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The Elements of Statistical Learning: Data Mining, Inference, and Prediction
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最近在看数据统计方面的资料，查到一本书，分享给大家，希望有帮助~ The Elements of Statistical Learning: Data Mining, Inference, and Prediction Second Edition Trevor Hastie Robert Tibshirani Jerome Friedman Springer，2008 内容简介 During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It is a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book. This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for "wide" data (p bigger than n), including multiple testing and false discovery rates. 目录 Preface to the Second Edition vii Preface to the First Edition xi 1 Introduction 1 2 Overview of Supervised Learning 9 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Variable Types and Terminology . . . . . . . . . . . . . . 9 2.3 Two Simple Approaches to Prediction: Least Squares and Nearest Neighbors . . . . . . . . . . . 11 2.3.1 Linear Models and Least Squares . . . . . . . . 11 2.3.2 Nearest-Neighbor Methods . . . . . . . . . . . . 14 2.3.3 From Least Squares to Nearest Neighbors . . . . 16 2.4 Statistical Decision Theory . . . . . . . . . . . . . . . . . 18 2.5 Local Methods in High Dimensions . . . . . . . . . . . . . 22 2.6 Statistical Models, Supervised Learning and Function Approximation . . . . . . . . . . . . . . . . 28 2.6.1 A Statistical Model for the Joint Distribution Pr(X,Y ) . . . . . . . 28 2.6.2 Supervised Learning . . . . . . . . . . . . . . . . 29 2.6.3 Function Approximation . . . . . . . . . . . . . 29 2.7 Structured Regression Models . . . . . . . . . . . . . . . 32 2.7.1 Difficulty of the Problem . . . . . . . . . . . . . 32 xiv Contents 2.8 Classes of Restricted Estimators . . . . . . . . . . . . . . 33 2.8.1 Roughness Penalty and Bayesian Methods . . . 34 2.8.2 Kernel Methods and Local Regression . . . . . . 34 2.8.3 Basis Functions and Dictionary Methods . . . . 35 2.9 Model Selection and the Bias–Variance Tradeoff . . . . . 37 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 39 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3 Linear Methods for Regression 43 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Linear Regression Models and Least Squares . . . . . . . 44 3.2.1 Example: Prostate Cancer . . . . . . . . . . . . 49 3.2.2 The Gauss–Markov Theorem . . . . . . . . . . . 51 3.2.3 Multiple Regression from Simple Univariate Regression . . . . . . . . 52 3.2.4 Multiple Outputs . . . . . . . . . . . . . . . . . 56 3.3 Subset Selection . . . . . . . . . . . . . . . . . . . . . . . 57 3.3.1 Best-Subset Selection . . . . . . . . . . . . . . . 57 3.3.2 Forward- and Backward-Stepwise Selection . . . 58 3.3.3 Forward-Stagewise Regression . . . . . . . . . . 60 3.3.4 Prostate Cancer Data Example (Continued) . . 61 3.4 Shrinkage Methods . . . . . . . . . . . . . . . . . . . . . . 61 3.4.1 Ridge Regression . . . . . . . . . . . . . . . . . 61 3.4.2 The Lasso . . . . . . . . . . . . . . . . . . . . . 68 3.4.3 Discussion: Subset Selection, Ridge Regression and the Lasso . . . . . . . . . . . . . . . . . . . 69 3.4.4 Least Angle Regression . . . . . . . . . . . . . . 73 3.5 Methods Using Derived Input Directions . . . . . . . . . 79 3.5.1 Principal Components Regression . . . . . . . . 79 3.5.2 Partial Least Squares . . . . . . . . . . . . . . . 80 3.6 Discussion: A Comparison of the Selection and Shrinkage Methods . . . . . . . . . . . . . . . . . . . 82 3.7 Multiple Outcome Shrinkage and Selection . . . . . . . . 84 3.8 More on the Lasso and Related Path Algorithms . . . . . 86 3.8.1 Incremental Forward Stagewise Regression . . . 86 3.8.2 Piecewise-Linear Path Algorithms . . . . . . . . 89 3.8.3 The Dantzig Selector . . . . . . . . . . . . . . . 89 3.8.4 The Grouped Lasso . . . . . . . . . . . . . . . . 90 3.8.5 Further Properties of the Lasso . . . . . . . . . . 91 3.8.6 Pathwise Coordinate Optimization . . . . . . . . 92 3.9 Computational Considerations . . . . . . . . . . . . . . . 93 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 94 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Contents xv 4 Linear Methods for Classification 101 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2 Linear Regression of an Indicator Matrix . . . . . . . . . 103 4.3 Linear Discriminant Analysis . . . . . . . . . . . . . . . . 106 4.3.1 Regularized Discriminant Analysis . . . . . . . . 112 4.3.2 Computations for LDA . . . . . . . . . . . . . . 113 4.3.3 Reduced-Rank Linear Discriminant Analysis . . 113 4.4 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . 119 4.4.1 Fitting Logistic Regression Models . . . . . . . . 120 4.4.2 Example: South African Heart Disease . . . . . 122 4.4.3 Quadratic Approximations and Inference . . . . 124 4.4.4 L1 Regularized Logistic Regression . . . . . . . . 125 4.4.5 Logistic Regression or LDA? . . . . . . . . . . . 127 4.5 Separating Hyperplanes . . . . . . . . . . . . . . . . . . . 129 4.5.1 Rosenblatt’s Perceptron Learning Algorithm . . 130 4.5.2 Optimal Separating Hyperplanes . . . . . . . . . 132 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 135 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5 Basis Expansions and Regularization 139 6 Kernel Smoothing Methods 191 7 Model Assessment and Selection 219 8 Model Inference and Averaging 261 9 Additive Models, Trees, and Related Methods 295 10 Boosting and Additive Trees 337 11 Neural Networks 389 12 Support Vector Machines and Flexible Discriminants 417 13 Prototype Methods and Nearest-Neighbors 459 14 Unsupervised Learning 485 15 Random Forests 587 16 Ensemble Learning 605 17 Undirected Graphical Models 625 18 High-Dimensional Problems: p ≫ N 649 |
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