Verfügbarkeit: The elements of statistical learning

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Bibliographische Detailangaben
Titel:	The elements of statistical learning data mining, inference, and prediction
Von:	Trevor Hastie ; Robert Tibshirani ; Jerome Friedman
Person:	Hastie, Trevor 1953- Verfasser aut Tibshirani, Robert Friedman, Jerome H. 1956- 1939-
Hauptverfassende:	Hastie, Trevor 1953- (VerfasserIn), Tibshirani, Robert 1956- (VerfasserIn), Friedman, Jerome H. 1939- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Springer 2013
Ausgabe:	2. ed., corrected at 7. print.
Schriftenreihe:	Springer series in statistics
Schlagworte:	Estatística computacional Estatística Inferência estatística Mineração de dados Supervised learning (Machine learning) Datenanalyse Maschinelles Lernen Statistik Anwendung
Online-Zugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026790972&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	XXII, 745 S. Ill., graph. Darst.
ISBN:	9780387848570

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520	1		\|a "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."--BOOK JACKET.
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Datensatz im Suchindex

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adam_text	Contents 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 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 Basis Expansions and Regularization 139 5.1 Introduction ......................... 139 5.2 Piecewise Polynomials and Splines ............. 141 5.2.1 Natural Cubic Splines ............... 144 5.2.2 Example: South African Heart Disease (Continued) 146 5.2.3 Example: Phoneme Recognition ......... 148 5.3 Filtering and Feature Extraction .............. 150 5.4 Smoothing Splines ...................... 151 5.4.1 Degrees of Freedom and Smoother Matrices . . . 153 5.5 Automatic Selection of the Smoothing Parameters .... 156 5.5.1 Fixing the Degrees of Freedom .......... 158 5.5.2 The Bias-Variance Tradeoff ............ 158 5.6 Nonpar ämet rie Logistic Regression ............. 161 5.7 Multidimensional Splines .................. 162 5.8 Regularization and Reproducing Kernel Hubert Spaces . 167 5.8.1 Spaces of Functions Generated by Kernels . . . 168 5.8.2 Examples of RKHS ................ 170 5.9 Wavelet Smoothing ..................... 174 5.9.1 Wavelet Bases and the Wavelet Transform ... 176 5.9.2 Adaptive Wavelet Filtering ............ 179 Bibliographic Notes ......................... 181 Exercises ............................... 181 Appendix: Computational Considerations for Splines ...... 186 Appendix: B-splines ..................... 186 Appendix: Computations for Smoothing Splines ..... 189 xvi Contents 6 Kernel Smoothing Methods 191 6.1 One-Dimensional Kernel Smoothers ............ 192 6.1.1 Local Linear Regression .............. 194 6.1.2 Local Polynomial Regression ........... 197 6.2 Selecting the Width of the Kernel ............. 198 6.3 Local Regression in IRP ................... 200 6.4 Structured Local Regression Models in TRP ........ 201 6.4.1 Structured Kernels ................. 203 6.4.2 Structured Regression Functions ......... 203 6.5 Local Likelihood and Other Models ............ 205 6.6 Kernel Density Estimation and Classification ....... 208 6.6.1 Kernel Density Estimation ............ 208 6.6.2 Kernel Density Classification ........... 210 6.6.3 The Naive Bayes Classifier ............ 210 6.7 Radial Basis Functions and Kernels ............ 212 6.8 Mixture Models for Density Estimation and Classification 214 6.9 Computational Considerations ............... 216 Bibliographic Notes ......................... 216 Exercises ............................... 216 7 Model Assessment and Selection 219 7.1 Introduction ......................... 219 7.2 Bias, Variance and Model Complexity ........... 219 7.3 The Bias—Variance Decomposition ............. 223 7.3.1 Example: Bias-Variance Tradeoff ........ 226 7.4 Optimism of the Training Error Rate ........... 228 7.5 Estimates of In-Sample Prediction Error .......... 230 7.6 The Effective Number of Parameters ............ 232 7.7 The Bayesian Approach and BIC .............. 233 7.8 Minimum Description Length ................ 235 7.9 Vápnik— Chervonenkis Dimension .............. 237 7.9.1 Example (Continued) ............... 239 7.10 Cross-Validation ....................... 241 7.10.1 üf-Fold Cross-Validation ............. 241 7.10.2 The Wrong and Right Way to Do Cross-validation ............... 245 7.10.3 Does Cross-Validation Really Work? ....... 247 7.11 Bootstrap Methods ..................... 249 7.11.1 Example (Continued) ............... 252 7.12 Conditional or Expected Test Error? ............ 254 Bibliographic Notes ......................... 257 Exercises ............................... 257 8 Model Inference and Averaging 261 8.1 Introduction ......................... 261 Contents xvii 8.2 The Bootstrap and Maximum Likelihood Methods .... 261 8.2.1 A Smoothing Example .............. 261 8.2.2 Maximum Likelihood Inference .......... 265 8.2.3 Bootstrap versus Maximum Likelihood ..... 267 8.3 Bayesian Methods ...................... 267 8.4 Relationship Between the Bootstrap and Bayesian Inference ................... 271 8.5 The EM Algorithm ..................... 272 8.5.1 Two-Component Mixture Model ......... 272 8.5.2 The EM Algorithm in General .......... 276 8.5.3 EM as a Maximization Maximization Procedure 277 8.6 MCMC for Sampling from the Posterior .......... 279 8.7 Bagging ............................ 282 8.7.1 Example: Trees with Simulated Data ...... 283 8.8 Model Averaging and Stacking ............... 288 8.9 Stochastic Search: Bumping ................. 290 Bibliographic Notes ......................... 292 Exercises ............................... 293 9 Additive Models, Trees, and Related Methods 295 9-.1 Generalized Additive Models ................ 295 9.1.1 Fitting Additive Models .............. 297 9.1.2 Example: Additive Logistic Regression ..... 299 9.1.3 Summary ...................... 304 9.2 Tree-Based Methods ..................... 305 9.2.1 Background .................... 305 9.2.2 Regression Trees .................. 307 9.2.3 Classification Trees ................ 308 9.2.4 Other Issues .................... 310 9.2.5 Spam Example (Continued) ........... 313 9.3 PRIM: Bump Hunting .................... 317 9.3.1 Spam Example (Continued) ........... 320 9.4 MARS: Multivariate Adaptive Regression Splines ..... 321 9.4.1 Spam Example (Continued) ........... 326 9.4.2 Example (Simulated Data) ............ 327 9.4.3 Other Issues .................... 328 9.5 Hierarchical Mixtures of Experts .............. 329 9.6 Missing Data ......................... 332 9.7 Computational Considerations ............... 334 Bibliographic Notes ......................... 334 Exercises ............................... 335 10 Boosting and Additive Trees 337 10.1 Boosting Methods ...................... 337 10.1.1 Outline of This Chapter .............. 340 xviii Contents 10.2 Boosting Fits an Additive Model .............. 341 10.3 Forward Stagewise Additive Modeling ........... 342 10.4 Exponential Loss and AdaBoost .............. 343 10.5 Why Exponential Loss? ................... 345 10.6 Loss Functions and Robustness ............... 346 10.7 Off-the-Shelf Procedures for Data Mining ........ 350 10.8 Example: Spam Data .................... 352 10.9 Boosting Trees ........................ 353 10.10 Numerical Optimization via Gradient Boosting ...... 358 10.10.1 Steepest Descent .................. 358 10 Д0. 2 Gradient Boosting ................. 359 10.10.3 Implementations of Gradient Boosting ...... 360 10.11 Right-Sized Trees for Boosting ............... 361 10.12 Regularization ........................ 364 10.12.1 Shrinkage ...................... 364 10.12.2 Subsampling .................... 365 10.13 Interpretation ........................ 367 10.13.1 Relative Importance of Predictor Variables . . . 367 10.13.2 Partial Dependence Plots ............. 369 10.14 Illustrations .......................... 371 10.14.1 California Housing ................. 371 10.14.2 New Zealand Fish ................. 375 10.14.3 Demographics Data ................ 379 Bibliographic Notes ......................... 380 Exercises ............................... 384 11 Neural Networks 389 11.1 Introduction ......................... 389 11.2 Projection Pursuit Regression ............... 389 11.3 Neural Networks ....................... 392 11.4 Fitting Neural Networks ................... 395 11.5 Some Issues in Training Neural Networks ......... 397 11.5.1 Starting Values ................... 397 11.5.2 Overrating ..................... 398 11.5.3 Scaling of the Inputs ............... 398 11.5.4 Number of Hidden Units and Layers ....... 400 11.5.5 Multiple Minima .................. 400 11.6 Example: Simulated Data .................. 401 11.7 Example: ZIP Code Data .................. 404 11.8 Discussion .......................... 408 11.9 Bayesian Neural Nets and the NIPS 2003 Challenge ... 409 11.9.1 Bayes, Boosting and Bagging ........... 410 11.9.2 Performance Comparisons ............ 412 11.10 Computational Considerations ............... 414 Bibliographic Notes ......................... 415 Contents xix Exercises ............................... 415 12 Support Vector Machines and Flexible Discriminants 417 12.1 Introduction ......................... 417 12.2 The Support Vector Classifier................ 417 12.2.1 Computing the Support Vector Classifier .... 420 12.2.2 Mixture Example (Continued) .......... 421 12.3 Support Vector Machines and Kernels ........... 423 12.3.1 Computing the SVM for Classification ...... 423 12.3.2 The SVM as a Penalization Method ....... 426 12.3.3 Function Estimation and Reproducing Kernels . 428 12.3.4 S VMs and the Curse of Dimensionality ..... 431 12.3.5 A Path Algorithm for the SVM Classifier .... 432 12.3.6 Support Vector Machines for Regression ..... 434 12.3.7 Regression and Kernels .............. 436 12.3.8 Discussion ..................... 438 12.4 Generalizing Linear Discriminant Analysis ........ 438 12.5 Flexible Discriminant Analysis ............... 440 12.5.1 Computing the FDA Estimates .......... 444 12.6 Penalized Discriminant Analysis .............. 446 12.7 Mixture Discriminant Analysis ............... 449 12.7.1 Example: Waveform Data ............. 451 Bibliographic Notes ......................... 455 Exercises ............................... 455 13 Prototype Methods and Nearest-Neighbors 459 13.1 Introduction ......................... 459 13.2 Prototype Methods ..................... 459 13.2.1 K-means Clustering ................ 460 13.2.2 Learning Vector Quantization .......... 462 13.2.3 Gaussian Mixtures ................. 463 13.3 fc-Nearest-Neighbor Classifiers ............... 463 13.3.1 Example: A Comparative Study ......... 468 13.3.2 Example: /c-Nearest-Neighbors and Image Scene Classification .......... 470 13.3.3 Invariant Metrics and Tangent Distance ..... 471 13.4 Adaptive Nearest-Neighbor Methods ............ 475 13.4.1 Example ...................... 478 13.4.2 Global Dimension Reduction for Nearest-Neighbors ............... 479 13.5 Computational Considerations ............... 480 Bibliographic Notes ......................... 481 Exercises ............................... 481 xx Contents 14 Unsupervised Learning 485 14.1 Introduction ......................... 485 14.2 Association Rules ...................... 487 14.2.1 Market Basket Analysis .............. 488 14.2.2 The Apriori Algorithm .............. 489 14.2.3 Example: Market Basket Analysis ........ 492 14.2.4 Unsupervised as Supervised Learning ...... 495 14.2.5 Generalized Association Rules .......... 497 14.2.6 Choice of Supervised Learning Method ..... 499 14.2.7 Example: Market Basket Analysis (Continued) . 499 14.3 Cluster Analysis ....................... 501 14.3.1 Proximity Matrices ................ 503 14.3.2 Dissimilarities Based on Attributes ....... 503 14.3.3 Object Dissimilarity ................ 505 14.3.4 Clustering Algorithms ............... 507 14.3.5 Combinatorial Algorithms ............ 507 14.3.6 K-means ...................... 509 14.3.7 Gaussian Mixtures as Soft K- means Clustering . 510 14.3.8 Example: Human Tumor Microarray Data . . . 512 14.3.9 Vector Quantization ................ 514 14.3.10 if-medoids ..................... 515 14.3.11 Practical Issues .................. 518 14.3.12 Hierarchical Clustering .............. 520 14.4 Self-Organizing Maps .................... 528 14.5 Principal Components, Curves and Surfaces ........ 534 14.5.1 Principal Components ............... 534 14.5.2 Principal Curves and Surfaces .......... 541 14.5.3 Spectral Clustering ................ 544 14.5.4 Kernel Principal Components ........... 547 14.5.5 Sparse Principal Components ........... 550 14.6 Non-negative Matrix Factorization ............. 553 14.6.1 Archetypal Analysis ................ 554 14.7 Independent Component Analysis and Exploratory Projection Pursuit ............ 557 14.7.1 Latent Variables and Factor Analysis ...... 558 14.7.2 Independent Component Analysis ........ 560 14.7.3 Exploratory Projection Pursuit .......... 565 14.7.4 A Direct Approach to ICA ............ 565 14.8 Multidimensional Scaling .................. 570 14.9 Nonlinear Dimension Reduction and Local Multidimensional Scaling ............ 572 14.10 The Google PageRank Algorithm ............. 576 Bibliographic Notes ......................... 578 Exercises ............................... 579 Contents xxi 15 Random Forests 587 15.1 Introduction ......................... 587 15.2 Definition of Random Forests ................ 587 15.3 Details of Random Forests ................. 592 15.3.1 Out of Bag Samples ................ 592 15.3.2 Variable Importance ................ 593 15.3.3 Proximity Plots .................. 595 15.3.4 Random Forests and Overfitting ......... 596 15.4 Analysis of Random Forests ................. 597 15.4.1 Variance and the De-Correlation Effect ..... 597 15.4.2 Bias ......................... 600 15.4.3 Adaptive Nearest Neighbors ........... 601 Bibliographic Notes ......................... 602 Exercises ............................... 603 16 Ensemble Learning 605 16.1 Introduction ......................... 605 16.2 Boosting and Regularization Paths ............. 607 16.2.1 Penalized Regression ............... 607 16.2.2 The Bet on Sparsity Principle ......... 610 16.2.3 Regularization Paths, Over-fitting and Margins . 613 16.3 Learning Ensembles ..................... 616 16.3.1 Learning a Good Ensemble ............ 617 16.3.2 Rule Ensembles .................. 622 Bibliographic Notes ......................... 623 Exercises ............................... 624 17 Undirected Graphical Models 625 17.1 Introduction ......................... 625 17.2 Markov Graphs and Their Properties ........... 627 17.3 Undirected Graphical Models for Continuous Variables . 630 17.3.1 Estimation of the Parameters when the Graph Structure is Known ....... 631 17.3.2 Estimation of the Graph Structure ........ 635 17.4 Undirected Graphical Models for Discrete Variables . . . 638 17.4.1 Estimation of the Parameters when the Graph Structure is Known ....... 639 17.4.2 Hidden Nodes ................... 641 17.4.3 Estimation of the Graph Structure ........ 642 17.4.4 Restricted Boltzmann Machines ......... 643 Exercises ............................... 645 18 High-Dimensional Problems: ρ » N 649 18.1 When ρ is Much Bigger than N .............. 649 xxii Contents 18.2 Diagonal Linear Discriminant Analysis and Nearest Shrunken Centroids .............. 651 18.3 Linear Classifiers with Quadratic Regularization ..... 654 18.3.1 Regularized Discriminant Analysis ........ 656 18.3.2 Logistic Regression with Quadratic Regularization .......... 657 18.3.3 The Support Vector Classifier .......... 657 18.3.4 Feature Selection .................. 658 18.3.5 Computational Shortcuts When ρ » N..... 659 18.4 Linear Classifiers with L Regularization ......... 661 18.4.1 Application of Lasso to Protein Mass Spectroscopy .......... 664 18.4.2 The Fused Lasso for Functional Data ...... 666 18.5 Classification When Features are Unavailable ....... 668 18.5.1 Example: String Kernels and Protein Classification ............. 668 18.5.2 Classification and Other Models Using Inner-Product Kernels and Pairwise Distances . 670 18.5.3 Example: Abstracts Classification ........ 672 18.6 High-Dimensional Regression: Supervised Principal Components ............. 674 18.6.1 Connection to Latent-Variable Modeling .... 678 18.6.2 Relationship with Partial Least Squares ..... 680 18.6.3 Pre-Conditioning for Feature Selection ..... 681 18.7 Feature Assessment and the Multiple-Testing Problem . . 683 18.7.1 The False Discovery Rate ............. 687 18.7.2 Asymmetric Cutpoints and the SAM Procedure 690 18.7.3 A Bayesian Interpretation of the FDR ...... 692 18.8 Bibliographic Notes ..................... 693 Exercises ............................... 694 References 699 Author Index 729 Index 737
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genre	(DE-588)4056995-0 Statistik gnd-content
genre_facet	Statistik
id	DE-604.BV041342225
illustrated	Illustrated
indexdate	2024-12-20T16:45:14Z
institution	BVB
isbn	9780387848570
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-026790972
oclc_num	862807539
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owner	DE-355 DE-BY-UBR DE-20 DE-634 DE-11 DE-706 DE-1051 DE-739 DE-188 DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-861 DE-523 DE-1028
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physical	XXII, 745 S. Ill., graph. Darst.
publishDate	2013
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publisher	Springer
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series2	Springer series in statistics
spellingShingle	Hastie, Trevor 1953- Tibshirani, Robert 1956- Friedman, Jerome H. 1939- The elements of statistical learning data mining, inference, and prediction Estatística computacional larpcal Estatística larpcal Inferência estatística larpcal Mineração de dados larpcal Supervised learning (Machine learning) Datenanalyse (DE-588)4123037-1 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Statistik (DE-588)4056995-0 gnd Anwendung (DE-588)4196864-5 gnd
subject_GND	(DE-588)4123037-1 (DE-588)4193754-5 (DE-588)4056995-0 (DE-588)4196864-5
title	The elements of statistical learning data mining, inference, and prediction
title_auth	The elements of statistical learning data mining, inference, and prediction
title_exact_search	The elements of statistical learning data mining, inference, and prediction
title_full	The elements of statistical learning data mining, inference, and prediction Trevor Hastie ; Robert Tibshirani ; Jerome Friedman
title_fullStr	The elements of statistical learning data mining, inference, and prediction Trevor Hastie ; Robert Tibshirani ; Jerome Friedman
title_full_unstemmed	The elements of statistical learning data mining, inference, and prediction Trevor Hastie ; Robert Tibshirani ; Jerome Friedman
title_short	The elements of statistical learning
title_sort	the elements of statistical learning data mining inference and prediction
title_sub	data mining, inference, and prediction
topic	Estatística computacional larpcal Estatística larpcal Inferência estatística larpcal Mineração de dados larpcal Supervised learning (Machine learning) Datenanalyse (DE-588)4123037-1 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Statistik (DE-588)4056995-0 gnd Anwendung (DE-588)4196864-5 gnd
topic_facet	Estatística computacional Estatística Inferência estatística Mineração de dados Supervised learning (Machine learning) Datenanalyse Maschinelles Lernen Statistik Anwendung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026790972&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT hastietrevor theelementsofstatisticallearningdatamininginferenceandprediction AT tibshiranirobert theelementsofstatisticallearningdatamininginferenceandprediction AT friedmanjeromeh theelementsofstatisticallearningdatamininginferenceandprediction

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