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BK

New York : Springer, 2001

xvi,533 s. : il.

ISBN 0-387-95284-5 (váz.)

Springer series in statistics

Obsahuje grafy, ilustrace, bibliografické citace, dodatky, předmluvu, úvod, rejstříky

Bibliografie na s. 509-522

Data - analýza statistická - učebnice vysokošk.

000026371

Preface vii // 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 // 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 41 // 3.1 Introduction 41 // 3.2 Linear Regression Models and Least Squares 42 // 3.2.1 Example: Prostate Cancer 47 // 3.2.2 The Gauss-Markov Theorem 49 // 3.3 Multiple Regression from Simple Univariate Regression 50 // 3.3.1 Multiple Outputs 54 // 3.4 Subset Selection and Coefficient Shrinkage 55 // 3.4.1 Subset Selection 55 // 3.4.2 Prostate Cancer Data Example (Continued) 57 // 3.4.3 Shrinkage Methods 59 // 3.4.4 Methods Using Derived Input Directions 66 // 3.4.5 Discussion: A Comparison of the Selection and // Shrinkage Methods 68 // 3.4.6 Multiple Outcome Shrinkage and Selection 73 // 3.5 Computational Considerations 75 // Bibliographic Notes 75 // Exercises 75 // 4 Linear Methods for Classification 79 // 4.1 Introduction 79 // 4.2 Linear Regression of an Indicator Matrix 81 // 4.3 Linear Discriminant Analysis 84 //

4.3.1 Regularized Discriminant Analysis 90 // 4.3.2 Computations for LDA 91 // 4.3.3 Reduced-Rank Linear Discriminant Analysis 91 // 4.4 Logistic Regression 95 // 4.4.1 Fitting Logistic Regression Models 98 // 4.4.2 Example: South African Heart Disease 100 // 4.4.3 Quadratic Approximations and Inference 102 // 4.4.4 Logistic Regression or LDA? 103 // 4.5 Separating Hyperplanes 105 // 4.5.1 Rosenblatt’s Perceptron Learning Algorithm 107 // 4.5.2 Optimal Separating Hyperplanes 108 // Bibliographic Notes 111 // Exercises 111 // 5 Basis Expansions and Regularization 115 // 5.1 Introduction 115 // 5.2 Piecewise Polynomials and Splines 117 // 5.2.1 Natural Cubic Splines 120 // 5.2.2 Example: South African Heart Disease (Continued) . 122 // 5.2.3 Example: Phoneme Recognition 124 // 5.3 Filtering and Feature Extraction 126 // 5.4 Smoothing Splines 127 // 5.4.1 Degrees of Freedom and Smoother Matrices 129 // 5.5 Automatic Selection of the Smoothing Parameters 134 // 5.5.1 Fixing the Degrees of Freedom 134 // 5.5.2 The Bias-Variance Tradeoff 134 // 5.6 Nonparametric Logistic Regression 137 // 5.7 Multidimensional Splines 138 // 5.8 Regularization and Reproducing Kernel Hilbert Spaces 144 // 5.8.1 Spaces of Functions Generated by Kernels 144 // 5.8.2 Examples of RKHS 146 // 5.9 Wavelet Smoothing 148 // 5.9.1 Wavelet Bases and the Wavelet Transform 150 // 5.9.2 Adaptive Wavelet Filtering 153 // Bibliographic Notes 155 // Exercises 155 // Appendix: Computational Considerations for Splines 160 // Appendix: B-splines 160 // Appendix: Computations for Smoothing Splines 163 // 6 Kernel Methods 165 // 6.1 One-Dimensional Kernel Smoothers 165 // 6.1.1 Local Linear Regression 168 // 6.1.2 Local Polynomial Regression 171 // 6.2 Selecting the Width of the Kernel 172 // 6.3 Local Regression in IRP 174 // 6.4 Structured Local Regression Models in IRP 175 // 6.4.1 Structured Kernels 177 //

6.4.2 Structured Regression Functions 177 // 6.5 Local Likelihood and Other Models 179 // 6.6 Kernel Density Estimation and Classification 182 // 6.6.1 Kernel Density Estimation 182 // 6.6.2 Kernel Density Classification 184 // 6.6.3 The Naive Bayes Classifier 184 // 6.7 Radial Basis Functions and Kernels 186 // 6.8 Mixture Models for Density Estimation and Classification . 188 // 6.9 Computational Considerations 190 // Bibliographic Notes 190 // Exercises 190 // 7 Model Assessment and Selection 193 // 7.1 Introduction 193 // 7.2 Bias, Variance and Model Complexity 193 // 7.3 The Bias-Variance Decomposition 196 // 7.3.1 Example: Bias-Variance Tradeoff 198 // 7.4 Optimism of the Training Error Rate 200 // 7.5 Estimates of In-Sample Prediction Error 203 // 7.6 The Effective Number of Parameters 205 // 7.7 The Bayesian Approach and BIC 206 // 7.8 Minimum Description Length 208 // 7.9 Vapnik-Chernovenkis Dimension 210 // 7.9.1 Example (Continued) 212 // 7.10 Cross-Validation 214 // 7.11 Bootstrap Methods 217 // 7.11.1 Example (Continued) 220 // Bibliographic Notes 222 // Exercises 222 // 8 Model Inference and Averaging 225 // 8.1 Introduction 225 // 8.2 The Bootstrap and Maximum Likelihood Methods 225 // 8.2.1 A Smoothing Example 225 // 8.2.2 Maximum Likelihood Inference 229 // 8.2.3 Bootstrap versus Maximum Likelihood 231 // 8.3 Bayesian Methods 231 // 8.4 Relationship Between the Bootstrap // and Bayesian Inference 235 // 8.5 The EM Algorithm 236 // 8.5.1 Two-Component Mixture Model 236 // 8.5.2 The EM Algorithm in General 240 // 8.5.3 EM as a Maximization-Maximization Procedure 241 // 8.6 MCMC for Sampling from the Posterior 243 // 8.7 Bagging 246 // 8.7.1 Example: Trees with Simulated Data 247 // 8.8 Model Averaging and Stacking 250 // 8.9 Stochastic Search: Bumping 253 // Bibliographic Notes 254 // Exercises 255 //

9 Additive Models, Trees, and Related Methods 257 // 9.1 Generalized Additive Models 257 // 9.1.1 Fitting Additive Models 259 // 9.1.2 Example: Additive Logistic Regression 261 // 9.1.3 Summary 266 // 9.2 Tree-Based Methods 266 // 9.2.1 Background 266 // 9.2.2 Regression Trees 267 // 9.2.3 Classification Trees 270 // 9.2.4 Other Issues 272 // 9.2.5 Spam Example (Continued) 275 // 9.3 PRIM-Bump Hunting 279 // 9.3.1 Spam Example (Continued) 282 // 9.4 MARS: Multivariate Adaptive Regression Splines 283 // 9.4.1 Spam Example (Continued) 287 // 9.4.2 Example (Simulated Data) 288 // 9.4.3 Other Issues 289 // 9.5 Hierarchical Mixtures of Experts 290 // 9.6 Missing Data 293 // 9.7 Computational Considerations 295 // Bibliographic Notes 295 // Exercises 296 // 10 Boosting and Additive Trees 299 // 10.1 Boosting Methods 299 // 10.1.1 Outline of this Chapter 302 // 10.2 Boosting Fits an Additive Model 303 // 10.3 Forward Stagewise Additive Modeling 304 // 10.4 Exponential Loss and AdaBoost 305 // 10.5 Why Exponential Loss? 306 // 10.6 Loss Functions and Robustness 308 // 10.7 "Off-the-Shelf” Procedures for Data Mining 312 // 10.8 Example-Spam Data 314 // 10.9 Boosting Trees 316 // 10.10 Numerical Optimization 319 // 10.10.1 Steepest Descent 320 // 10.10.2 Gradient Boosting 320 // 10.10.3 MART 322 // 10.11 Right-Sized Trees for Boosting 323 // 10.12 Regularization 324 // 10.12.1 Shrinkage 326 // 10.12.2 Penalized Regression 328 // 10.12.3 Virtues of the L1 Penalty (Lasso) over L2 330 // 10.13 Interpretation 331 // 10.13.1 Relative Importance of Predictor Variables 331 // 10.13.2 Partial Dependence Plots 333 // 10.14 Illustrations 335 // 10.14.1 California Housing 335 // 10.14.2 Demographics Data 339 // Bibliographic Notes 340 // Exercises 344 // 11 Neural Networks 347 // 11.1 Introduction 347 // 11.2 Projection Pursuit Regression 347 // 11.3 Neural Networks 350 //

11.4 Fitting Neural Networks 353 // 11.5 Some Issues in Training Neural Networks 355 // 11.5.1 Starting Values 355 // 11.5.2 Over fitting 356 // 11.5.3 Scaling of the Inputs 358 // 11.5.4 Number of Hidden Units and Layers 358 // 11.5.5 Multiple Minima 359 // 11.6 Example: Simulated Data 359 // 11.7 Example: ZIP Code Data 362 // 11.8 Discussion 366 // 11.9 Computational Considerations 367 // Bibliographic Notes 367 // Exercises 369 // 12 Support Vector Machines and // Flexible Discriminants 371 // 12.1 Introduction 371 // 12.2 The Support Vector Classifier 371 // 12.2.1 Computing the Support Vector Classifier 373 // 12.2.2 Mixture Example (Continued) 375 // 12.3 Support Vector Machines 377 // 12.3.1 Computing the SVM for Classification 377 // 12.3.2 The SVM as a Penalization Method 380 // 12.3.3 Function Estimation and Reproducing Kernels 381 // 12.3.4 SVMs and the Curse of Dimensionality 384 // 12.3.5 Support Vector Machines for Regression 385 // 12.3.6 Regression and Kernels 387 // 12.3.7 Discussion 389 // 12.4 Generalizing Linear Discriminant Analysis 390 // 12.5 Flexible Discriminant Analysis 391 // 12.5.1 Computing the FDA Estimates 394 // 12.6 Penalized Discriminant Analysis 397 // 12.7 Mixture Discriminant Analysis 399 // 12.7.1 Example: Waveform Data 402 // Bibliographic Notes 406 // Exercises 406 // 13 Prototype Methods and Nearest-Neighbors 411 // 13.1 Introduction 411 // 13.2 Prototype Methods 411 // 13.2.1 K-means Clustering 412 // 13.2.2 Learning Vector Quantization 414 // 13.2.3 Gaussian Mixtures 415 // 13.3 k-Nearest-Neighbor Classifiers 415 // 13.3.1 Example: A Comparative Study 420 // 13.3.2 Example: k-Nearest-Neighbors and Image Scene // Classification 422 // 13.3.3 Invariant Metrics and Tangent Distance 423 // 13.4 Adaptive Nearest-Neighbor Methods 427 // 13.4.1 Example 430 // 13.4.2 Global Dimension Reduction for Nearest-Neighbors 431 //

13.5 Computational Considerations 432 // Bibliographic Notes 433 // Exercises 433 // 14 Unsupervised Learning 437 // 14.1 Introduction 437 // 14.2 Association Rules 439 // 14.2.1 Market Basket Analysis 440 // 14.2.2 The Apriori Algorithm 441 // 14.2.3 Example: Market Basket Analysis 444 // 14.2.4 Unsupervised as Supervised Learning 447 // 14.2.5 Generalized Association Rules 449 // 14.2.6 Choice of Supervised Learning Method 451 // 14.2.7 Example: Market Basket Analysis (Continued) 451 // 14.3 Cluster Analysis 453 // 14.3.1 Proximity Matrices 455 // 14.3.2 Dissimilarities Based on Attributes 455 // 14.3.3 Object Dissimilarity 457 // 14.3.4 Clustering Algorithms 459 // 14.3.5 Combinatorial Algorithms 460 // 14.3.6 K-means 461 // 14.3.7 Gaussian Mixtures as Soft K-means Clustering 463 // 14.3.8 Example: Human Tumor Microarray Data 463 // 14.3.9 Vector Quantization 466 // 14.3.10 K-medoids 468 // 14.3.11 Practical Issues 470 // 14.3.12 Hierarchical Clustering 472 // 14.4 Self-Organizing Maps 480 // 14.5 Principal Components, Curves and Surfaces 485 // 14.5.1 Principal Components 485 // 14.5.2 Principal Curves and Surfaces 491 // 14.6 Independent Component Analysis and Exploratory // Projection Pursuit 494 // 14.6.1 Latent Variables and Factor Analysis 494 // 14.6.2 Independent Component Analysis 496 // 14.6.3 Exploratory Projection Pursuit 500 // 14.6.4 A Different Approach to ICA 500 // 14.7 Multidimensional Scaling 502 // Bibliographic Notes 503 // Exercises 504 // References 509 // Author Index 523 // Index 527