Learning linear classifiers: theory and algorithms
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 202 S. Ill., graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Herbrich, Ralf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Learning linear classifiers |b theory and algorithms |c vorgelegt von Ralf Herbrich |
| 264 | 1 | |c 2001 | |
| 300 | |a XVI, 202 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 502 | |a Berlin, Techn. Univ., Diss., 2000 | ||
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Record in the Search Index
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| adam_text |
CONTENTS
1 LEARNING ALGORITHMS 1
X LEARNING I^INEAR ^LLA
SSI^LERS M XERNEL S^#ACES 3
1.1 THE BASIC SETTING. 3
1.2 LEARNING BY RISK MINIMISATION. 7
1.2.1 THE (PRIMAL) PERCEPTRON ALGORITHM. 8
1.2.2 REGULARISED RISK FUNCTIONALS. 9
1.2.3 DUALITY THEORY. 11
1.3 KERNELS AND REPRODUCING KERNEL HILBERT SPACES. 12
1.3.1 EXPLICIT MAPPINGS AND KERNELS. 13
1.3.2 THE KERNEL TECHNIQUE. 14
1.3.3 REPRODUCING KERNEL HILBERT SPACES. 17
1.3.4 A GEOMETRICAL PICTURE. 18
1.4 SUPPORT VECTOR CLASSIFICATION LEARNING. 20
1.4.1 MAXIMISING THE MARGIN. 20
1.4.2 SOFT MARGINS - LEARNING WITH TRAINING ERROR. 23
1.4.3 GEOMETRICAL VIEWPOINTS ON MARGIN MAXIMISATION. 25
1.4.4 THE I/-TYICK AND OTHER VARIANTS. 26
1.5 DISCUSSION. 29
2 SUPPORT VECTOR MACHINES FOR
ORDINAL REGRESSION 31
2.1 THE,ORDINAL REGRESSION SETTING. 31
2.2 GENERATIVE MODELS FOR ORDINAL REGRESSION. 32
2.2.1 STOCHASTIC ORDERING AND STOCHASTIC TRANSITIVITY. 33
2.2.2 THE CUMULATIVE THRESHOLD MODEL . 34
2.3 A RISK FORMULATION FOR ORDINAL REGRESSION . 35
2.4 SUPPORT VECTOR MACHINES FOR ORDINAL REGRESSION. 38
2.5 EXPERIMENTAL RESULTS.,. 40
2.5.1 LEARNING CURVES FOR ORDINAL REGRESSION. 40
2.5.2 AN APPLICATION TO INFORMATION RETRIEVAL. 43
2.6 DISCUSSION . 44
3 LINEAR PROGRAMMING MACHINES FOR PROXIMITY DATA 45
3.1 THE NATURE OF PROXIMITY DATA. 45
3.1.1 EUCLIDEAN AND PSEUDO-EUCLIDEAN SPACES. 46
3.1.2 PROXIMITY SPACES. 47
3.2 LINEAR PROGRAMMING MACHINES. 47
3.2.1 I/-LP MACHINES. 48
3.3 EXPERIMENTAL RESULTS. 49
3.3.1 SURROGATE DATA. 49
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/961358823
VI
3.3.2 REAL WORLD DATA. 50
3.4 DISCUSSION. 51
4 ADAPTIVE MARGIN MACHINES
53
4.1 MINIMISING A LEAVE-ONE-OUT BOUND . 53
4.1.1 A RECENT LEAVE-ONE-OUT BOUND. 54
4.1.2 PITFALLS OF MINIMISING A LEAVE-ONE-OUT BOUND. 55
4.2 LEAVE-ONE-OUT MACHINES. 56
4.3 ADAPTIVE MARGIN MACHINES .
57
4.3.1 CLUSTERING IN KERNEL SPACE . 58
4.4 EXPERIMENTAL RESULTS. 60
4.4.1 SURROGATE DATA. 60
4.4.2 BENCHMARK DATASETS. 62
4.5 DISCUSSION. 64
5 BAYES POINT MACHINES 65
5.1 THE OPTIMAL HYPERPLANE . 65
5.1.1 THE STATISTICAL PHYSICS APPROACH TO LEARNING LINEAR CLASSIFIERS
66
5.1.2 THE OPTIMAL HYPERPLANE IN A BAYESIAN FRAMEWORK. 67
5.2 ESTIMATING THE BAYES POINT IN KERNEL SPACE. 69
5.2.1 MARKOV-CHAIN-MONTE-CARLO SAMPLING METHODS. 69
5.2.2 THE KERNEL BILLIARD. 70
5.3 BAYES POINT ESTIMATION WITH IVAINING ERROR. 72
5.4 EXPERIMENTAL RESULTS.
74
5.4.1 SURROGATE DATA.
74
5.4.2 REAL WORLD DATA. 75
5.5 DISCUSSION .
75
II LEARNING THEORY
77
6
MATHEMATICAL MODELS OF LEARNING 79 *
6.1 DESCRIPTIVE VS. PREDICTIVE MODELS. 79
6.2
GENERATIVE MODELS. 84
6.2.1 THE FISHER LINEAR DISCRIMINANT. 85
6
.
2.2
THE CURSE OF DIMENSIONALITY - PITFALLS OF GENERATIVE MODELS
86
6.3 PAC AND VC FRAMEWORK. 87
6.3.1 CLASSICAL PAC AND VC ANALYSIS .
88
6.3.2 GROWTH FUNCTION AND VC DIMENSION. 91
6.3.3 STRUCTURED RISK MINIMISATION.
94
6.3.4 THE LUCKINESS FRAMEWORK. 96
6.4 BAYESIAN FRAMEWORK.100
6.4.1 THE POWER OF CONDITIONING ON THE DATA.
102
6.4.2 THE NO-FREE-LUNCH THEOREM AND ITS IMPLICATIONS.103
6.5 DISCUSSION.105
7 BOUNDS IN THE PAC FRAMEWORK 107
7.1 A CLASSICAL MARGIN BOUND.107
7.1.1 VC DIMENSIONS FOR REED-VALUED FUNCTION CLASSES.ILL
7.1.2 THE MARGIN BOUND.
114
7.1.3 APPLICATION TO ORDINAL REGRESSION.
115
VTI
7.2 ROBUST MARGIN BOUNDS .117
7.2.1 THE "ROBUSTNESS" TRICK.117
7.2.2 APPLICATION TO ADAPTIVE MARGIN MACHINES.120
7.3 DISCUSSION.121
8 BOUNDS IN THE PAC-BAYESIAN FRAMEWORK 123
8.1 PAC-BAYESIAN FYAMEWORK.123
8.2 PAC-BAYESIAN BOUNDS FOR BAYESIAN ALGORITHMS.124
8.2.1 A BOUND FOR THE MAP ESTIMATOR.124
8.2.2 A BOUND FOR THE GIBBS CLASSIFIER.125
8.2.3 GIBBS-BAYES LEMMA.126
8.2.4 BOUNDS FOR SINGLE CLASSIFIER - BAYES ADMISSIBILITY.128
8.3 A MARGIN BOUND IN THE PAC-BAYESIAN FRAMEWORK.129
8.4 AN EXPERIMENTAL STUDY.131
8.4.1 MODEL SELECTION ABILITY.131
8.4.2 LEARNING CURVES.132
8.5 DISCUSSION.133
A THEORETICAL BACKGROUND AND BASIC INEQUALITIES 139
A.L THEORETICAL BACKGROUND.139
A. 1.1 PROBABILITY THEORY.139
A.1.2 FUNCTIONAL ANALYSIS .142
A. 1.3 ILL-POSED PROBLEMS.145
A. 2 BASIC INEQUALITIES.146
B PROOFS AND DERIVATIONS 151
B. L GENERALISED REPRESENTER THEOREM.151
B.2 CONVERGENCE OF THE PEREEPTRON .152
B.3 CONVEX OPTIMISATION PROBLEMS OF SUPPORT VECTOR MACHINES . 152
B. 3.1 HARD MARGIN SVM.153
B.3.2 LINEAR SOFT MARGIN LOSS SVM.153
B.3.3 QUADRATIC SOFT MARGIN LOSS SVM.154
B.3,4 I/-LINEAR MARGIN LOSS SVM.154
B.4 T/-LINEAR PROGRAMMING MACHINES .155
B.5 LEAVE-ONE-OUT BOUND FOR KERNEL CLASSIFIERS.156
B.6 FISHER LINEAR DISCRIMINANT .158
B.7 BASIC LEMMATA.159
B.8 DEVIATIONS OF MEANS.161
B.9 LUCKINESS BOUND.,.162
B.10 BOUND ON THE FAT SHATTERING DIMENSION.166
B.LL MARGIN DISTRIBUTION BOUND.167
B.12 THE QUANTIFIER REVERSAL LEMMA.168
B.13 ALIGNMENT MEASURE.170
B.14 GEOMETRY IN AN RKHS.170
B.14.1 FLIGHT TIMES IN KERNEL SPACE .171
B.14.2 REFLECTIONS IN KERNEL SPACE.171
B.14.3 A DERIVATION OF THE OPERATION .172
B.15 BALLS IN VERSION SPACE.174
B.16 VOLUME RATIO THEOREM .176
B.17 A VOLUME RATIO BOUND .179
B.18 BOLLMANN'S LEMMA.180
VLTJ
C PSEUDOCODES 183
C.L PERCEPTRON ALGORITHM.183
C.1.1 PRIMAL PERCEPTRON LEARNING.183
C.L.2 DUAL PERCEPTRON LEARNING.183
C.2 SUPPORT VECTOR MACHINES.183
C.2.1 STANDARD SUPPORT VECTOR MACHINES.184
C.2.2 ^-SUPPORT VECTOR MACHINES.184
C.3 LINEAR PROGRAMMING MACHINES.184
C.3.1 STANDARD LINEAR PROGRAMMING MACHINES.185
C.3.2 I/-LINEAR PROGRAMMING MACHINES.185
C.4 ADAPTIVE MARGIN MACHINES .185
C.5 BAYES POINT MACHINES.186
C.5.1 KERNEL BILLIARD.186 |
| any_adam_object | 1 |
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| discipline | Informatik |
| format | Thesis Book |
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| indexdate | 2024-10-09T18:07:51Z |
| institution | BVB |
| language | English |
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| spelling | Herbrich, Ralf Verfasser aut Learning linear classifiers theory and algorithms vorgelegt von Ralf Herbrich 2001 XVI, 202 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berlin, Techn. Univ., Diss., 2000 Hochschulschrift gtt Lernendes System gtt Support-Vektor-Maschine (DE-588)4505517-8 gnd rswk-swf Klassifikator Informatik (DE-588)4288547-4 gnd rswk-swf Fehlerschranke (DE-588)4199964-2 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Maschinelles Lernen (DE-588)4193754-5 s Support-Vektor-Maschine (DE-588)4505517-8 s Bayes-Entscheidungstheorie (DE-588)4144220-9 s Klassifikator Informatik (DE-588)4288547-4 s Fehlerschranke (DE-588)4199964-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009356572&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Herbrich, Ralf Learning linear classifiers theory and algorithms Hochschulschrift gtt Lernendes System gtt Support-Vektor-Maschine (DE-588)4505517-8 gnd Klassifikator Informatik (DE-588)4288547-4 gnd Fehlerschranke (DE-588)4199964-2 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
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| title | Learning linear classifiers theory and algorithms |
| title_auth | Learning linear classifiers theory and algorithms |
| title_exact_search | Learning linear classifiers theory and algorithms |
| title_full | Learning linear classifiers theory and algorithms vorgelegt von Ralf Herbrich |
| title_fullStr | Learning linear classifiers theory and algorithms vorgelegt von Ralf Herbrich |
| title_full_unstemmed | Learning linear classifiers theory and algorithms vorgelegt von Ralf Herbrich |
| title_short | Learning linear classifiers |
| title_sort | learning linear classifiers theory and algorithms |
| title_sub | theory and algorithms |
| topic | Hochschulschrift gtt Lernendes System gtt Support-Vektor-Maschine (DE-588)4505517-8 gnd Klassifikator Informatik (DE-588)4288547-4 gnd Fehlerschranke (DE-588)4199964-2 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Hochschulschrift Lernendes System Support-Vektor-Maschine Klassifikator Informatik Fehlerschranke Bayes-Entscheidungstheorie Maschinelles Lernen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009356572&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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