Adaptive Learning of Polynomial Networks: genetic programming, backpropagation and Bayesian methods
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer US
2006
|
| Ausgabe: | 1. Ed. |
| Schriftenreihe: | Genetic and Evolutionary Computation
|
| Online-Zugang: | BTU01 FHM01 UBG01 UBR01 UBY01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | Erscheint: 3. Mai 2006 |
| Beschreibung: | 1 Online-Ressource (XIV, 316 S.) 62 schw.-w. Ill., 1 schw.-w. Fotos, 61 schw.-w. graph. Darst. |
| ISBN: | 9780387312392 9780387312408 |
| DOI: | 10.1007/0-387-31240-4 |
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| 100 | 1 | |a Nikolaev, Nikolay |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Adaptive Learning of Polynomial Networks |b genetic programming, backpropagation and Bayesian methods |c Nikolay Nikolaev ; Hitoshi Iba |
| 250 | |a 1. Ed. | ||
| 264 | 1 | |a Berlin |b Springer US |c 2006 | |
| 300 | |a 1 Online-Ressource (XIV, 316 S.) |b 62 schw.-w. Ill., 1 schw.-w. Fotos, 61 schw.-w. graph. Darst. | ||
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| 500 | |a Erscheint: 3. Mai 2006 | ||
| 700 | 1 | |a Iba, Hitoshi |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804136402062934016 |
|---|---|
| adam_text | Contents
Preface xi
1. INTRODUCTION 1
1.1 Inductive Learning 3
1.1.1 Learning and Regression 4
1.1.2 Polynomial Models 5
1.1.3 Inductive Computation Machinery 5
1.2 Why Polynomial Networks? 7
1.2.1 Advantages of Polynomial Networks 8
1.2.2 Multilayer Polynomial Networks 9
1.3 Evolutionary Search 16
1.3.1 STROGANOFF and its Variants 17
1.4 Neural Network Training 21
1.5 Bayesian Inference 22
1.6 Statistical Model Validation 23
1.7 Organization of the Book 23
2. INDUCTIVE GENETIC PROGRAMMING 25
2.1 Polynomial Neural Networks (PNN) 26
2.1.1 PNN Approaches 27
2.1.2 Tree structured PNN 29
2.2 IGP Search Mechanisms 35
2.2.1 Sampling and Control Issues 36
2.2.2 Biological Interpretation 36
2.3 Genetic Learning Operators 38
2.3.1 Context preserving Mutation 38
2.3.2 Crossover Operator 40
vi ADAPTIVE LEARNING OF POLYNOMIAL NETWORKS
2.3.3 Size biasing of the Genetic Operators 41
2.3.4 Tree to TVee Distance 42
2.4 Random Tree Generation 46
2.5 Basic IGP Framework 48
2.6 IGP Convergence Characteristics 50
2.6.1 Schema Theorem of IGP 50
2.6.2 Markov Model of IGP 51
2.7 Chapter Summary 54
3. TREE LIKE PNN REPRESENTATIONS 55
3.1 Discrete Volterra Series 56
3.2 Mapping Capabilities of PNN 57
3.3 Errors of Approximation 59
3.3.1 Approximation Error Bounds 59
3.3.2 Empirical Risk 60
3.4 Linear Polynomial Networks 62
3.4.1 Horizontal PNN Models 62
3.4.2 Kernel PNN Models 66
3.5 Nonlinear Polynomial Networks 68
3.5.1 Block PNN Models 68
3.5.2 Orthogonal PNN Models 69
3.5.3 Trigonometric PNN Models 71
3.5.4 Rational PNN Models 75
3.5.5 Dynamic PNN Models 77
3.6 Chapter Summary 80
4. FITNESS FUNCTIONS AND LANDSCAPES 81
4.1 Fitness Functions 83
4.1.1 Static Fitness Functions 84
4.1.2 Dynamic Fitness Functions 91
4.1.3 Fitness Magnitude 94
4.2 Fitness Landscape Structure 95
4.3 Fitness Landscape Measures 96
4.3.1 Statistical Correlation Measures 96
4.3.2 Probabilistic Measures 102
4.3.3 Information Measures 104
4.3.4 Quantitative Measures 107
4.4 Chapter Summary 109
Contents vii
5. SEARCH NAVIGATION 111
5.1 The Reproduction Operator 112
5.1.1 Selection Strategies 113
5.1.2 Replacement Strategies 117
5.1.3 Implementing Reproduction 118
5.2 Advanced Search Control 119
5.2.1 Macroevolutionary Search 119
5.2.2 Memetic Search 120
5.2.3 Search by Genetic Annealing 122
5.2.4 Stochastic Genetic Hillclimbing 124
5.2.5 Coevolutionary Search 125
5.2.6 Distributed Search 128
5.3 Performance Examination 128
5.3.1 Fitness Evolvability 129
5.3.2 Convergence Measures 130
5.3.3 Diversity Measures 133
5.3.4 Measures of Self Organization 139
5.4 Chapter Summary 146
6. BACKPROPAGATION TECHNIQUES 147
6.1 Multilayer Feed forward PNN 148
6.2 First Order Backpropagation 149
6.2.1 Gradient Descent Search 150
6.2.2 First Order Error Derivatives 151
6.2.3 Batch Backpropagation 157
6.2.4 Incremental Backpropagation 158
6.2.5 Control of the Learning Step 159
6.2.6 Regularized Delta Rule 162
6.3 Second Order Backpropagation 163
6.3.1 Second Order Error Derivatives 164
6.3.2 Newton s Method 169
6.3.3 Pseudo Newton Training 170
6.3.4 Conjugate Gradients 170
6.3.5 Levenberg Marquardt Method 171
6.4 Rational Backpropagation 172
6.5 Network Pruning 176
6.5.1 First Order Network Pruning 176
6.5.2 Second Order Network Pruning 177
viii ADAPTIVE LEARNING OF POLYNOMIAL NETWORKS
6.6 Chapter Summary 179
7. TEMPORAL BACKPROPAGATION 181
7.1 Recurrent PNN as State Space Models 182
7.2 Backpropagation Through Time 184
7.2.1 Derivation of BPTT Algorithms 185
7.2.2 Real Time BPTT Algorithm 189
7.2.3 Epochwise BPTT Algorithm 190
7.3 Real Time Recurrent Learning 191
7.4 Improved Dynamic Training 198
7.4.1 Teacher Enforced Training 198
7.4.2 Truncating in Time 199
7.4.3 Subgrouping 199
7.4.4 Common Temporal Training Problem 200
7.5 Second Order Temporal BP 200
7.6 Recursive Backpropagation 204
7.7 Recurrent Network Optimization 206
7.7.1 Regularization 207
7.7.2 Recurrent Network Pruning 207
7.8 Chapter Summary 208
8. BAYESIAN INFERENCE TECHNIQUES 209
8.1 Bayesian Error Function 211
8.2 Bayesian Neural Network Inference 212
8.2.1 Deriving Hyperparameters 215
8.2.2 Local vs. Global Regularization 217
8.2.3 Evidence Procedure for PNN Models 218
8.2.4 Predictive Data Distribution 221
8.2.5 Choosing a Weight Prior 221
8.3 Bayesian Network Pruning 222
8.4 Sparse Bayesian Learning 224
8.5 Recursive Bayesian Learning 229
8.5.1 Sequential Weight Estimation 229
8.5.2 Sequential Dynamic Hessian Estimation 230
8.5.3 Sequential Hyperparameter Estimation 232
8.6 Monte Carlo Training 234
8.6.1 Markov Chain Monte Carlo 235
8.6.2 Importance Resampling 237
Contents ix
8.6.3 Hybrid Sampling Resampling 237
8.7 Chapter Summary 239
9. STATISTICAL MODEL DIAGNOSTICS 241
9.1 Deviations of PNN Models 242
9 2 Residual Bootstrap Sampling 243
9 3 The Bias/Variance Dilemma 244
9.3.1 Statistical Bias and Variance 244
9.3.2 Measuring Bias and Variance 245
9 4 Confidence Intervals 248
9.4.1 Interval Estimation by the Delta Method 248
9.4.2 Bootstrapping Confidence Intervals 252
9 5 Prediction Intervals 254
9.5.1 Analytical Prediction Intervals 255
9.5.2 Empirical Learning of Prediction Bars 256
9.6 Bayesian Intervals 262
9.6.1 Analytical Bayesian Intervals 263
9.6.2 Empirical Bayesian Intervals 265
9.7 Model Validation Tests 267
9.8 Chapter Summary 271
10. TIME SERIES MODELLING 273
10.1 Time Series Modelling 274
10.2 Data Preprocessing 276
10.3 PNN vs. Linear ARMA Models 277
10.4 PNN vs. Genetically Programmed Functions 279
10.5 PNN vs. Statistical Learning Networks 281
10.6 PNN vs. Neural Network Models 283
10.7 PNN vs. Kernel Models 285
10.8 Recurrent PNN vs. Recurrent Neural Networks 288
10.9 Chapter Summary 290
11. CONCLUSIONS 291
References 295
Index 313
|
| adam_txt |
Contents
Preface xi
1. INTRODUCTION 1
1.1 Inductive Learning 3
1.1.1 Learning and Regression 4
1.1.2 Polynomial Models 5
1.1.3 Inductive Computation Machinery 5
1.2 Why Polynomial Networks? 7
1.2.1 Advantages of Polynomial Networks 8
1.2.2 Multilayer Polynomial Networks 9
1.3 Evolutionary Search 16
1.3.1 STROGANOFF and its Variants 17
1.4 Neural Network Training 21
1.5 Bayesian Inference 22
1.6 Statistical Model Validation 23
1.7 Organization of the Book 23
2. INDUCTIVE GENETIC PROGRAMMING 25
2.1 Polynomial Neural Networks (PNN) 26
2.1.1 PNN Approaches 27
2.1.2 Tree structured PNN 29
2.2 IGP Search Mechanisms 35
2.2.1 Sampling and Control Issues 36
2.2.2 Biological Interpretation 36
2.3 Genetic Learning Operators 38
2.3.1 Context preserving Mutation 38
2.3.2 Crossover Operator 40
vi ADAPTIVE LEARNING OF POLYNOMIAL NETWORKS
2.3.3 Size biasing of the Genetic Operators 41
2.3.4 Tree to TVee Distance 42
2.4 Random Tree Generation 46
2.5 Basic IGP Framework 48
2.6 IGP Convergence Characteristics 50
2.6.1 Schema Theorem of IGP 50
2.6.2 Markov Model of IGP 51
2.7 Chapter Summary 54
3. TREE LIKE PNN REPRESENTATIONS 55
3.1 Discrete Volterra Series 56
3.2 Mapping Capabilities of PNN 57
3.3 Errors of Approximation 59
3.3.1 Approximation Error Bounds 59
3.3.2 Empirical Risk 60
3.4 Linear Polynomial Networks 62
3.4.1 Horizontal PNN Models 62
3.4.2 Kernel PNN Models 66
3.5 Nonlinear Polynomial Networks 68
3.5.1 Block PNN Models 68
3.5.2 Orthogonal PNN Models 69
3.5.3 Trigonometric PNN Models 71
3.5.4 Rational PNN Models 75
3.5.5 Dynamic PNN Models 77
3.6 Chapter Summary 80
4. FITNESS FUNCTIONS AND LANDSCAPES 81
4.1 Fitness Functions 83
4.1.1 Static Fitness Functions 84
4.1.2 Dynamic Fitness Functions 91
4.1.3 Fitness Magnitude 94
4.2 Fitness Landscape Structure 95
4.3 Fitness Landscape Measures 96
4.3.1 Statistical Correlation Measures 96
4.3.2 Probabilistic Measures 102
4.3.3 Information Measures 104
4.3.4 Quantitative Measures 107
4.4 Chapter Summary 109
Contents vii
5. SEARCH NAVIGATION 111
5.1 The Reproduction Operator 112
5.1.1 Selection Strategies 113
5.1.2 Replacement Strategies 117
5.1.3 Implementing Reproduction 118
5.2 Advanced Search Control 119
5.2.1 Macroevolutionary Search 119
5.2.2 Memetic Search 120
5.2.3 Search by Genetic Annealing 122
5.2.4 Stochastic Genetic Hillclimbing 124
5.2.5 Coevolutionary Search 125
5.2.6 Distributed Search 128
5.3 Performance Examination 128
5.3.1 Fitness Evolvability 129
5.3.2 Convergence Measures 130
5.3.3 Diversity Measures 133
5.3.4 Measures of Self Organization 139
5.4 Chapter Summary 146
6. BACKPROPAGATION TECHNIQUES 147
6.1 Multilayer Feed forward PNN 148
6.2 First Order Backpropagation 149
6.2.1 Gradient Descent Search 150
6.2.2 First Order Error Derivatives 151
6.2.3 Batch Backpropagation 157
6.2.4 Incremental Backpropagation 158
6.2.5 Control of the Learning Step 159
6.2.6 Regularized Delta Rule 162
6.3 Second Order Backpropagation 163
6.3.1 Second Order Error Derivatives 164
6.3.2 Newton's Method 169
6.3.3 Pseudo Newton Training 170
6.3.4 Conjugate Gradients 170
6.3.5 Levenberg Marquardt Method 171
6.4 Rational Backpropagation 172
6.5 Network Pruning 176
6.5.1 First Order Network Pruning 176
6.5.2 Second Order Network Pruning 177
viii ADAPTIVE LEARNING OF POLYNOMIAL NETWORKS
6.6 Chapter Summary 179
7. TEMPORAL BACKPROPAGATION 181
7.1 Recurrent PNN as State Space Models 182
7.2 Backpropagation Through Time 184
7.2.1 Derivation of BPTT Algorithms 185
7.2.2 Real Time BPTT Algorithm 189
7.2.3 Epochwise BPTT Algorithm 190
7.3 Real Time Recurrent Learning 191
7.4 Improved Dynamic Training 198
7.4.1 Teacher Enforced Training 198
7.4.2 Truncating in Time 199
7.4.3 Subgrouping 199
7.4.4 Common Temporal Training Problem 200
7.5 Second Order Temporal BP 200
7.6 Recursive Backpropagation 204
7.7 Recurrent Network Optimization 206
7.7.1 Regularization 207
7.7.2 Recurrent Network Pruning 207
7.8 Chapter Summary 208
8. BAYESIAN INFERENCE TECHNIQUES 209
8.1 Bayesian Error Function 211
8.2 Bayesian Neural Network Inference 212
8.2.1 Deriving Hyperparameters 215
8.2.2 Local vs. Global Regularization 217
8.2.3 Evidence Procedure for PNN Models 218
8.2.4 Predictive Data Distribution 221
8.2.5 Choosing a Weight Prior 221
8.3 Bayesian Network Pruning 222
8.4 Sparse Bayesian Learning 224
8.5 Recursive Bayesian Learning 229
8.5.1 Sequential Weight Estimation 229
8.5.2 Sequential Dynamic Hessian Estimation 230
8.5.3 Sequential Hyperparameter Estimation 232
8.6 Monte Carlo Training 234
8.6.1 Markov Chain Monte Carlo 235
8.6.2 Importance Resampling 237
Contents ix
8.6.3 Hybrid Sampling Resampling 237
8.7 Chapter Summary 239
9. STATISTICAL MODEL DIAGNOSTICS 241
9.1 Deviations of PNN Models 242
9 2 Residual Bootstrap Sampling 243
9 3 The Bias/Variance Dilemma 244
9.3.1 Statistical Bias and Variance 244
9.3.2 Measuring Bias and Variance 245
9 4 Confidence Intervals 248
9.4.1 Interval Estimation by the Delta Method 248
9.4.2 Bootstrapping Confidence Intervals 252
9 5 Prediction Intervals 254
9.5.1 Analytical Prediction Intervals 255
9.5.2 Empirical Learning of Prediction Bars 256
9.6 Bayesian Intervals 262
9.6.1 Analytical Bayesian Intervals 263
9.6.2 Empirical Bayesian Intervals 265
9.7 Model Validation Tests 267
9.8 Chapter Summary 271
10. TIME SERIES MODELLING 273
10.1 Time Series Modelling 274
10.2 Data Preprocessing 276
10.3 PNN vs. Linear ARMA Models 277
10.4 PNN vs. Genetically Programmed Functions 279
10.5 PNN vs. Statistical Learning Networks 281
10.6 PNN vs. Neural Network Models 283
10.7 PNN vs. Kernel Models 285
10.8 Recurrent PNN vs. Recurrent Neural Networks 288
10.9 Chapter Summary 290
11. CONCLUSIONS 291
References 295
Index 313 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Nikolaev, Nikolay Iba, Hitoshi |
| author_facet | Nikolaev, Nikolay Iba, Hitoshi |
| author_role | aut aut |
| author_sort | Nikolaev, Nikolay |
| author_variant | n n nn h i hi |
| building | Verbundindex |
| bvnumber | BV022355761 |
| collection | ZDB-2-SCS |
| ctrlnum | (OCoLC)873398998 (DE-599)BVBBV022355761 |
| discipline | Biologie Informatik |
| discipline_str_mv | Biologie Informatik |
| doi_str_mv | 10.1007/0-387-31240-4 |
| edition | 1. Ed. |
| format | Electronic eBook |
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| id | DE-604.BV022355761 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:01:27Z |
| indexdate | 2024-07-09T20:55:49Z |
| institution | BVB |
| isbn | 9780387312392 9780387312408 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015565175 |
| oclc_num | 873398998 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-739 DE-706 DE-M347 DE-634 DE-355 DE-BY-UBR |
| owner_facet | DE-473 DE-BY-UBG DE-739 DE-706 DE-M347 DE-634 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (XIV, 316 S.) 62 schw.-w. Ill., 1 schw.-w. Fotos, 61 schw.-w. graph. Darst. |
| psigel | ZDB-2-SCS |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer US |
| record_format | marc |
| series2 | Genetic and Evolutionary Computation |
| spelling | Nikolaev, Nikolay Verfasser aut Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods Nikolay Nikolaev ; Hitoshi Iba 1. Ed. Berlin Springer US 2006 1 Online-Ressource (XIV, 316 S.) 62 schw.-w. Ill., 1 schw.-w. Fotos, 61 schw.-w. graph. Darst. txt rdacontent c rdamedia cr rdacarrier Genetic and Evolutionary Computation Erscheint: 3. Mai 2006 Iba, Hitoshi Verfasser aut Erscheint auch als Druck-Ausgabe, Hardcover 0-387-31239-0 https://doi.org/10.1007/0-387-31240-4 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015565175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nikolaev, Nikolay Iba, Hitoshi Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods |
| title | Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods |
| title_auth | Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods |
| title_exact_search | Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods |
| title_exact_search_txtP | Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods |
| title_full | Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods Nikolay Nikolaev ; Hitoshi Iba |
| title_fullStr | Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods Nikolay Nikolaev ; Hitoshi Iba |
| title_full_unstemmed | Adaptive Learning of Polynomial Networks genetic programming, backpropagation and Bayesian methods Nikolay Nikolaev ; Hitoshi Iba |
| title_short | Adaptive Learning of Polynomial Networks |
| title_sort | adaptive learning of polynomial networks genetic programming backpropagation and bayesian methods |
| title_sub | genetic programming, backpropagation and Bayesian methods |
| url | https://doi.org/10.1007/0-387-31240-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015565175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nikolaevnikolay adaptivelearningofpolynomialnetworksgeneticprogrammingbackpropagationandbayesianmethods AT ibahitoshi adaptivelearningofpolynomialnetworksgeneticprogrammingbackpropagationandbayesianmethods |