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AN INTRODUCTION TO MACHINE LEARNING THAT INCLUDES THE FUNDAMENTAL TECHNIQUES, METHODS, AND APPLICATIONS PROSE Award Finalist 2019 Association of American Publishers Award for Professional and Scholarly Excellence Machine Learning: a Concise Introduction offers a comprehensive introduction to the core concepts, approaches, and applications of machine learning. The author--an expert in the field--presents fundamental ideas, terminology, and techniques for solving applied problems in classification, regression, clustering, density estimation, and dimension reduction. The design principles behind the techniques are emphasized, including the bias-variance trade-off and its influence on the design of ensemble methods. Understanding these principles leads to more flexible and successful applications. Machine Learning: a Concise Introduction also includes methods for optimization, risk estimation, and model selection-- essential elements of most applied projects. This important resource: Illustrates many classification methods with a single, running example, highlighting similarities and differences between methods Presents R source code which shows how to apply and interpret many of the techniques covered Includes many thoughtful exercises as an integral part of the text, with an appendix of selected solutions Contains useful information for effectively communicating with clients A volume in the popular Wiley Series in Probability and Statistics, Machine Learning a Concise Introduction offers the practical information needed for an understanding of the methods and application of machine learning. STEVEN W. KNOX holds a Ph.D. in Mathematics from the University of Illinois and an M.S. in Statistics from Carnegie Mellon University. He has over twenty years' experience in using Machine Learning, Statistics, and Mathematics to solve real-world problems. He currently serves as Technical Director of Mathematics Research and Senior Advocate for Data Science at the National Security Agency.

Preface xi Organization How to Use This Book xiii Acknowledgments xvii About the Companion Website xix 1 Introduction Examples from Real Life 1 2 The Problem of Learning 3 2.1 Domain 4 2.2 Range 4 2.3 Data 4 2.4 Loss 6 2.5 Risk 8 2.6 The Reality of the Unknown Function 12 2.7 Training and Selection of Models, and Purposes of Learning 12 2.8 Notation 13 3 Regression 15 3.1 General Framework 16 3.2 Loss 17 3.3 Estimating the Model Parameters 17 3.4 Properties of Fitted Values 19 3.5 Estimating the Variance 22 3.6 A Normality Assumption 23 3.7 Computation 24 3.8 Categorical Features 25 3.9 Feature Transformations, Expansions, and Interactions 27 3.10 Variations in Linear Regression 28 3.11 Nonparametric Regression 32 4 Survey of Classification Techniques 33 4.1 The Bayes Classifier 34 4.2 Introduction to Classifiers 37 4.3 A Running Example 38 4.4 Likelihood Methods 40 4.4.1 Quadratic Discriminant Analysis 41 4.4.2 Linear Discriminant Analysis 43 4.4.3 Gaussian Mixture Models 45 4.4.4 Kernel Density Estimation 47 4.4.5 Histograms 51 4.4.6 The Naive Bayes Classifier 54 4.5 Prototype Methods 54 4.5.1 k-Nearest-Neighbor 55 4.5.2 Condensed k-Nearest-Neighbor 56 4.5.3 Nearest-Cluster 56 4.5.4 Learning Vector Quantization 58 4.6 Logistic Regression 59 4.7 Neural Networks 62 4.7.1 Activation Functions 62 4.7.2 Neurons 64 4.7.3 Neural Networks 65 4.7.4 Logistic Regression and Neural Networks 73 4.8 Classification Trees 74 4.8.1 Classification of Data by Leaves (Terminal Nodes) 74 4.8.2 Impurity of Nodes and Trees 75 4.8.3 Growing Trees 76 4.8.4 Pruning Trees 79 4.8.5 Regression Trees 81 4.9 Support Vector Machines 81 4.9.1 Support Vector Machine Classifiers 81 4.9.2 Kernelization 88 4.9.3 Proximal Support Vector Machine Classifiers 92 4.10 Postscript: Example Problem Revisited 93 5 Bias Variance Trade-off 97 5.1 Squared-Error Loss 98 5.2 Arbitrary Loss 101 6 Combining Classifiers 107 6.1 Ensembles 107 6.2 Ensemble Design 110 6.3 Bootstrap Aggregation (Bagging) 112 6.4 Bumping 115 6.5 Random Forests 116 6.6 Boosting 118 6.7 Arcing 121 6.8 Stacking and Mixture of Experts 121 7 Risk Estimation and Model Selection 127 7.1 Risk Estimation via Training Data 128 7.2 Risk Estimation via Validation or Test Data 128 7.2.1 Training, Validation, and Test Data 128 7.2.2 Risk Estimation 129 7.2.3 Size of Training, Validation, and Test Sets 130 7.2.4 Testing Hypotheses About Risk 131 7.2.5 Example of Use of Training, Validation, and Test Sets 132 7.3 Cross-Validation 133 7.4 Improvements on Cross-Validation 135 7.5 Out-of-Bag Risk Estimation 137 7.6 Akaike s Information Criterion 138 7.7 Schwartz s Bayesian Information Criterion 138 7.8 Rissanen s Minimum Description Length Criterion 139 7.9 R2 and Adjusted R2 140 7.10 Stepwise Model Selection 141 7.11 Occam s Razor 142 8 Consistency 143 8.1 Convergence of Sequences of Random Variables 144 8.2 Consistency for Parameter Estimation 144 8.3 Consistency for Prediction 145 8.4 There Are Consistent and Universally Consistent Classifiers 145 8.5 Convergence to Asymptopia Is Not Uniform and May Be Slow 147 9 Clustering 149 9.1 Gaussian Mixture Models 150 9.2 k-Means 150 9.3 Clustering by Mode-Hunting in a Density Estimate 151 9.4 Using Classifiers to Cluster 152 9.5 Dissimilarity 153 9.6 k-Medoids 153 9.7 Agglomerative Hierarchical Clustering 154 9.8 Divisive Hierarchical Clustering 155 9.9 How Many Clusters Are There? Interpretation of Clustering 155 9.10 An Impossibility Theorem 157 10 Optimization 159 10.1 Quasi-Newton Methods 160 10.1.1 Newton s Method for Finding Zeros 160 10.1.2 Newton s Method for Optimization 161 10.1.3 Gradient Descent 161 10.1.4 The BFGS Algorithm 162 10.1.5 Modifications to Quasi-Newton Methods 162 10.1.6 Gradients for Logistic Regression and Neural Networks 163 10.2 The Nelder Mead Algorithm 166 10.3 Simulated Annealing 168 10.4 Genetic Algorithms 168 10.5 Particle Swarm Optimization 169 10.6 General Remarks on Optimization 170 10.6.1 Imperfectly Known Objective Functions 170 10.6.2 Objective Functions Which Are Sums 171 10.6.3 Optimization from Multiple Starting Points 172 10.7 The Expectation-Maximization Algorithm 173 10.7.1 The General Algorithm 173 10.7.2 EM Climbs the Marginal Likelihood of the Observations 173 10.7.3 Example Fitting a Gaussian Mixture Model Via EM 176 10.7.4 Example The Expectation Step 177 10.7.5 Example The Maximization Step 178 11 High-Dimensional Data 179 11.1 The Curse of Dimensionality 180 11.2 Two Running Examples 187 11.2.1 Example 1: Equilateral Simplex 187 11.2.2 Example 2: Text 187 11.3 Reducing Dimension While Preserving Information 190 11.3.1 The Geometry of Means and Covariances of Real Features 190 11.3.2 Principal Component Analysis 192 11.3.3 Working in Dissimilarity Space 193 11.3.4 Linear Multidimensional Scaling 195 11.3.5 The Singular Value Decomposition and Low-Rank Approximation 197 11.3.6 Stress-Minimizing Multidimensional Scaling 199 11.3.7 Projection Pursuit 199 11.3.8 Feature Selection 201 11.3.9 Clustering 202 11.3.10 Manifold Learning 202 11.3.11 Autoencoders 205 11.4 Model Regularization 209 11.4.1 Duality and the Geometry of Parameter Penalization 212 11.4.2 Parameter Penalization as Prior Information 213 12 Communication with Clients 217 12.1 Binary Classification and Hypothesis Testing 218 12.2 Terminology for Binary Decisions 219 12.3 ROC Curves 219 12.4 One-Dimensional Measures of Performance 224 12.5 Confusion Matrices 225 12.6 Multiple Testing 226 12.6.1 Control the Familywise Error 226 12.6.2 Control the False Discovery Rate 227 12.7 Expert Systems 228 13 Current Challenges in Machine Learning 231 13.1 Streaming Data 231 13.2 Distributed Data 231 13.3 Semi-supervised Learning 232 13.4 Active Learning 232 13.5 Feature Construction via Deep Neural Networks 233 13.6 Transfer Learning 233 13.7 Interpretability of Complex Models 233 14 R Source Code 235 14.1 Author s Biases 236 14.2 Libraries 236 14.3 The Running Example (Section 4.3) 237 14.4 The Bayes Classifier (Section 4.1) 241 14.5 Quadratic Discriminant Analysis (Section 4.4.1) 243 14.6 Linear Discriminant Analysis (Section 4.4.2) 243 14.7 Gaussian Mixture Models (Section 4.4.3) 244 14.8 Kernel Density Estimation (Section 4.4.4) 245 14.9 Histograms (Section 4.4.5) 248 14.10 The Naive Bayes Classifier (Section 4.4.6) 253 14.11 k-Nearest-Neighbor (Section 4.5.1) 255 14.12 Learning Vector Quantization (Section 4.5.4) 257 14.13 Logistic Regression (Section 4.6) 259 14.14 Neural Networks (Section 4.7) 260 14.15 Classification Trees (Section 4.8) 263 14.16 Support Vector Machines (Section 4.9) 267 14.17 Bootstrap Aggregation (Section 6.3) 272 14.18 Boosting (Section 6.6) 274 14.19 Arcing (Section 6.7) 275 14.20 Random Forests (Section 6.5) 275 A List of Symbols 277 B Solutions to Selected Exercises 279 C Converting Between Normal Parameters and Level-Curve Ellipsoids 299 D Training Data and Fitted Parameters 301 References 305 Index 315

STEVEN W. KNOX holds a Ph.D. in Mathematics from the University of Illinois and an M.S. in Statistics from Carnegie Mellon University. He has over twenty years' experience in using Machine Learning, Statistics, and Mathematics to solve real-world problems. He currently serves as Technical Director of Mathematics Research and Senior Advocate for Data Science at the National Security Agency.