An Introduction to Statistical Learning - with Applications in R

Preface
Contents
1 Introduction
2 Statistical Learning
	2.1 What Is Statistical Learning?
		2.1.1 Why Estimate f?
		2.1.2 How Do We Estimate f?
		2.1.3 The Trade-Off Between Prediction Accuracy and Model Interpretability
		2.1.4 Supervised Versus Unsupervised Learning
		2.1.5 Regression Versus Classification Problems
	2.2 Assessing Model Accuracy
		2.2.1 Measuring the Quality of Fit
		2.2.2 The Bias-Variance Trade-Off
		2.2.3 The Classification Setting
	2.3 Lab: Introduction to R
		2.3.1 Basic Commands
		2.3.2 Graphics
		2.3.3 Indexing Data
		2.3.4 Loading Data
		2.3.5 Additional Graphical and Numerical Summaries
	2.4 Exercises
3 Linear Regression
	3.1 Simple Linear Regression
		3.1.1 Estimating the Coefficients
		3.1.2 Assessing the Accuracy of the Coefficients Estimates
		3.1.3 Assessing the Accuracy of the Model
	3.2 Multiple Linear Regression
		3.2.1 Estimating the Regression Coefficients
		3.2.2 Some Important Questions
	3.3 Other Considerations in the Regression Model
		3.3.1 Qualitative Predictors
		3.3.2 Extensions of the Linear Model
		3.3.3 Potential Problems
	3.4 The Marketing Plan
	3.5 Comparison of Linear Regression with K-Nearest Neighbors
	3.6 Lab: Linear Regression
		3.6.1 Libraries
		3.6.2 Simple Linear Regression
		3.6.3 Multiple Linear Regression
		3.6.4 Interaction Terms
		3.6.5 Non-linear Transformations of the Predictors
		3.6.6 Qualitative Predictors
		3.6.7 Writing Functions
	3.7 Exercises
4 Classification
	4.1 An Overview of Classification
	4.2 Why Not Linear Regression?
	4.3 Logistic Regression
		4.3.1 The Logistic Model
		4.3.2 Estimating the Regression Coefficients
		4.3.3 Making Predictions
		4.3.4 Multiple Logistic Regression
		4.3.5 Multinomial Logistic Regression
	4.4 Generative Models for Classification
		4.4.1 Linear Discriminant Analysis for p = 1
		4.4.2 Linear Discriminant Analysis for p >1
		4.4.3 Quadratic Discriminant Analysis
		4.4.4 Naive Bayes
	4.5 A Comparison of Classification Methods
		4.5.1 An Analytical Comparison
		4.5.2 An Empirical Comparison
	4.6 Generalized Linear Models
		4.6.1 Linear Regression on the Bikeshare Data
		4.6.2 Poisson Regression on the Bikeshare Data
		4.6.3 Generalized Linear Models in Greater Generality
	4.7 Lab: Classification Methods
		4.7.1 The Stock Market Data
		4.7.2 Logistic Regression
		4.7.3 Linear Discriminant Analysis
		4.7.4 Quadratic Discriminant Analysis
		4.7.5 Naive Bayes
		4.7.6 K-Nearest Neighbors
		4.7.7 Poisson Regression
	4.8 Exercises
5 Resampling Methods
	5.1 Cross-Validation
		5.1.1 The Validation Set Approach
		5.1.2 Leave-One-Out Cross-Validation
		5.1.3 k-Fold Cross-Validation
		5.1.4 Bias-Variance Trade-Off for k-Fold Cross-Validation
		5.1.5 Cross-Validation on Classification Problems
	5.2 The Bootstrap
	5.3 Lab: Cross-Validation and the Bootstrap
		5.3.1 The Validation Set Approach
		5.3.2 Leave-One-Out Cross-Validation
		5.3.3 k-Fold Cross-Validation
		5.3.4 The Bootstrap
	5.4 Exercises
6 Linear Model Selection and Regularization
	6.1 Subset Selection
		6.1.1 Best Subset Selection
		6.1.2 Stepwise Selection
		6.1.3 Choosing the Optimal Model
	6.2 Shrinkage Methods
		6.2.1 Ridge Regression
		6.2.2 The Lasso
		6.2.3 Selecting the Tuning Parameter
	6.3 Dimension Reduction Methods
		6.3.1 Principal Components Regression
		6.3.2 Partial Least Squares
	6.4 Considerations in High Dimensions
		6.4.1 High-Dimensional Data
		6.4.2 What Goes Wrong in High Dimensions?
		6.4.3 Regression in High Dimensions
		6.4.4 Interpreting Results in High Dimensions
	6.5 Lab: Linear Models and Regularization Methods
		6.5.1 Subset Selection Methods
		6.5.2 Ridge Regression and the Lasso
		6.5.3 PCR and PLS Regression
	6.6 Exercises
7 Moving Beyond Linearity
	7.1 Polynomial Regression
	7.2 Step Functions
	7.3 Basis Functions
	7.4 Regression Splines
		7.4.1 Piecewise Polynomials
		7.4.2 Constraints and Splines
		7.4.3 The Spline Basis Representation
		7.4.4 Choosing the Number and Locations of the Knots
		7.4.5 Comparison to Polynomial Regression
	7.5 Smoothing Splines
		7.5.1 An Overview of Smoothing Splines
		7.5.2 Choosing the Smoothing Parameter λ
	7.6 Local Regression
	7.7 Generalized Additive Models
		7.7.1 GAMs for Regression Problems
		7.7.2 GAMs for Classification Problems
	7.8 Lab: Non-linear Modeling
		7.8.1 Polynomial Regression and Step Functions
		7.8.2 Splines
		7.8.3 GAMs
	7.9 Exercises
8 Tree-Based Methods
	8.1 The Basics of Decision Trees
		8.1.1 Regression Trees
		8.1.2 Classification Trees
		8.1.3 Trees Versus Linear Models
		8.1.4 Advantages and Disadvantages of Trees
	8.2 Bagging, Random Forests, Boosting, and Bayesian Additive Regression Trees
		8.2.1 Bagging
		8.2.2 Random Forests
		8.2.3 Boosting
		8.2.4 Bayesian Additive Regression Trees
		8.2.5 Summary of Tree Ensemble Methods
	8.3 Lab: Decision Trees
		8.3.1 Fitting Classification Trees
		8.3.2 Fitting Regression Trees
		8.3.3 Bagging and Random Forests
		8.3.4 Boosting
		8.3.5 Bayesian Additive Regression Trees
	8.4 Exercises
9 Support Vector Machines
	9.1 Maximal Margin Classifier
		9.1.1 What Is a Hyperplane?
		9.1.2 Classification Using a Separating Hyperplane
		9.1.3 The Maximal Margin Classifier
		9.1.4 Construction of the Maximal Margin Classifier
		9.1.5 The Non-separable Case
	9.2 Support Vector Classifiers
		9.2.1 Overview of the Support Vector Classifier
		9.2.2 Details of the Support Vector Classifier
	9.3 Support Vector Machines
		9.3.1 Classification with Non-Linear Decision Boundaries
		9.3.2 The Support Vector Machine
		9.3.3 An Application to the Heart Disease Data
	9.4 SVMs with More than Two Classes
		9.4.1 One-Versus-One Classification
		9.4.2 One-Versus-All Classification
	9.5 Relationship to Logistic Regression
	9.6 Lab: Support Vector Machines
		9.6.1 Support Vector Classifier
		9.6.2 Support Vector Machine
		9.6.3 ROC Curves
		9.6.4 SVM with Multiple Classes
		9.6.5 Application to Gene Expression Data
	9.7 Exercises
10 Deep Learning
	10.1 Single Layer Neural Networks
	10.2 Multilayer Neural Networks
	10.3 Convolutional Neural Networks
		10.3.1 Convolution Layers
		10.3.2 Pooling Layers
		10.3.3 Architecture of a Convolutional Neural Network
		10.3.4 Data Augmentation
		10.3.5 Results Using a Pretrained Classifier
	10.4 Document Classification
	10.5 Recurrent Neural Networks
		10.5.1 Sequential Models for Document Classification
		10.5.2 Time Series Forecasting
		10.5.3 Summary of RNNs
	10.6 When to Use Deep Learning
	10.7 Fitting a Neural Network
		10.7.1 Backpropagation
		10.7.2 Regularization and Stochastic Gradient Descent
		10.7.3 Dropout Learning
		10.7.4 Network Tuning
	10.8 Interpolation and Double Descent
	10.9 Lab: Deep Learning
		10.9.1 A Single Layer Network on the Hitters Data
		10.9.2 A Multilayer Network on the MNIST Digit Data
		10.9.3 Convolutional Neural Networks
		10.9.4 Using Pretrained CNN Models
		10.9.5 IMDb Document Classification
		10.9.6 Recurrent Neural Networks
	10.10 Exercises
11 Survival Analysis and Censored Data
	11.1 Survival and Censoring Times
	11.2 A Closer Look at Censoring
	11.3 The Kaplan-Meier Survival Curve
	11.4 The Log-Rank Test
	11.5 Regression Models With a Survival Response
		11.5.1 The Hazard Function
		11.5.2 Proportional Hazards
		11.5.3 Example: Brain Cancer Data
		11.5.4 Example: Publication Data
	11.6 Shrinkage for the Cox Model
	11.7 Additional Topics
		11.7.1 Area Under the Curve for Survival Analysis
		11.7.2 Choice of Time Scale
		11.7.3 Time-Dependent Covariates
		11.7.4 Checking the Proportional Hazards Assumption
		11.7.5 Survival Trees
	11.8 Lab: Survival Analysis
		11.8.1 Brain Cancer Data
		11.8.2 Publication Data
		11.8.3 Call Center Data
	11.9 Exercises
12 Unsupervised Learning
	12.1 The Challenge of Unsupervised Learning
	12.2 Principal Components Analysis
		12.2.1 What Are Principal Components?
		12.2.2 Another Interpretation of Principal Components
		12.2.3 The Proportion of Variance Explained
		12.2.4 More on PCA
		12.2.5 Other Uses for Principal Components
	12.3 Missing Values and Matrix Completion
	12.4 Clustering Methods
		12.4.1 K-Means Clustering
		12.4.2 Hierarchical Clustering
		12.4.3 Practical Issues in Clustering
	12.5 Lab: Unsupervised Learning
		12.5.1 Principal Components Analysis
		12.5.2 Matrix Completion
		12.5.3 Clustering
		12.5.4 NCI60 Data Example
	12.6 Exercises
13 Multiple Testing
	13.1 A Quick Review of Hypothesis Testing
		13.1.1 Testing a Hypothesis
		13.1.2 Type I and Type II Errors
	13.2 The Challenge of Multiple Testing
	13.3 The Family-Wise Error Rate
		13.3.1 What is the Family-Wise Error Rate?
		13.3.2 Approaches to Control the Family-Wise Error Rate
		13.3.3 Trade-Off Between the FWER and Power
	13.4 The False Discovery Rate
		13.4.1 Intuition for the False Discovery Rate
		13.4.2 The Benjamini-Hochberg Procedure
	13.5 A Re-Sampling Approach to p-Values and False Discovery Rates
		13.5.1 A Re-Sampling Approach to the p-Value
		13.5.2 A Re-Sampling Approach to the False Discovery Rate
		13.5.3 When Are Re-Sampling Approaches Useful?
	13.6 Lab: Multiple Testing
		13.6.1 Review of Hypothesis Tests
		13.6.2 The Family-Wise Error Rate
		13.6.3 The False Discovery Rate
		13.6.4 A Re-Sampling Approach
	13.7 Exercises
Index