Neural network learning: theoretical foundations
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
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| Ausgabe: | digitally printed version |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 389 Seiten Diagramme |
| ISBN: | 9780521118620 9780521573535 |
Internformat
MARC
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| 245 | 1 | 0 | |a Neural network learning |b theoretical foundations |c Martin Anthony and Peter L. Bartlett |
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Datensatz im Suchindex
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| adam_text | Contents Preface page xiü 1 Introduction 1 1.1 Supervised learning 1 1.2 Artificial neural networks 2 1.3 Outline of the book 7 1.4 Bibliographical notes 9 Part one: Pattern Classification with Binary-Output Neural Networks 11 2 The Pattern Classification Problem 13 2.1 The learning problem 13 2.2 Learning finite function classes 19 2.3 Applications to perceptrons 22 2.4 Restricted model 23 2.5 Remarks 25 2.6 Bibliographical notes 27 3 The Growth Function and VC-Dimension 29 3.1 Introduction 29 3.2 The growth function 29 3.3 The Vapnik-Chervonenkis dimension 35 3.4 Bibliographical notes 41 4 General Upper Bounds on Sample Complexity 42 4.1 Learning by minimizing sample error 42 4.2 Uniform convergence and learnability 43 4.3 Proof of uniform convergence result 45 4.4 Application to the perceptron 50 4.5 The restricted model 52 4.6 Remarks 53 4.7 Bibliographical notes 58 vii
viii 5 5.1 5.2 5.3 5.4 5.5 5.6 6 6.1 6.2 6.3 6.4 6.5 7 7.1 7.2 7.3 7.4 7.5 7.6 8 8.1 8.2 8.3 8.4 8.5 8.6 9 9.1 9.2 9.3 9.4 10 10.1 10.2 10.3 10.4 10.5 Contents General Lower Bounds on Sample Complexity 59 Introduction 59 A lower bound for learning 59 The restricted model 65 VC-dimension quantifies sample complexity 69 Remarks 71 Bibliographical notes 72 The VC-Dimension of Linear Threshold Networks 74 Feed-forward neural networks 74 Upper bound 77 Lower bounds 80 Sigmoid networks 83 Bibliographical notes 85 Bounding the VC-Dimension using Geometric Techniques 86 Introduction 86 The need for conditions on the activation functions 86 A bound on the growth function 89 Proof of the growth function bound 92 More on solution set components bounds 102 Bibliographical notes 106 Vapnik-Chervonenkis Dimension Bounds for Neural Networks 108 Introduction 108 Function classes that are polynomial in their parameters 108 Piecewise-polynomial networks 112 Standard sigmoid networks 122 Remarks 128 Bibliographical notes 129 Part two: Pattern Classification with Real-Output Networks 131 Classification with Real-Valued Functions 133 Introduction 133 Large margin classifiers 135 Remarks 138 Bibliographical notes 138 Covering Numbers and Uniform Convergence 140 Introduction 140 Covering numbers 140 A uniform convergence result 143 Covering numbers in general 147 Remarks 149
Contents ix 10.6 11 Bibliographical notes The Pseudo-Dimension and Fat-Shattering Dimension 150 151 11.1 Introduction 151 11.2 The pseudo-dimension 151 11.3 The fat-shattering dimension 159 11.4 12 Bibliographical notes Bounding Covering Numbers with Dimensions 163 165 12.1 Introduction 165 12.2 Packing numbers 165 12.3 Bounding with the pseudo-dimension 167 12.4 Bounding with the fat-shattering dimension 174 12.5 Comparing the two approaches 181 12.6 Remarks 182 12.7 13 Bibliographical notes The Sample Complexity of Classification Learning 183 184 13.1 Large margin SEM algorithms 184 13.2 Large margin SEM algorithms as learning algorithms 185 13.3 Lower bounds for certain function classes 188 13.4 Using the pseudo-dimension 191 13.5 Remarks 191 13.6 14 Bibliographical notes The Dimensions of Neural Networks 192 193 14.1 Introduction 193 14.2 Pseudo-dimension of neural networks 194 14.3 Fat-shattering dimension bounds: number of parameters 196 14.4 Fat-shattering dimension bounds: size of parameters 203 14.5 Remarks 213 14.6 15 Bibliographical notes Model Selection 216 218 15.1 Introduction 218 15.2 Model selection results 220 15.3 Proofs of the results 223 15.4 Remarks 225 15.5 Bibliographical notes 227
X 16 16.1 16.2 16.3 16.4 16.5 16.6 17 17.1 17.2 17.3 18 18.1 18.2 18.3 18.4 18.5 18.6 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 20 20.1 20.2 20.3 20.4 20.5 21 21.1 21.2 21.3 21.4 21.5 21.6 Contents Part three: Learning Real-Valued Functions 229 Learning Classes of Real Functions Introduction The learning framework for real estimation Learning finite classes of real functions A substitute for finiteness Remarks Bibliographical notes Uniform Convergence Results for Real Function Classes Uniform convergence for real functions Remarks Bibliographical notes Bounding Covering Numbers Introduction Bounding with the fat-shattering dimension Bounding with the pseudo-dimension Comparing the different approaches Remarks Bibliographical notes Sample Complexity of Learning Real Function Classes Introduction Classes with finite fat-shattering dimension Classes with finite pseudo-dimension Results for neural networks Lower bounds Remarks Bibliographical notes Convex Classes Introduction Lower bounds for non-convex classes Upper bounds for convex classes Remarks Bibliographical notes Other Learning Problems Loss functions in general Convergence for general loss functions Learning in multiple-output networks Interpolation models Remarks Bibliographical notes 231 231 232 234 236 239 240 241 241 245 246 247 247 247 250 254 255 256 258 258 258 260 261 262 265 267 269 269 270 277 280 282 284 284 285 286 289 295 296
Contents Part four: Algorithmics xi 297 299 22 Efficient Learning 22.1 Introduction 299 299 22.2 ‘ Graded function classes 301 22.3 Efficient learning 302 22.4 General classes of efficient learning algorithms 305 22.5 Efficient learning in the restricted model 306 22.6 Bibliographical notes 307 23 Learning as Optimization 307 23.1 Introduction 307 23.2 Randomized algorithms 311 23.3 Learning as randomized optimization 312 23.4 A characterization of efficient learning 312 23.5 The hardness of learning 314 23.6 Remarks 315 23.7 Bibliographical notes 316 24 The Boolean Perceptron 316 24.1 Introduction 316 24.2 Learning is hard for the simple perceptron 24.3 Learning is easy for fixed fan-in perceptrons 319 322 24.4 Perceptron learning in the restricted model 328 24.5 Remarks 329 24.6 Bibliographical notes 25 Hardness Results for Feed-Forward Networks 331 331 25.1 Introduction 331 25.2 Linear threshold networks with binary inputs 335 25.3 Linear threshold networks with real inputs 337 25.4 Sigmoid networks 338 25.5 Remarks 339 25.6 Bibliographical notes 26 Constructive Learning Algorithms for Two-Layer Networks 342 342 26.1 Introduction 342 26.2 Real estimation with convex combinations 351 26.3 Classification learning using boosting 355 26.4 Bibliographical notes 357 Appendix 1 Useful Results 365 Bibliography 379 Author index 382 Subject index
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| isbn | 9780521118620 9780521573535 |
| language | English |
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| physical | XIV, 389 Seiten Diagramme |
| publishDate | 2009 |
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| spelling | Anthony, Martin 1967- Verfasser (DE-588)114372675 aut Neural network learning theoretical foundations Martin Anthony and Peter L. Bartlett digitally printed version Cambridge [u.a.] Cambridge Univ. Press 2009 XIV, 389 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Neuronales Netz (DE-588)4226127-2 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 s Neuronales Netz (DE-588)4226127-2 s DE-604 Bartlett, Peter L. 1966- Verfasser (DE-588)140240780 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=020438118&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anthony, Martin 1967- Bartlett, Peter L. 1966- Neural network learning theoretical foundations Neuronales Netz (DE-588)4226127-2 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| subject_GND | (DE-588)4226127-2 (DE-588)4193754-5 |
| title | Neural network learning theoretical foundations |
| title_auth | Neural network learning theoretical foundations |
| title_exact_search | Neural network learning theoretical foundations |
| title_full | Neural network learning theoretical foundations Martin Anthony and Peter L. Bartlett |
| title_fullStr | Neural network learning theoretical foundations Martin Anthony and Peter L. Bartlett |
| title_full_unstemmed | Neural network learning theoretical foundations Martin Anthony and Peter L. Bartlett |
| title_short | Neural network learning |
| title_sort | neural network learning theoretical foundations |
| title_sub | theoretical foundations |
| topic | Neuronales Netz (DE-588)4226127-2 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Neuronales Netz Maschinelles Lernen |
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