A First Course in Machine Learning

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ISBN: 9781439824146 | 1439824142
Cover: Hardcover
Copyright: 10/25/2011

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Offering a complete introduction to the fundamental concepts underlying machine learning theory, this text presents modern methods and mathematical foundations needed to enable further study. The text requires minimal mathematical prerequisites, making it appropriate for students who are new to the field. Emphasizing a practical approach to the material, each chapter includes worked examples. Case studies illustrate interesting applications from engineering, computer science, and the life sciences. A supporting website provides MATLAB#xAE;implementations of all methods described in the text as well as lecture slides and a solutions manual for qualifying instructors.

List of Tables	p. xi
List of Figures	p. xiii
Preface	p. xix
Linear Modelling: A Least Squares Approach	p. 1
Linear modelling	p. 1
Defining the model	p. 2
Modelling assumptions	p. 3
Defining what a good model is	p. 4
The least squares solution - a worked example	p. 6
Worked example	p. 9
Least squares fit to the Olympics data	p. 10
Summary	p. 11
Making predictions	p. 12
A second Olympics dataset	p. 12
Summary	p. 15
Vector/matrix notation	p. 15
Example	p. 22
Numerical example	p. 23
Making predictions	p. 24
Summary	p. 24
Nonlinear response from a linear model	p. 25
Generalisation and over-fitting	p. 28
Validation data	p. 29
Cross-validation	p. 29
Computational scaling of K-fold cross-validation	p. 32
Regularised least squares	p. 33
Exercises	p. 35
Further reading	p. 37
Linear Modelling: A Maximum Likelihood Approach	p. 39
Errors as noise	p. 39
Thinking generatively	p. 40
Random variables and probability	p. 41
Random variables	p. 41
Probability and distributions	p. 42
Adding probabilities	p. 44
Conditional probabilities	p. 44
Joint probabilities	p. 45
Marginalisation	p. 47
Aside - Bayes' rule	p. 49
Expectations	p. 50
Popular discrete distributions	p. 53
Bernoulli distribution	p. 53
Binomial distribution	p. 53
Multinomial distribution	p. 54
Continuous random variables - density functions	p. 55
Popular continuous density functions	p. 58
The uniform density function	p. 58
The beta density function	p. 60
The Gaussian density function	p. 61
Multivariate Gaussian	p. 62
Summary	p. 65
Thinking generatively...continued	p. 65
Likelihood	p. 67
Dataset likelihood	p. 68
Maximum likelihood	p. 69
Characteristics of the maximum likelihood solution	p. 71
Maximum likelihood favours complex models	p. 74
The bias-variance tradeoff	p. 75
Summary	p. 75
Effect of noise on parameter estimates	p. 76
Uncertainty in estimates	p. 78
Comparison with empirical values	p. 81
Variability in model parameters - Olympics data	p. 82
Variability in predictions	p. 83
Predictive variability - an example	p. 85
Expected values of the estimators	p. 86
Summary	p. 90
Exercises	p. 90
Further reading	p. 93
The Bayesian Approach to Machine Learning	p. 95
A coin game	p. 95
Counting heads	p. 97
The Bayesian way	p. 98
The exact posterior	p. 103
The three scenarios	p. 104
No prior knowledge	p. 104
The fair coin scenario	p. 111
A biased coin	p. 114
The three scenarios - a summary	p. 116
Adding more data	p. 116
Marginal likelihoods,T>117
Model comparison with the marginal likelihood	p. 118
Summary	p. 121
A Bayesian treatment of the Olympics 100 m data	p. 122
The model	p. 122
The likelihood	p. 124
The prior	p. 124
The posterior	p. 124
A first-order polynomial	p. 126
Making predictions	p. 129
Marginal likelihood for polynomial model order selection	p. 131
Chapter summary	p. 133
Exercises	p. 133
Further reading	p. 137
Non-conjugate models	p. 139
Binary responses	p. 140
A model for binary responses	p. 140
A point estimate - the MAP solution	p. 143
The Laplace approximation	p. 149
Laplace approximation example: Approximating a gamma density	p. 150
Laplace approximation for the binary response model	p. 151
Sampling techniques	p. 154
Playing darts	p. 154
The Metropolis-Hastings algorithm	p. 156
The at of sampling	p. 164
Summary	p. 165
Exercises	p. 165
Further reading	p. 167
The general problem	p. 169
Probabilistic classifiers	p. 170
The Bayes classifier	p. 170
Likelihood - class-conditional distributions	p. 171
Prior class distribution	p. 171
Example - Gaussian class-conditionals	p. 172
Making predictions	p. 173
The naive Bayes assumption	p. 175
Example - classifying text	p. 175
Smoothing	p. 177
Logistic regression	p. 179
Motivation	p. 180
Nonlinear decision functions	p. 181
Nonparametric models - the Gaussian process	p. 182
Nonprobabilistic classifiers	p. 183
K-nearest neighbours	p. 183
Choosing K	p. 184
Support vector machines and other kernel methods	p. 186
The margin	p. 186
Maximising the margin	p. 187
Making predictions	p. 190
Support vectors	p. 191
Soft margins	p. 192
Kernels	p. 193
Summary	p. 197
Assessing classification performance	p. 198
Accuracy - 0/1 loss	p. 198
Sensitivity and specificity	p. 198
The area under the ROC curve	p. 199
Confusion matrices	p. 201
Discriminative and generative classifiers	p. 203
Summary	p. 203
Exercises	p. 203
Further reading	p. 205
Clustering	p. 207
The general problem	p. 207
K-means clustering	p. 208
Choosing the number of clusters	p. 210
Where K-means fails	p. 212
Kernelised K-means	p. 212
Summary	p. 214
Mixture models	p. 215
A generative process	p. 216
Mixture model likelihood	p. 217
The EM algorithm	p. 219
Updating ¿_k	p. 220
Updating ¿_k	p. 221
Updating ∑_k	p. 222
Updating q_nk	p. 223
Some intuition	p. 224
Example	p. 225
EM finds local optima	p. 226
Choosing the number of components	p. 228
Other forms of mixture components	p. 230
MAP estimates with EM	p. 232
Bayesian mixture models	p. 233
Summary	p. 234
Exercises	p. 234
Further reading	p. 237
Principal Components Analysis and Latent Variable Models	p. 239
The general problem	p. 239
Variance as a proxy for interest	p. 239
Principal components analysis	p. 242
Choosing D	p. 247
Limitations of PCA	p. 247
Latent variable models	p. 248
Mixture models as latent variable models	p. 248
Summary	p. 249
Variational Bayes	p. 249
Choosing Q(¿)	p. 251
Optimising the bound	p. 252
A probabilistic model for PCA	p. 252
Q_¿(¿)	p. 254
Q_{x_n}(x_n)	p. 256
Q_{w_m} (w_m)	p. 257
The required expectations	p. 258
The algorithm	p. 258
An example	p. 260
Missing values	p. 260
Missing values as latent variables	p. 262
Predicting missing values	p. 264
Non-real-valued data	p. 264
Probit PPCA	p. 264
Visualising parliamentary data	p. 268
Aside - relationship to classification	p. 272
Summary	p. 273
Exercises	p. 273
Further reading	p. 275
Glossary	p. 277
Index	p. 283
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