms Künstliche Intelligenz (DE-588)4033447-8 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 s Künstliche Intelligenz (DE-588)4033447-8 s DE-604 Rostamizadeh, Afshin Verfasser (DE-588)1029198446 aut Talwalkar, Ameet Verfasser (DE-588)1029198578 aut 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=030647834&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mohri, Mehryar Rostamizadeh, Afshin Talwalkar, Ameet Foundations of machine learning Machine learning Computer algorithms Künstliche Intelligenz (DE-588)4033447-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
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| 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, Ameet Talwalkar |
| title_fullStr | Foundations of machine learning Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar |
| title_full_unstemmed | Foundations of machine learning Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar |
| title_short | Foundations of machine learning |
| title_sort | foundations of machine learning |
| topic | Machine learning Computer algorithms Künstliche Intelligenz (DE-588)4033447-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Machine learning Computer algorithms Künstliche Intelligenz Maschinelles Lernen |
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