A first course in machine learning:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
[2017]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxix, 397 Seiten Illustrationen, Diagramme |
| ISBN: | 9781498738484 |
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Record in the Search Index
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| adam_text | Contents
List of Tables xv
List of Figures xvii
Preface to the First Edition xxvii
Preface to the Second Edition xxix
Section I Basic Topics
Chapter 1 ■ Linear Modelling: A Least Squares Approach 3
1.1 LINEAR MODELLING 3
1.1.1 Defining the model 4
1.1.2 Modelling assumptions 5
1.1.3 Defining a good model 6
1.1.4 The least squares solution --- a worked example 8
1.1.5 Worked example 12
1.1.6 Least squares fit to the Olympic data 13
1.1.7 Summary 14
1.2 MAKING PREDICTIONS 15
1.2.1 A second Olympic dataset 15
1.2.2 Summary 17
1.3 VECTOR/MATRIX NOTATION 17
1.3.1 Example 25
1.3.2 Numerical example 26
1.3.3 Making predictions 27
1.3.4 Summary 27
1.4 NON- LINEAR RESPONSE FROM A LINEAR MODEL 28
1.5 GENERALISATION AND OVER-FITTING 31
V
vi ■ Contents
1.5.1 Validation data 31
1.5.2 Cross-validation 32
1.5.3 Computational scaling of K-fold cross-validation 34
1.6 REGULARISED LEAST SQUARES 34
1.7 EXERCISES 37
1.8 FURTHER READING 39
Chapter 2 ■ Linear Modelling: A Maximum Likelihood
Approach 41
2.1 ERRORS AS NOISE 41
2.1.1 Thinking generatively 42
2.2 RANDOM VARIABLES AND PROBABILITY 43
2.2.1 Random variables 43
2.2.2 Probability and distributions 44
2.2.3 Adding probabilities 46
2.2.4 Conditional probabilities 46
2.2.5 Joint probabilities 47
2.2.6 Marginalisation 49
2.2.7 Aside - Bayes rule 51
2.2.8 Expectations 52
2.3 POPULAR DISCRETE DISTRIBUTIONS 55
2.3.1 Bernoulli distribution 55
2.3.2 Binomial distribution 55
2.3.3 Multinomial distribution 56
2.4 CONTINUOUS RANDOM VARIABLES - DENSITY
FUNCTIONS 57
2.5 POPULAR CONTINUOUS DENSITY FUNCTIONS 60
2.5.1 The uniform density function 60
2.5.2 The beta density function 62
2.5.3 The Gaussian density function 63
2.5.4 Multivariate Gaussian 64
2.6 SUMMARY 66
2.7 THINKING GENERATIVELY...CONTINUED 67
2.8 LIKELIHOOD 68
2.8.1 Dataset likelihood 69
2.8.2 Maximum likelihood 70
Contents ■ vii
2.8.3 Characteristics of the maximum likelihood solution 73
2.8.4 Maximum likelihood favours complex models 75
2.9 THE BIAS-VARIANCE TRADE-OFF 75
2.9.1 Summary 76
2.10 EFFECT OF NOISE ON PARAMETER ESTIMATES 77
2.10.1 Uncertainty in estimates 78
2.10.2 Comparison with empirical values 83
2.10.3 Variability in model parameters - Olympic data 84
2.11 VARIABILITY IN PREDICTIONS 84
2.11.1 Predictive variability — an example 86
2.11.2 Expected values of the estimators 86
2.12 CHAPTER SUMMARY 91
2.13 EXERCISES 92
2.14 FURTHER READING 93
Chapter 3 ■ The Bayesian Approach to Machine Learning 95
3.1 A COIN GAME 95
3.1.1 Counting heads 97
3.1.2 The Bayesian way 98
3.2 THE EXACT POSTERIOR 103
3.3 THE THREE SCENARIOS 104
3.3.1 No prior knowledge 104
3.3.2 The fair coin scenario 112
3.3.3 A biased coin 114
3.3.4 The three scenarios - a summary 116
3.3.5 Adding more data 117
3.4 MARGINAL LIKELIHOODS 117
3.4.1 Model comparison with the marginal likelihood 119
3.5 HYPERPARAMETERS 119
3.6 GRAPHICAL MODELS 120
3.7 SUMMARY 122
3.8 A BAYESIAN TREATMENT OF THE OLYMPIC 100m
DATA 122
3.8.1 The model 122
3.8.2 The likelihood 124
3.8.3 The prior 124
viii ■ Contents
3.8.4 The posterior 124
3.8.5 A first-order polynomial 126
3.8.6 Making predictions 129
3.9 MARGINAL LIKELIHOOD FOR POLYNOMIAL MODEL
ORDER SELECTION 130
3.10 CHAPTER SUMMARY 133
3.11 EXERCISES 133
3.12 FURTHER READING 135
Chapter 4 Bayesian Inference 137
4.1 NON-CONJUGATE MODELS 137
4.2 BINARY RESPONSES 138
4.2.1 A model for binary responses 138
4.3 A POINT ESTIMATE - THE MAP SOLUTION 141
4.4 THE LAPLACE APPROXIMATION 147
4.4.1 Laplace approximation example: Approximating a
gamma density 148
4.4.2 Laplace approximation for the binary response model 150
4.5 SAMPLING TECHNIQUES 152
4.5.1 Playing darts 152
4.5.2 The Metropolis-Hastings algorithm 154
4.5.3 The art of sampling 162
4.6 CHAPTER SUMMARY 163
4.7 EXERCISES 163
4.8 FURTHER READING 164
Chapter 5 ■ Classification 167
5.1 THE GENERAL PROBLEM 167
5.2 PROBABILISTIC CLASSIFIERS 168
5.2.1 The Bayes classifier 168
5.2.1.1 Likelihood — class-conditional distributions 169
5.2.1.2 Prior class distribution 169
5.2.1.3 Example - Gaussian class-conditionals 170
5.2.1.4 Making predictions 171
5.2.1.5 The naive-Bayes assumption 172
Contents ■ ix
5.2.1.6 Example - classifying text 174
5.2.1.7 Smoothing 176
5.2.2 Logistic regression 178
5.2.2.1 Motivation 178
5.2.2.2 Non-linear decision functions 179
5.2.2.3 Non-parametric models - the Gaussian
process 180
5.3 NON-PROBABILISTIC CLASSIFIERS 181
5.3.1 iC-nearest neighbours 181
5.3.1.1 Choosing K 182
5.3.2 Support vector machines and other kernel methods 185
5.3.2.1 The margin 185
5.3.2.2 Maximising the margin 186
5.3.2.3 Making predictions 189
5.3.2.4 Support vectors 189
5.3.2.5 Soft margins 191
5.3.2.6 Kernels 193
5.3.3 Summary 196
5.4 ASSESSING CLASSIFICATION PERFORMANCE 196
5.4.1 Accuracy — 0/1 loss 196
5.4.2 Sensitivity and specificity 197
5.4.3 The area under the ROC curve 198
5.4.4 Confusion matrices 200
5.5 DISCRIMINATIVE AND GENERATIVE CLASSIFIERS 202
5.6 CHAPTER SUMMARY 202
5.7 EXERCISES 202
5.8 FURTHER READING 203
Chapter 6-Clustering 205
6.1 THE GENERAL PROBLEM 205
6.2 iC-MEANS CLUSTERING 206
6.2.1 Choosing the number of clusters 208
6.2.2 Where iC-means fails 210
6.2.3 Kernelised TC-means 210
6.2.4 Summary 212
6.3 MIXTURE MODELS 213
x ■ Contents
6.3.1 A generative process 214
6.3.2 Mixture model likelihood 215
6.3.3 The EM algorithm 217
6.3.3.1 Updating 7rk 218
6.3.3.2 Updating j,k 219
6.3.3.3 Updating 220
6.3.3.4 Updating qnk 221
6.3.3.5 Some intuition 222
6.3.4 Example 223
6.3.5 EM finds local optima 224
6.3.6 Choosing the number of components 226
6.3.7 Other forms of mixture component 228
6.3.8 MAP estimates with EM 230
6.3.9 Bayesian mixture models 231
6.4 CHAPTER SUMMARY 232
6.5 EXERCISES 232
6.6 FURTHER READING 233
Chapter 7 ■ Principal Components Analysis and Latent
Variable Models 235
7.1 THE GENERAL PROBLEM 235
7.1.1 Variance as a proxy for interest 236
7.2 PRINCIPAL COMPONENTS ANALYSIS 238
7.2.1 Choosing D 242
7.2.2 Limitations of PCA 243
7.3 LATENT VARIABLE MODELS 244
7.3.1 Mixture models as latent variable models 244
7.3.2 Summary 245
7.4 VARIATIONAL BAYES 245
7.4.1 Choosing Q{0) 247
7.4.2 Optimising the bound 248
7.5 A PROBABILISTIC MODEL FOR PCA 248
7.5.1 Qt(t ) 250
7.5.2 2xn. (xn) 252
7.5.3 (wm) 253
Contents ■ xi
7.5.4 The required expectations 254
7.5.5 The algorithm 254
7.5.6 An example 256
7.6 MISSING VALUES 256
7.6.1 Missing values as latent variables 259
7.6.2 Predicting missing values 260
7.7 NON- -REAL-VALUED DATA 260
7.7.1 Probit PPCA 260
7.7.2 Visualising parliamentary data 264
7.7.2.1 Aside - relationship to classification 267
7.8 CHAPTER SUMMARY 269
7.9 EXERCISES 270
7.10 FURTHER READING 270
Section II Advanced Topics
Chapter 8 ■ Gaussian Processes 275
8.1 PROLOGUE - NON-PARAMETRIC MODELS 275
8.2 GAUSSIAN PROCESS REGRESSION 278
8.2.1 The Gaussian process prior 278
8.2.2 Noise-free regression 283
8.2.3 Noisy regression 287
8.2.4 Summary 288
8.2.5 Noisy regression - an alternative route 289
8.2.6 Alternative covariance functions 292
8.2.6.1 Linear 292
8.2.6.2 Polynomial 293
8.2.6.3 Neural network 294
8.2.7 ARD 296
8.2.8 Composite covariance functions 297
8.2.9 Summary 297
8.3 GAUSSIAN PROCESS CLASSIFICATION 297
8.3.1 A classification likelihood 297
8.3.2 A classification roadmap 299
8.3.3 The point estimate approximation 300
8.3.4 Propagating uncertainty through the sigmoid 303
xii ■ Contents
8.3.5 The Laplace approximation 305
8.3.6 Summary 308
8.4 HYPERPARAMETER OPTIMISATION 309
8.5 EXTENSIONS 311
8.5.1 Non-zero mean 311
8.5.2 Multiclass classification 311
8.5.3 Other likelihood functions and models 311
8.5.4 Other inference schemes 311
8.6 CHAPTER SUMMARY 312
8.7 EXERCISES 312
8.8 FURTHER READING 314
Chapter 9 ■ Markov Chain Monte Carlo Sampling 315
9.1 GIBBS SAMPLING 316
9.2 EXAMPLE: GIBBS SAMPLING FOR GP
CLASSIFICATION 320
9.2.1 Conditional densities for GP classification via Gibbs
sampling 322
9.2.2 Summary 324
9.3 WHY DOES MCMC WORK? 327
9.4 SOME SAMPLING PROBLEMS AND SOLUTIONS 331
9.4.1 Burn-in and convergence 331
9.4.2 Autocorrelation 333
9.4.3 Summary 337
9.5 ADVANCED SAMPLING TECHNIQUES 338
9.5.1 Adaptive proposals and Hamiltonian Monte Carlo 338
9.5.2 Approximate Bayesian computation 341
9.5.3 Population MCMC and temperature schedules 345
9.5.4 Sequential Monte Carlo 346
9.6 CHAPTER SUMMARY 348
9.7 EXERCISES 349
9.8 FURTHER READING 350
Chapter 10 ■ Advanced Mixture Modelling 351
10.1 A GIBBS SAMPLER FOR MIXTURE MODELS
351
Contents ■ xiii
10.2 COLLAPSED GIBBS SAMPLING 359
10.3 AN INFINITE MIXTURE MODEL 364
10.3.1 The Chinese restaurant process 366
10.3.2 Inference in the infinite mixture model 367
10.3.3 Summary 371
10.4 DIRICHLET PROCESSES 371
10.4.1 Hierarchical Dirichlet processes 377
10.4.2 Summary 380
10.5 BEYOND STANDARD MIXTURES - TOPIC MODELS 380
10.6 CHAPTER SUMMARY 382
10.7 EXERCISES 383
10.8 FURTHER READING 385
Glossary 387
Index 395
|
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| spelling | Rogers, Simon 1979- Verfasser (DE-588)1129383253 aut A first course in machine learning Simon Rogers (University of Glasgow, United Kingdom), Mark Girolami (University of Warwick, United Kingdom) Second edition Boca Raton ; London ; New York CRC Press [2017] © 2017 xxix, 397 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Maschinelles Lernen (DE-588)4193754-5 s DE-604 Girolami, Mark 1963- Verfasser (DE-588)12096595X 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=029439535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rogers, Simon 1979- Girolami, Mark 1963- A first course in machine learning Maschinelles Lernen (DE-588)4193754-5 gnd |
| subject_GND | (DE-588)4193754-5 (DE-588)4151278-9 |
| title | A first course in machine learning |
| title_auth | A first course in machine learning |
| title_exact_search | A first course in machine learning |
| title_full | A first course in machine learning Simon Rogers (University of Glasgow, United Kingdom), Mark Girolami (University of Warwick, United Kingdom) |
| title_fullStr | A first course in machine learning Simon Rogers (University of Glasgow, United Kingdom), Mark Girolami (University of Warwick, United Kingdom) |
| title_full_unstemmed | A first course in machine learning Simon Rogers (University of Glasgow, United Kingdom), Mark Girolami (University of Warwick, United Kingdom) |
| title_short | A first course in machine learning |
| title_sort | a first course in machine learning |
| topic | Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Maschinelles Lernen Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029439535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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