Statistical Learning With Math And R: 100 Exercises For Building Logic

✍ Scribed by Joe Suzuki

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 226
• Edition: 1st Edition
• Category: Library

✦ Synopsis

The most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of machine learning and data science by considering math problems and building R programs. As the preliminary part, Chapter 1 provides a concise introduction to linear algebra, which will help novices read further to the following main chapters. Those succeeding chapters present essential topics in statistical learning: linear regression, classification, resampling, information criteria, regularization, nonlinear regression, decision trees, support vector machines, and unsupervised learning.
Each chapter mathematically formulates and solves machine learning problems and builds the programs. The body of a chapter is accompanied by proofs and programs in an appendix, with exercises at the end of the chapter. Because the book is carefully organized to provide the solutions to the exercises in each chapter, readers can solve the total of 100 exercises by simply following the contents of each chapter. This textbook is suitable for an undergraduate or graduate course consisting of about 12 lectures. Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning.

✦ Table of Contents

Preface......Page 5
Contents......Page 9
1.1 Inverse Matrix......Page 12
1.2 Determinant......Page 14
1.3 Linear Independence......Page 17
1.4 Vector Spaces and Their Dimensions......Page 19
1.5 Eigenvalues and Eigenvectors......Page 21
1.6 Orthonormal Bases and Orthogonal Matrix......Page 23
1.7 Diagonalization of Symmetric Matrices......Page 24
2.1 Least Squares Method......Page 28
2.2 Multiple Regression......Page 31
2.3 Distribution of......Page 33
2.4 Distribution of the RSS Values......Page 35
2.5 Hypothesis Testing for j=0......Page 37
2.6 Coefficient of Determination and the Detection of Collinearity......Page 44
2.7 Confidence and Prediction Intervals......Page 46
3.1 Logistic Regression......Page 58
3.2 Newton–Raphson Method......Page 60
3.3 Linear and Quadratic Discrimination......Page 65
3.4 k-Nearest Neighbor Method......Page 68
3.5 ROC Curves......Page 69
4.1 Cross-Validation......Page 77
4.2 CV Formula for Linear Regression......Page 81
4.3 Bootstrapping......Page 84
5.1 Information Criteria......Page 93
5.2 Efficient Estimation and the Fisher Information Matrix......Page 97
5.3 Kullback-Leibler Divergence......Page 100
5.4 Derivation of Akaike's Information Criterion......Page 102
6.1 Ridge......Page 111
6.2 Subderivative......Page 113
6.3 Lasso......Page 116
6.4 Comparing Ridge and Lasso......Page 119
6.5 Setting the λ Value......Page 121
7.1 Polynomial Regression......Page 126
7.2 Spline Regression......Page 129
7.3 Natural Spline Regression......Page 131
7.4 Smoothing Spline......Page 135
7.5 Local Regression......Page 139
7.6 Generalized Additive Models......Page 143
8.1 Decision Trees for Regression......Page 156
8.2 Decision Tree for Classification......Page 165
8.4 Random Forest......Page 169
8.5 Boosting......Page 172
9.1 Optimum Boarder......Page 180
9.2 Theory of Optimization......Page 183
9.3 The Solution of Support Vector Machines......Page 186
9.4 Extension of Support Vector Machines Using a Kernel......Page 189
10.1 K-means Clustering......Page 202
10.2 Hierarchical Clustering......Page 206
10.3 Principle Component Analysis......Page 213
Index......Page 224

✦ Subjects

Artificial Intelligence