A Concise Introduction to Machine Learning (Chapman & Hall/CRC Machine Learning & Pattern Recognition)

Description

A Concise Introduction to Machine Learning uses mathematics as the common language to explain a variety of machine learning concepts from basic principles and illustrates every concept using examples in both Python and MATLAB®, which are available on GitHub and can be run from there in Binder in a web browser. Each chapter concludes with exercises to explore the content. The emphasis of the book is on the question of Why―only if “why” an algorithm is successful is understood, can it be properly applied and the results trusted. Standard techniques are treated rigorously, including an introduction to the necessary probability theory. This book addresses the commonalities of methods, aims to give a thorough and in-depth treatment and develop intuition for the inner workings of algorithms, while remaining concise. This useful reference should be essential on the bookshelf of anyone employing machine learning techniques, since it is born out of strong experience in university teaching and research on algorithms, while remaining approachable and readable. Cover Page Endorsements Page Half-Title Page Series Page Title Page Copyright Page Dedication Page Contents List of Figures List of Listings Foreword Preface Acknowledgments Chapter 1 Introduction Bibliography Chapter 2 Probability Theory 2.1 Independence, Probability Rules and Simpson's Paradox 2.2 Probability Densities, Expectation, Variance and Moments 2.3 Examples of Discrete Probability Mass Functions 2.4 Examples of Continuous Probability Density Functions 2.5 Functions of Continuous Random Variables 2.6 Conjugate, Prior and Posterior Distributions and Maximum Likelihood 2.7 Graphical Representations Exercises Bibliography Chapter 3 Sampling 3.1 Inverse Transform Sampling 3.2 Rejection Sampling 3.3 Importance Sampling 3.4 Markov Chains 3.5 Markov Chain Monte Carlo Exercises Bibliography Chapter 4 Linear Classification 4.1 Features 4.2 Projections onto Subspaces 4.3 Fisher's and Linear Discriminant Analysis 4.4 Multiple Classes 4.5 Online Learning and the Perceptron 4.6 The Support Vector Machine Exercises Bibliography Chapter 5 Non-Linear Classification 5.1 Quadratic Discriminant Analysis 5.2 Kernel Trick 5.3 k Nearest Neighbours 5.4 Decision Trees 5.5 Neural Networks 5.6 Boosting and Cascades Exercises Bibliography Chapter 6 Clustering 6.1 K Means Clustering 6.2 Mixture Models 6.3 Gaussian Mixture Models 6.4 Expectation-Maximization 6.5 Bayesian Mixture Models 6.6 The Chinese Restaurant Process 6.7 Dirichlet Process Exercises Bibliography Chapter 7 Dimensionality Reduction 7.1 Principal Component Analysis 7.2 Probabilistic View 7.3 Expectation-Maximization 7.4 Factor Analysis 7.5 Kernel Principal Component Analysis Exercises Bibliography Chapter 8 Regression 8.1 Problem description 8.2 Linear Regression 8.3 Polynomial Regression 8.4 Ordinary Least Squares 8.5 Over- and Underfitting 8.6 Bias and Variance 8.7 Cross-validation 8.8 Multicollinearity and Principal Component Regression 8.9 Partial Least Squares 8.10 Regularization 8.11 Bayesian Regression 8.12 Expectation–Maximization 8.13 Bayesian Learning 8.14 Gaussian Process Exercises Bibliography Chapter 9 Feature Learning 9.1 Neural Networks 9.2 Error Backpropagation 9.3 Autoencoders 9.4 Autoencoder Example 9.5 Relationship to Other Techniques 9.6 Indian Buffet Process Exercises Bibliography Appendix A Matrix Formulae A.1 Determinants and inverses A.1.1 Block Matrix Inversion A.1.2 Block Matrix Determinant A.1.3 Woodbury Identity A.1.4 Sherman–Morrison Formula A.1.5 Matrix Determinant Lemma A.2 Derivatives A.2.1 Derivative of squared norm A.2.2 Derivative of inner product A.2.3 Derivative of second order vector product A.2.4 Derivative of determinant A.2.5 Derivative of matrix times vectors A.2.6 Derivative of transpose matrix times vectors A.2.7 Derivative of inverse A.2.8 Derivative of inverse times vectors A.2.9 Derivative of trace of second order products A.2.10 Derivative of trace of product with diagonal matrix Index