Support vector machines:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | Information science and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 601 S. Ill., graph. Darst. |
| ISBN: | 0387772413 9780387772417 9781489989635 |
Staff View
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| adam_text | Contents
Preface ........................................................... vii
Reading Guide ...................................................... xi
1 Introduction...................................................... 1
1.1 Statistical Learning......................................... 1
1.2 Support Vector Machines: An Overview......................... 7
1.3 History of SVMs and Geometrical Interpretation.............. 13
1.4 Alternatives to SVMs........................................ 19
2 Loss Functions and Their Risks................................ 21
2.1 Loss Functions: Definition and Examples..................... 21
2.2 Basic Properties of Loss Functions and Their Risks.......... 28
2.3 Margin-Based Losses for Classification Problems............. 34
2.4 Distance-Based Losses for Regression Problems............... 38
2.5 Further Reading and Advanced Topics......................... 45
2.6 Summary..................................................... 46
2.7 Exercises................................................... 46
3 Surrogate Loss Functions (*) ................................. 49
3.1 Inner Risks and the Calibration Function.................... 51
3.2 Asymptotic Theory of Surrogate Losses....................... 60
3.3 Inequalities between Excess Risks .......................... 63
3.4 Surrogates for Unweighted Binary Classification............. 71
3.5 Surrogates for Weighted Binary Classification............... 76
3.6 Template Loss Functions..................................... 80
3.7 Surrogate Losses for Regression Problems.................... 81
3.8 Surrogate Losses for the Density Level Problem.............. 93
3.9 Self-Calibrated Loss Functions.............................. 97
3.10 Further Reading and Advanced Topics........................105
3.11 Summary....................................................106
3.12 Exercises..................................................107
Ill
112
119
124
132
149
151
159
161
162
165
166
169
173
178
187
197
200
200
203
204
210
218
223
229
234
235
236
239
240
242
246
258
270
279
282
283
Contents
Kernels and Reproducing Kernel Hilbert Spaces...........
4.1 Basic Properties and Examples of Kernels...........
4.2 The Reproducing Kernel Hilbert Space of a Kernel
4.3 Properties of RKHSs................................
4.4 Gaussian Kernels and Their RKHSs ..................
4.5 Mercer’s Theorem (*)...............................
4.6 Large Reproducing Kernel Hilbert Spaces............
4.7 Further Reading and Advanced Topics................
4.8 Summary............................................
4.9 Exercises..........................................
Infinite-Sample Versions of Support Vector Machines
5.1 Existence and Uniqueness of SVM Solutions..........
5.2 A General Representer Theorem......................
5.3 Stability of Infinite-Sample SVMs .................
5.4 Behavior for Small Regularization Parameters.......
5.5 Approximation Error of RKHSs.......................
5.6 Further Reading and Advanced Topics................
5.7 Summary............................................
5.8 Exercises..........................................
Basic Statistical Analysis of SVMs......................
6.1 Notions of Statistical Learning....................
6.2 Basic Concentration Inequalities...................
6.3 Statistical Analysis of Empirical Risk Minimization
6.4 Basic Oracle Inequalities for SVMs ................
6.5 Data-Dependent Parameter Selection for SVMs .......
6.6 Further Reading and Advanced Topics................
6.7 Summary............................................
6.8 Exercises..........................................
Advanced Statistical Analysis of SVMs (*) ..............
7.1 Why Do We Need a Refined Analysis?.................
7.2 A Refined Oracle Inequality for ERM................
7.3 Some Advanced Machinery............................
7.4 Refined Oracle Inequalities for SVMs ..............
7.5 Some Bounds on Average Entropy Numbers.............
7.6 Further Reading and Advanced Topics................
7.7 Summary............................................
7.8 Exercises..........................................
Contents
XV
8 Support Vector Machines for Classification....................287
8.1 Basic Oracle Inequalities for Classifying with SVMs......288
8.2 Classifying with SVMs Using Gaussian Kernels.............290
8.3 Advanced Concentration Results for SVMs (*)........307
8.4 Sparseness of SVMs Using the Hinge Loss..................310
8.5 Classifying with other Margin-Based Losses (*)........314
8.6 Further Reading and x dvanced Topics.....................326
8.7 Summary..................................................329
8.8 Exercises................................................330
9 Support Vector Machines for Regression........................333
9.1 Introduction.............................................333
9.2 Consistency..............................................335
9.3 SVMs for Quantile Regression.............................340
9.4 Numerical Results for Quantile Regression................344
9.5 Median Regression with the eps-Insensitive Loss (*)......348
9.6 Further Reading and Advanced Topics......................352
9.7 Summary..................................................353
9.8 Exercises................................................353
10 Robustness....................................................355
10.1 Motivation ..............................................356
10.2 Approaches to Robust Statistics..........................362
10.3 Robustness of SVMs for Classification....................368
10.4 Robustness of SVMs for Regression (*)....................379
10.5 Robust Learning from Bites (*) ..........................391
10.6 Further Reading and Advanced Topics......................403
10.7 Summary..................................................408
10.8 Exercises................................................409
11 Computational Aspects.........................................411
11.1 SVMs, Convex Programs, and Duality ......................412
11.2 Implementation Techniques................................420
11.3 Determination of Hyperparameters.........................443
11.4 Software Packages........................................448
11.5 Further Reading and Advanced Topics......................450
11.6 Summary..................................................452
11.7 Exercises................................................453
12 Data Mining...................................................455
12.1 Introduction.............................................456
12.2 CRISP-DM Strategy........................................457
12.3 Role of SVMs in Data Mining..............................467
12.4 Software Tools for Data Mining...........................467
12.5 Further Reading and Advanced Topics......................468
XVI
Contents
12.6 Summary....................................................469
12.7 Exercises..................................................469
Appendix.............................................................471
A.l Basic Equations, Inequalities, and Functions................471
A.2 Topology....................................................475
A.3 Measure and Integration Theory..............................479
A.3.1 Some Basic Facts......................................480
A.3.2 Measures on Topological Spaces........................486
A.3.3 Aumann’s Measurable Selection Principle...............487
A.4 Probability Theory and Statistics...........................489
A.4.1 Some Basic Facts......................................489
A.4.2 Some Limit Theorems...................................492
A.4.3 The Weak* Topology and Its Metrization................494
A.5 Functional Analysis.........................................497
A.5.1 Essentials on Banach Spaces and Linear Operators .... 497
A.5.2 Hilbert Spaces........................................501
A.5.3 The Calculus in Normed Spaces.........................507
A.5.4 Banach Space Valued Integration.......................508
A.5.5 Some Important Banach Spaces..........................511
A.5.6 Entropy Numbers.......................................516
A.6 Convex Analysis.............................................519
A.6.1 Basic Properties of Convex Functions..................520
A.6.2 Subdifferential Calculus for Convex Functions.........523
A.6.3 Some Further Notions of Convexity.....................526
A.6.4 The Fenchel-Legendre Bi-conjugate.....................529
A.6.5 Convex Programs and Lagrange Multipliers..............530
A.7 Complex Analysis............................................534
A.8 Inequalities Involving Rademacher Sequences ................534
A.9 Talagrand’s Inequality......................................538
References...........................................................553
Notation and Symbols.................................................579
Abbreviations .......................................................583
Author Index.........................................................585
Subject Index
591
|
| adam_txt |
Contents
Preface . vii
Reading Guide . xi
1 Introduction. 1
1.1 Statistical Learning. 1
1.2 Support Vector Machines: An Overview. 7
1.3 History of SVMs and Geometrical Interpretation. 13
1.4 Alternatives to SVMs. 19
2 Loss Functions and Their Risks. 21
2.1 Loss Functions: Definition and Examples. 21
2.2 Basic Properties of Loss Functions and Their Risks. 28
2.3 Margin-Based Losses for Classification Problems. 34
2.4 Distance-Based Losses for Regression Problems. 38
2.5 Further Reading and Advanced Topics. 45
2.6 Summary. 46
2.7 Exercises. 46
3 Surrogate Loss Functions (*) . 49
3.1 Inner Risks and the Calibration Function. 51
3.2 Asymptotic Theory of Surrogate Losses. 60
3.3 Inequalities between Excess Risks . 63
3.4 Surrogates for Unweighted Binary Classification. 71
3.5 Surrogates for Weighted Binary Classification. 76
3.6 Template Loss Functions. 80
3.7 Surrogate Losses for Regression Problems. 81
3.8 Surrogate Losses for the Density Level Problem. 93
3.9 Self-Calibrated Loss Functions. 97
3.10 Further Reading and Advanced Topics.105
3.11 Summary.106
3.12 Exercises.107
Ill
112
119
124
132
149
151
159
161
162
165
166
169
173
178
187
197
200
200
203
204
210
218
223
229
234
235
236
239
240
242
246
258
270
279
282
283
Contents
Kernels and Reproducing Kernel Hilbert Spaces.
4.1 Basic Properties and Examples of Kernels.
4.2 The Reproducing Kernel Hilbert Space of a Kernel
4.3 Properties of RKHSs.
4.4 Gaussian Kernels and Their RKHSs .
4.5 Mercer’s Theorem (*).
4.6 Large Reproducing Kernel Hilbert Spaces.
4.7 Further Reading and Advanced Topics.
4.8 Summary.
4.9 Exercises.
Infinite-Sample Versions of Support Vector Machines
5.1 Existence and Uniqueness of SVM Solutions.
5.2 A General Representer Theorem.
5.3 Stability of Infinite-Sample SVMs .
5.4 Behavior for Small Regularization Parameters.
5.5 Approximation Error of RKHSs.
5.6 Further Reading and Advanced Topics.
5.7 Summary.
5.8 Exercises.
Basic Statistical Analysis of SVMs.
6.1 Notions of Statistical Learning.
6.2 Basic Concentration Inequalities.
6.3 Statistical Analysis of Empirical Risk Minimization
6.4 Basic Oracle Inequalities for SVMs .
6.5 Data-Dependent Parameter Selection for SVMs .
6.6 Further Reading and Advanced Topics.
6.7 Summary.
6.8 Exercises.
Advanced Statistical Analysis of SVMs (*) .
7.1 Why Do We Need a Refined Analysis?.
7.2 A Refined Oracle Inequality for ERM.
7.3 Some Advanced Machinery.
7.4 Refined Oracle Inequalities for SVMs .
7.5 Some Bounds on Average Entropy Numbers.
7.6 Further Reading and Advanced Topics.
7.7 Summary.
7.8 Exercises.
Contents
XV
8 Support Vector Machines for Classification.287
8.1 Basic Oracle Inequalities for Classifying with SVMs.288
8.2 Classifying with SVMs Using Gaussian Kernels.290
8.3 Advanced Concentration Results for SVMs (*).307
8.4 Sparseness of SVMs Using the Hinge Loss.310
8.5 Classifying with other Margin-Based Losses (*).314
8.6 Further Reading and x\dvanced Topics.326
8.7 Summary.329
8.8 Exercises.330
9 Support Vector Machines for Regression.333
9.1 Introduction.333
9.2 Consistency.335
9.3 SVMs for Quantile Regression.340
9.4 Numerical Results for Quantile Regression.344
9.5 Median Regression with the eps-Insensitive Loss (*).348
9.6 Further Reading and Advanced Topics.352
9.7 Summary.353
9.8 Exercises.353
10 Robustness.355
10.1 Motivation .356
10.2 Approaches to Robust Statistics.362
10.3 Robustness of SVMs for Classification.368
10.4 Robustness of SVMs for Regression (*).379
10.5 Robust Learning from Bites (*) .391
10.6 Further Reading and Advanced Topics.403
10.7 Summary.408
10.8 Exercises.409
11 Computational Aspects.411
11.1 SVMs, Convex Programs, and Duality .412
11.2 Implementation Techniques.420
11.3 Determination of Hyperparameters.443
11.4 Software Packages.448
11.5 Further Reading and Advanced Topics.450
11.6 Summary.452
11.7 Exercises.453
12 Data Mining.455
12.1 Introduction.456
12.2 CRISP-DM Strategy.457
12.3 Role of SVMs in Data Mining.467
12.4 Software Tools for Data Mining.467
12.5 Further Reading and Advanced Topics.468
XVI
Contents
12.6 Summary.469
12.7 Exercises.469
Appendix.471
A.l Basic Equations, Inequalities, and Functions.471
A.2 Topology.475
A.3 Measure and Integration Theory.479
A.3.1 Some Basic Facts.480
A.3.2 Measures on Topological Spaces.486
A.3.3 Aumann’s Measurable Selection Principle.487
A.4 Probability Theory and Statistics.489
A.4.1 Some Basic Facts.489
A.4.2 Some Limit Theorems.492
A.4.3 The Weak* Topology and Its Metrization.494
A.5 Functional Analysis.497
A.5.1 Essentials on Banach Spaces and Linear Operators . 497
A.5.2 Hilbert Spaces.501
A.5.3 The Calculus in Normed Spaces.507
A.5.4 Banach Space Valued Integration.508
A.5.5 Some Important Banach Spaces.511
A.5.6 Entropy Numbers.516
A.6 Convex Analysis.519
A.6.1 Basic Properties of Convex Functions.520
A.6.2 Subdifferential Calculus for Convex Functions.523
A.6.3 Some Further Notions of Convexity.526
A.6.4 The Fenchel-Legendre Bi-conjugate.529
A.6.5 Convex Programs and Lagrange Multipliers.530
A.7 Complex Analysis.534
A.8 Inequalities Involving Rademacher Sequences .534
A.9 Talagrand’s Inequality.538
References.553
Notation and Symbols.579
Abbreviations .583
Author Index.585
Subject Index
591 |
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| indexdate | 2024-07-09T21:16:38Z |
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| series2 | Information science and statistics |
| spelling | Steinwart, Ingo 1970- Verfasser (DE-588)121972682 aut Support vector machines Ingo Steinwart ; Andreas Christmann New York, NY Springer 2008 XVI, 601 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Information science and statistics Support vector machines Support-Vektor-Maschine (DE-588)4505517-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Support-Vektor-Maschine (DE-588)4505517-8 s DE-604 Christmann, Andreas 1963- Verfasser (DE-588)129120898 aut Erscheint auch als Online-Ausgabe 978-0-387-77242-4 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=016536358&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Steinwart, Ingo 1970- Christmann, Andreas 1963- Support vector machines Support vector machines Support-Vektor-Maschine (DE-588)4505517-8 gnd |
| subject_GND | (DE-588)4505517-8 (DE-588)4151278-9 |
| title | Support vector machines |
| title_auth | Support vector machines |
| title_exact_search | Support vector machines |
| title_exact_search_txtP | Support vector machines |
| title_full | Support vector machines Ingo Steinwart ; Andreas Christmann |
| title_fullStr | Support vector machines Ingo Steinwart ; Andreas Christmann |
| title_full_unstemmed | Support vector machines Ingo Steinwart ; Andreas Christmann |
| title_short | Support vector machines |
| title_sort | support vector machines |
| topic | Support vector machines Support-Vektor-Maschine (DE-588)4505517-8 gnd |
| topic_facet | Support vector machines Support-Vektor-Maschine Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016536358&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT steinwartingo supportvectormachines AT christmannandreas supportvectormachines |