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Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty
| Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty |
| Autore | Braga-Neto Ulisses de Mendon AÀca |
| Pubbl/distr/stampa | Chichester, West Sussex : , : Wiley Blackwell, , 2015 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina | 610.28 |
| Collana | IEEE press series on biomedical engineering |
| Soggetto topico |
Biomedical engineering -- Congresses
Image processing -- Digital techniques Optical pattern recognition Pattern recognition systems - Mathematics Pattern perception Error analysis (Mathematics) Electrical Engineering Electrical & Computer Engineering Engineering & Applied Sciences |
| ISBN |
1-119-07937-3
1-119-07933-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | PREFACE XIII -- ACKNOWLEDGMENTS XIX -- LIST OF SYMBOLS XXI -- 1 CLASSIFICATION 1 -- 1.1 Classifiers 1 -- 1.2 Population-Based Discriminants 3 -- 1.3 Classification Rules 8 -- 1.4 Sample-Based Discriminants 13 -- 1.4.1 Quadratic Discriminants 14 -- 1.4.2 Linear Discriminants 15 -- 1.4.3 Kernel Discriminants 16 -- 1.5 Histogram Rule 16 -- 1.6 Other Classification Rules 20 -- 1.6.1 k-Nearest-Neighbor Rules 20 -- 1.6.2 Support Vector Machines 21 -- 1.6.3 Neural Networks 22 -- 1.6.4 Classification Trees 23 -- 1.6.5 Rank-Based Rules 24 -- 1.7 Feature Selection 25 -- Exercises 28 -- 2 ERROR ESTIMATION35 -- 2.1 Error Estimation Rules 35 -- 2.2 Performance Metrics 38 -- 2.2.1 Deviation Distribution 39 -- 2.2.2 Consistency 41 -- 2.2.3 Conditional Expectation 41 -- 2.2.4 Linear Regression 42 -- 2.2.5 Confidence Intervals 42 -- 2.3 Test-Set Error Estimation 43 -- 2.4 Resubstitution 46 -- 2.5 Cross-Validation 48 -- 2.6 Bootstrap 55 -- 2.7 Convex Error Estimation 57 -- 2.8 Smoothed Error Estimation 61 -- 2.9 Bolstered Error Estimation 63 -- 2.9.1 Gaussian-Bolstered Error Estimation 67 -- 2.9.2 Choosing the Amount of Bolstering 68 -- 2.9.3 Calibrating the Amount of Bolstering 71 -- Exercises 73 -- 3 PERFORMANCE ANALYSIS77 -- 3.1 Empirical Deviation Distribution 77 -- 3.2 Regression 79 -- 3.3 Impact on Feature Selection 82 -- 3.4 Multiple-Data-Set Reporting Bias 84 -- 3.5 Multiple-Rule Bias 86 -- 3.6 Performance Reproducibility 92 -- Exercises 94 -- 4 ERROR ESTIMATION FOR DISCRETE CLASSIFICATION 97 -- 4.1 Error Estimators 98 -- 4.1.1 Resubstitution Error 98 -- 4.1.2 Leave-One-Out Error 98 -- 4.1.3 Cross-Validation Error 99 -- 4.1.4 Bootstrap Error 99 -- 4.2 Small-Sample Performance 101 -- 4.2.1 Bias 101 -- 4.2.2 Variance 103 -- 4.2.3 Deviation Variance, RMS, and Correlation 105 -- 4.2.4 Numerical Example 106 -- 4.2.5 Complete Enumeration Approach 108 -- 4.3 Large-Sample Performance 110 -- Exercises 114 -- 5 DISTRIBUTION THEORY 115 -- 5.1 Mixture Sampling Versus Separate Sampling 115 -- 5.2 Sample-Based Discriminants Revisited 119 -- 5.3 True Error 120 -- 5.4 Error Estimators 121 -- 5.4.1 Resubstitution Error 121 -- 5.4.2 Leave-One-Out Error 122 -- 5.4.3 Cross-Validation Error 122 -- 5.4.4 Bootstrap Error 124 -- 5.5 Expected Error Rates 125 -- 5.5.1 True Error 125 -- 5.5.2 Resubstitution Error 128 -- 5.5.3 Leave-One-Out Error 130 -- 5.5.4 Cross-Validation Error 132 -- 5.5.5 Bootstrap Error 133 -- 5.6 Higher-Order Moments of Error Rates 136 -- 5.6.1 True Error 136 -- 5.6.2 Resubstitution Error 137 -- 5.6.3 Leave-One-Out Error 139 -- 5.7 Sampling Distribution of Error Rates 140 -- 5.7.1 Resubstitution Error 140 -- 5.7.2 Leave-One-Out Error 141 -- Exercises 142 -- 6 GAUSSIAN DISTRIBUTION THEORY: UNIVARIATE CASE 145 -- 6.1 Historical Remarks 146 -- 6.2 Univariate Discriminant 147 -- 6.3 Expected Error Rates 148 -- 6.3.1 True Error 148 -- 6.3.2 Resubstitution Error 151 -- 6.3.3 Leave-One-Out Error 152 -- 6.3.4 Bootstrap Error 152 -- 6.4 Higher-Order Moments of Error Rates 154 -- 6.4.1 True Error 154 -- 6.4.2 Resubstitution Error 157 -- 6.4.3 Leave-One-Out Error 160 -- 6.4.4 Numerical Example 165 -- 6.5 Sampling Distributions of Error Rates 166 -- 6.5.1 Marginal Distribution of Resubstitution Error 166 -- 6.5.2 Marginal Distribution of Leave-One-Out Error 169 -- 6.5.3 Joint Distribution of Estimated and True Errors 174 -- Exercises 176 -- 7 GAUSSIAN DISTRIBUTION THEORY: MULTIVARIATE CASE 179 -- 7.1 Multivariate Discriminants 179 -- 7.2 Small-Sample Methods 180 -- 7.2.1 Statistical Representations 181 -- 7.2.2 Computational Methods 194 -- 7.3 Large-Sample Methods 199 -- 7.3.1 Expected Error Rates 200 -- 7.3.2 Second-Order Moments of Error Rates 207 -- Exercises 218 -- 8 BAYESIAN MMSE ERROR ESTIMATION221 -- 8.1 The Bayesian MMSE Error Estimator 222 -- 8.2 Sample-Conditioned MSE 226 -- 8.3 Discrete Classification 227 -- 8.4 Linear Classification of Gaussian Distributions 238 -- 8.5 Consistency 246 -- 8.6 Calibration 253 -- 8.7 Concluding Remarks 255 -- Exercises 257 -- A BASIC PROBABILITY REVIEW 259 -- A.1 Sample Spaces and Events 259 -- A.2 Definition of Probability 260 -- A.3 Borel-Cantelli Lemmas 261 -- A.4 Conditional Probability 262 -- A.5 Random Variables 263 -- A.6 Discrete Random Variables 265 -- A.7 Expectation 266 -- A.8 Conditional Expectation 268 -- A.9 Variance 269 -- A.10 Vector Random Variables 270 -- A.11 The Multivariate Gaussian 271 -- A.12 Convergence of Random Sequences 273 -- A.13 Limiting Theorems 275 -- B VAPNIK-CHERVONENKIS THEORY 277 -- B.1 Shatter Coefficients 277 -- B.2 The VC Dimension 278 -- B.3 VC Theory of Classification 279 -- B.3.1 Linear Classification Rules 279 -- B.3.2 kNN Classification Rule 280 -- B.3.3 Classification Trees 280 -- B.3.4 Nonlinear SVMs 281 -- B.3.5 Neural Networks 281 -- B.3.6 Histogram Rules 281 -- B.4 Vapnik-Chervonenkis Theorem 282 -- C DOUBLE ASYMPTOTICS 285 -- BIBLIOGRAPHY 291 -- AUTHOR INDEX 301 -- SUBJECT INDEX 305. |
| Record Nr. | UNINA-9910131376903321 |
Braga-Neto Ulisses de Mendon AÀca
|
||
| Chichester, West Sussex : , : Wiley Blackwell, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty
| Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty |
| Autore | Braga-Neto Ulisses de Mendon AÀca |
| Pubbl/distr/stampa | Chichester, West Sussex : , : Wiley Blackwell, , 2015 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina | 610.28 |
| Collana | IEEE press series on biomedical engineering |
| Soggetto topico |
Biomedical engineering -- Congresses
Image processing -- Digital techniques Optical pattern recognition Pattern recognition systems - Mathematics Pattern perception Error analysis (Mathematics) Electrical Engineering Electrical & Computer Engineering Engineering & Applied Sciences |
| ISBN |
1-119-07937-3
1-119-07933-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | PREFACE XIII -- ACKNOWLEDGMENTS XIX -- LIST OF SYMBOLS XXI -- 1 CLASSIFICATION 1 -- 1.1 Classifiers 1 -- 1.2 Population-Based Discriminants 3 -- 1.3 Classification Rules 8 -- 1.4 Sample-Based Discriminants 13 -- 1.4.1 Quadratic Discriminants 14 -- 1.4.2 Linear Discriminants 15 -- 1.4.3 Kernel Discriminants 16 -- 1.5 Histogram Rule 16 -- 1.6 Other Classification Rules 20 -- 1.6.1 k-Nearest-Neighbor Rules 20 -- 1.6.2 Support Vector Machines 21 -- 1.6.3 Neural Networks 22 -- 1.6.4 Classification Trees 23 -- 1.6.5 Rank-Based Rules 24 -- 1.7 Feature Selection 25 -- Exercises 28 -- 2 ERROR ESTIMATION35 -- 2.1 Error Estimation Rules 35 -- 2.2 Performance Metrics 38 -- 2.2.1 Deviation Distribution 39 -- 2.2.2 Consistency 41 -- 2.2.3 Conditional Expectation 41 -- 2.2.4 Linear Regression 42 -- 2.2.5 Confidence Intervals 42 -- 2.3 Test-Set Error Estimation 43 -- 2.4 Resubstitution 46 -- 2.5 Cross-Validation 48 -- 2.6 Bootstrap 55 -- 2.7 Convex Error Estimation 57 -- 2.8 Smoothed Error Estimation 61 -- 2.9 Bolstered Error Estimation 63 -- 2.9.1 Gaussian-Bolstered Error Estimation 67 -- 2.9.2 Choosing the Amount of Bolstering 68 -- 2.9.3 Calibrating the Amount of Bolstering 71 -- Exercises 73 -- 3 PERFORMANCE ANALYSIS77 -- 3.1 Empirical Deviation Distribution 77 -- 3.2 Regression 79 -- 3.3 Impact on Feature Selection 82 -- 3.4 Multiple-Data-Set Reporting Bias 84 -- 3.5 Multiple-Rule Bias 86 -- 3.6 Performance Reproducibility 92 -- Exercises 94 -- 4 ERROR ESTIMATION FOR DISCRETE CLASSIFICATION 97 -- 4.1 Error Estimators 98 -- 4.1.1 Resubstitution Error 98 -- 4.1.2 Leave-One-Out Error 98 -- 4.1.3 Cross-Validation Error 99 -- 4.1.4 Bootstrap Error 99 -- 4.2 Small-Sample Performance 101 -- 4.2.1 Bias 101 -- 4.2.2 Variance 103 -- 4.2.3 Deviation Variance, RMS, and Correlation 105 -- 4.2.4 Numerical Example 106 -- 4.2.5 Complete Enumeration Approach 108 -- 4.3 Large-Sample Performance 110 -- Exercises 114 -- 5 DISTRIBUTION THEORY 115 -- 5.1 Mixture Sampling Versus Separate Sampling 115 -- 5.2 Sample-Based Discriminants Revisited 119 -- 5.3 True Error 120 -- 5.4 Error Estimators 121 -- 5.4.1 Resubstitution Error 121 -- 5.4.2 Leave-One-Out Error 122 -- 5.4.3 Cross-Validation Error 122 -- 5.4.4 Bootstrap Error 124 -- 5.5 Expected Error Rates 125 -- 5.5.1 True Error 125 -- 5.5.2 Resubstitution Error 128 -- 5.5.3 Leave-One-Out Error 130 -- 5.5.4 Cross-Validation Error 132 -- 5.5.5 Bootstrap Error 133 -- 5.6 Higher-Order Moments of Error Rates 136 -- 5.6.1 True Error 136 -- 5.6.2 Resubstitution Error 137 -- 5.6.3 Leave-One-Out Error 139 -- 5.7 Sampling Distribution of Error Rates 140 -- 5.7.1 Resubstitution Error 140 -- 5.7.2 Leave-One-Out Error 141 -- Exercises 142 -- 6 GAUSSIAN DISTRIBUTION THEORY: UNIVARIATE CASE 145 -- 6.1 Historical Remarks 146 -- 6.2 Univariate Discriminant 147 -- 6.3 Expected Error Rates 148 -- 6.3.1 True Error 148 -- 6.3.2 Resubstitution Error 151 -- 6.3.3 Leave-One-Out Error 152 -- 6.3.4 Bootstrap Error 152 -- 6.4 Higher-Order Moments of Error Rates 154 -- 6.4.1 True Error 154 -- 6.4.2 Resubstitution Error 157 -- 6.4.3 Leave-One-Out Error 160 -- 6.4.4 Numerical Example 165 -- 6.5 Sampling Distributions of Error Rates 166 -- 6.5.1 Marginal Distribution of Resubstitution Error 166 -- 6.5.2 Marginal Distribution of Leave-One-Out Error 169 -- 6.5.3 Joint Distribution of Estimated and True Errors 174 -- Exercises 176 -- 7 GAUSSIAN DISTRIBUTION THEORY: MULTIVARIATE CASE 179 -- 7.1 Multivariate Discriminants 179 -- 7.2 Small-Sample Methods 180 -- 7.2.1 Statistical Representations 181 -- 7.2.2 Computational Methods 194 -- 7.3 Large-Sample Methods 199 -- 7.3.1 Expected Error Rates 200 -- 7.3.2 Second-Order Moments of Error Rates 207 -- Exercises 218 -- 8 BAYESIAN MMSE ERROR ESTIMATION221 -- 8.1 The Bayesian MMSE Error Estimator 222 -- 8.2 Sample-Conditioned MSE 226 -- 8.3 Discrete Classification 227 -- 8.4 Linear Classification of Gaussian Distributions 238 -- 8.5 Consistency 246 -- 8.6 Calibration 253 -- 8.7 Concluding Remarks 255 -- Exercises 257 -- A BASIC PROBABILITY REVIEW 259 -- A.1 Sample Spaces and Events 259 -- A.2 Definition of Probability 260 -- A.3 Borel-Cantelli Lemmas 261 -- A.4 Conditional Probability 262 -- A.5 Random Variables 263 -- A.6 Discrete Random Variables 265 -- A.7 Expectation 266 -- A.8 Conditional Expectation 268 -- A.9 Variance 269 -- A.10 Vector Random Variables 270 -- A.11 The Multivariate Gaussian 271 -- A.12 Convergence of Random Sequences 273 -- A.13 Limiting Theorems 275 -- B VAPNIK-CHERVONENKIS THEORY 277 -- B.1 Shatter Coefficients 277 -- B.2 The VC Dimension 278 -- B.3 VC Theory of Classification 279 -- B.3.1 Linear Classification Rules 279 -- B.3.2 kNN Classification Rule 280 -- B.3.3 Classification Trees 280 -- B.3.4 Nonlinear SVMs 281 -- B.3.5 Neural Networks 281 -- B.3.6 Histogram Rules 281 -- B.4 Vapnik-Chervonenkis Theorem 282 -- C DOUBLE ASYMPTOTICS 285 -- BIBLIOGRAPHY 291 -- AUTHOR INDEX 301 -- SUBJECT INDEX 305. |
| Record Nr. | UNINA-9910830222903321 |
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Braga-Neto Ulisses de Mendon AÀca
|
||
| Chichester, West Sussex : , : Wiley Blackwell, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Genomic signal processing / / Ilya Shmulevich and Edward R. Dougherty
| Genomic signal processing / / Ilya Shmulevich and Edward R. Dougherty |
| Autore | Shmulevich Ilya <1969-> |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2007 |
| Descrizione fisica | 1 online resource (314 p.) |
| Disciplina | 572.8/65 |
| Collana | Princeton Series in Applied Mathematics |
| Soggetto topico |
Cellular signal transduction
Genetic regulation Genomics - Mathematical models Gene regulatory networks |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4008-6526-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Biological Foundations -- Chapter Two. Deterministic Models of Gene Networks -- Chapter Three. Stochastic Models of Gene Networks -- Chapter Four. Classification -- Chapter Five. Regularization -- Chapter Six. Clustering -- Index |
| Record Nr. | UNINA-9910465346503321 |
|
Shmulevich Ilya <1969->
|
||
| Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Genomic signal processing / / Ilya Shmulevich and Edward R. Dougherty
| Genomic signal processing / / Ilya Shmulevich and Edward R. Dougherty |
| Autore | Shmulevich Ilya <1969-> |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2007 |
| Descrizione fisica | 1 online resource (314 p.) |
| Disciplina | 572.8/65 |
| Collana | Princeton Series in Applied Mathematics |
| Soggetto topico |
Cellular signal transduction
Genetic regulation Genomics - Mathematical models Gene regulatory networks |
| ISBN | 1-4008-6526-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Biological Foundations -- Chapter Two. Deterministic Models of Gene Networks -- Chapter Three. Stochastic Models of Gene Networks -- Chapter Four. Classification -- Chapter Five. Regularization -- Chapter Six. Clustering -- Index |
| Record Nr. | UNINA-9910786749503321 |
|
Shmulevich Ilya <1969->
|
||
| Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Genomic signal processing / / Ilya Shmulevich and Edward R. Dougherty
| Genomic signal processing / / Ilya Shmulevich and Edward R. Dougherty |
| Autore | Shmulevich Ilya <1969-> |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2007 |
| Descrizione fisica | 1 online resource (314 p.) |
| Disciplina | 572.8/65 |
| Collana | Princeton Series in Applied Mathematics |
| Soggetto topico |
Cellular signal transduction
Genetic regulation Genomics - Mathematical models Gene regulatory networks |
| ISBN | 1-4008-6526-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Biological Foundations -- Chapter Two. Deterministic Models of Gene Networks -- Chapter Three. Stochastic Models of Gene Networks -- Chapter Four. Classification -- Chapter Five. Regularization -- Chapter Six. Clustering -- Index |
| Record Nr. | UNINA-9910828604703321 |
|
Shmulevich Ilya <1969->
|
||
| Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||