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An Introduction to Statistical Learning with Applications in R (Hastie Tibshirani)


 
 
 Author(s)  Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
 Title  An Introduction to Statistical Learning with Applications in R
 Edition  1st
 Year  2013
 Publisher  Springer
 ISBN  978-1-4614-7138-0 (paper)
 978-1-4614-7138-7 (eBook)
 Website  www.StatLearning.com  (book website)
 

Data files, figures, and R code are available at the book's website.
 



Table of Contents



Preface

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 Coefficient 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 Logistic Regression for >2 Response Classes

4.4 Linear Discriminant Analysis
  • 4.4.1 Using Bayes’ Theorem for Classification
  • 4.4.2 Linear Discriminant Analysis for p=1
  • 4.4.3 Linear Discriminant Analysis for p >1
  • 4.4.4 Quadratic Discriminant Analysis

4.5 A Comparison of Classification Methods

4.6 Lab: Logistic Regression, LDA, QDA, and KNN
  • 4.6.1 The Stock Market Data
  • 4.6.2 Logistic Regression
  • 4.6.3 Linear Discriminant Analysis
  • 4.6.4 Quadratic Discriminant Analysis
  • 4.6.5 K-Nearest Neighbors
  • 4.6.6 An Application to Caravan Insurance Data

4.7 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 1: Subset Selection Methods
  • 6.5.1 Best Subset Selection
  • 6.5.2 Forward and Backward Stepwise Selection
  • 6.5.3 Choosing Among Models Using the Validation Set Approach and Cross-Validation

6.6 Lab 2: Ridge Regression and the Lasso
  • 6.6.1 Ridge Regression
  • 6.6.2 The Lasso

6.7 Lab 3: PCR and PLS Regression
  • 6.7.1 Principal Components Regression
  • 6.7.2 Partial Least Squares

6.8 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
  • 8.2.1 Bagging
  • 8.2.2 Random Forests
  • 8.2.3 Boosting

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

8.4 Exercises

9 Support Vector Machines 337

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 withMore 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 Unsupervised Learning

10.1 The Challenge of Unsupervised Learning

10.2 Principal Components Analysis
  • 10.2.1 What Are Principal Components?
  • 10.2.2 Another Interpretation of Principal Components
  • 10.2.3 More on PCA
  • 10.2.4 Other Uses for Principal Components

10.3 Clustering Methods
  • 10.3.1 K-Means Clustering
  • 10.3.2 Hierarchical Clustering
  • 10.3.3 Practical Issues in Clustering

10.4 Lab 1: Principal Components Analysis

10.5 Lab 2: Clustering
  • 10.5.1 K-Means Clustering
  • 10.5.2 Hierarchical Clustering

10.6 Lab 3: NCI60 Data Example
  • 10.6.1 PCA on the NCI60 Data
  • 10.6.2 Clustering the Observations of the NCI60 Data

10.7 Exercises

Index




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