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Main Authors:	Clarke, Bertrand 1963- (Author), Fokoué, Ernest (Author), Zhang, Hao Helen (Author)
Format:	Book
Language:	English
Published:	Dordrecht ; Heidelberg ; London ; New York Springer [2009]
Series:	Springer series in statistics
Subjects:	Data mining Machine learning > Statistical methods Data Mining Maschinelles Lernen
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017660324&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	xv, 781 Seiten Illustrationen, Diagramme
ISBN:	9780387981345 9781461417071

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adam_text	Contents Preface ..................................................... v 1 Variability, Information, and Prediction ............................ 1 1.0.1 The Curse of Dimensionality ............................ З 1.0.2 The Two Extremes ..................................... 4 1.1 Perspectives on the Curse ...................................... 5 1.1.1 Sparsity .............................................. 6 1.1.2 Exploding Numbers of Models ........................... 8 1.1.3 Multicollinearity and Concurvity ......................... 9 1.1.4 The Effect of Noise .................................... 10 1.2 Coping with the Curse ........................................ 11 1.2.1 Selecting Design Points ................................. 11 1.2.2 Local Dimension ...................................... 12 1.2.3 Parsimony ............................................ 17 1.3 Two Techniques .............................................. 18 1.3.1 The Bootstrap ......................................... 18 1.3.2 Cross-Validation ....................................... 27 1.4 Optimization and Search ...................................... 32 1.4.1 Univariate Search ...................................... 32 1.4.2 Multivariate Search .................................... 33 1.4.3 General Searches ___.................................. 34 1.4.4 Constraint Satisfaction and Combinatorial Search ........... 35 1.5 Notes ......................................................... 38 1.5.1 Hammersley Points .................................... 38 viu Contents 1.5.2 Edgeworth Expansions for the Mean ...................... 39 1.5.3 Bootstrap Asymptotics for the Studentized Mean ............ 41 1.6 Exercises ................................................... 43 2 Local Smoothers ................................................. 53 2.1 Early Smoothers ............................................. 55 2.2 Transition to Classical Smoothers ............................... 59 2.2.1 Global Versus Local Approximations ..................... 60 2.2.2 LOESS ............................................... 64 2.3 Kernel Smoothers ............................................ 67 2.3.1 Statistical Function Approximation ....................... 68 2.3.2 The Concept of Kernel Methods and the Discrete Case ....... 73 2.3.3 Kernels and Stochastic Designs: Density Estimation ......... 78 2.3.4 Stochastic Designs: Asymptotics for Kernel Smoothers ...... 81 2.3.5 Convergence Theorems and Rates for Kernel Smoothers ..... 86 2.3.6 Kernel and Bandwidth Selection .......................... 90 2.3.7 Linear Smoothers ...................................... 95 2.4 Nearest Neighbors ............................................ 96 2.5 Applications of Kernel Regression .............................. 100 2.5.1 A Simulated Example ..................................100 2.5.2 Ethanol Data ..........................................102 2.6 Exercises ...................................................107 3 Spline Smoothing ................................................117 3.1 Interpolating Splines ..........................................117 3.2 Natural Cubic Splines .........................................123 3.3 Smoothing Splines for Regression ...............................126 3.3.1 Model Selection for Spline Smoothing ....................129 3.3.2 Spline Smoothing Meets Kernel Smoothing ................130 3.4 Asymptotic Bias, Variance, and MISE for Spline Smoothers .........131 3.4.1 Ethanol Data Example - Continued .......................133 3.5 Splines Redux: Hubert Space Formulation ........................136 3.5.1 Reproducing Kernels ...................................138 3.5.2 Constructing an RKHS .................................141 3.5.3 Direct Sum Construction for Splines ......................146 Contents ix 3.5.4 Explicit Forms ........................................149 3.5.5 Nonparametrics in Data Mining and Machine Learning ......152 3.6 Simulated Comparisons .......................................154 3.6.1 What Happens with Dependent Noise Models? .............157 3.6.2 Higher Dimensions and the Curse of Dimensionality ........159 3.7 Notes .......................................................163 3.7.1 Sobolev Spaces: Definition ..............................163 3.8 Exercises ...................................................164 4 New Wave Nonparametrics ........................................171 4.1 Additive Models .............................................172 4.1.1 The Backfitting Algorithm ..............................173 4.1.2 Concurvity and Inference ...............................177 4.1.3 Nonparametric Optimality ...............................180 4.2 Generalized Additive Models ...................................181 4.3 Projection Pursuit Regression ..................................184 4.4 Neural Networks .............................................189 4.4.1 Backpropagation and Inference ..........................192 4.4.2 Barren s Result and the Curse ............................197 4.4.3 Approximation Properties ...............................198 4.4.4 Barren s Theorem: Formal Statement .....................200 4.5 Recursive Partitioning Regression ...............................202 4.5.1 Growing Trees ........................................204 4.5.2 Pruning and Selection ..................................207 4.5.3 Regression ............................................208 4.5.4 Bayesian Additive Regression Trees: BART ................210 4.6 MARS .....................................................210 4.7 Sliced Inverse Regression ......................................215 4.8 ACE and AVAS ..............................................218 4.9 Notes .......................................................220 4.9.1 Proof of Barren s Theorem ..............................220 4.10 Exercises ...................................................224 5 Supervised Learning: Partition Methods ............................231 5.1 Multiclass Learning. ......................................___233 x Contents 5.2 Discriminant Analysis .........................................235 5.2.1 Distance-Based Discriminant Analysis ....................236 5.2.2 Bayes Rules ...........................................241 5.2.3 Probability-Based Discriminant Analysis ..................245 5.3 Tree-Based Classifiers ........................................249 5.3.1 Splitting Rules ........................................249 5.3.2 Logic Trees ...........................................253 5.3.3 Random Forests .......................................254 5.4 Support Vector Machines ......................................262 5.4.1 Margins and Distances ..................................262 5.4.2 Binary Classification and Risk ...........................265 5.4.3 Prediction Bounds for Function Classes ...................268 5.4.4 Constructing SVM Classifiers ............................271 5.4.5 SVM Classification for Nonlinearly Separable Populations ... 279 5.4.6 SVMs in the General Nonlinear Case .....................282 5.4.7 Some Kernels Used in SVM Classification .................288 5.4.8 Kernel Choice, SVMs and Model Selection ................289 5.4.9 Support Vector Regression ..............................290 5.4.10 Multiclass Support Vector Machines ......................293 5.5 Neural Networks .............................................294 5.6 Notes .......................................................296 5.6.1 Hoeffding s Inequality ..................................296 5.6.2 VC Dimension ........................................297 5.7 Exercises ...................................................300 6 Alternative Nonparametrics .......................................307 6.1 Ensemble Methods ...........................................308 6.1.1 Bayes Model Averaging .................................310 6.1.2 Bagging ..............................................312 6.1.3 Stacking ..............................................316 6.1.4 Boosting .............................................318 6.1.5 Other Averaging Methods ...............................326 6.1.6 Oracle Inequalities .....................................328 6.2 Bayes Nonparametrics ........................................334 Contents xi 6.2.1 Dirichlet Process Priors.................................334 6.2.2 Polya Tree Priors......................................336 6.2.3 Gaussian Process Priors.................................338 6.3 The Relevance Vector Machine .................................344 6.3.1 RVM Regression: Formal Description .....................345 6.3.2 RVM Classification ....................................349 6.4 Hidden Markov Models - Sequential Classification ................352 6.5 Notes .......................................................354 6.5.1 Proof of Yang s Oracle Inequality ........................354 6.5.2 Proof of Lecue s Oracle Inequality ........................357 6.6 Exercises ...................................................359 7 Computational Comparisons ......................................365 7.1 Computational Results: Classification ...........................366 7.1.1 Comparison on Fisher s Iris Data .........................366 7.1.2 Comparison on Ripley s Data ............................369 7.2 Computational Results: Regression ..............................376 7.2.1 Vapnik s sine Function .................................377 7.2.2 Friedman s Function ...................................389 7.2.3 Conclusions ...........................................392 7.3 Systematic Simulation Study ...................................397 7.4 No Free Lunch ...............................................400 7.5 Exercises ...................................................402 8 Unsupervised Learning: Clustering ................................405 8.1 Centroid-Based Clustering .....................................408 8.1.1 iř-Means Clustering ....................................409 8.1.2 Variants ..............................................412 8.2 Hierarchical Clustering ........................................413 8.2.1 Agglomerative Hierarchical Clustering ....................414 8.2.2 Divisive Hierarchical Clustering ..........................422 8.2.3 Theory for Hierarchical Clustering ........................426 8.3 Parütional Clustering .........................................430 8.3.1 Model-Based Clustering ................................432 8.3.2 Graph-Theoretic Clustering ..............................447 Contents 8.3.3 Spectral Clustering .....................................452 8.4 Bayesian Clustering ..........................................458 8.4.1 Probabilistic Clustering .................................458 8.4.2 Hypothesis Testing .....................................461 8.5 Computed Examples ..........................................463 8.5.1 Ripley s Data .........................................465 8.5.2 Ms Data ..............................................475 8.6 Cluster Validation ............................................480 8.7 Notes .......................................................484 8.7.1 Derivatives of Functions of a Matrix: ......................484 8.7.2 Kruskal s Algorithm: Proof ..............................484 8.7.3 Prim s Algorithm: Proof ................................485 8.8 Exercises ...................................................485 Learning in High Dimensions ......................................493 9.1 Principal Components .........................................495 9.1.1 Main Theorem ........................................496 9.1.2 Key Properties ........................................498 9.1.3 Extensions ............................................500 9.2 Factor Analysis ..............................................502 9.2.1 Finding Λ and ψ· .......................................504 9.2.2 Finding К ............................................506 9.2.3 Estimating Factor Scores ................................507 9.3 Projection Pursuit ............................................508 9.4 Independent Components Analysis ..............................511 9.4.1 Main Definitions .......................................511 9.4.2 Key Results ...........................................513 9.4.3 Computational Approach ................................515 9.5 Nonlinear PCs and ICA .......................................516 9.5.1 Nonlinear PCs .........................................517 9.5.2 Nonlinear ICA ........................................518 9.6 Geometric Summarization .....................................518 9.6.1 Measuring Distances to an Algebraic Shape ................519 9.6.2 Principal Curves and Surfaces ............................ 520 Contents xiii 9.7 Supervised Dimension Reduction: Partial Least Squares ............523 9.7.1 Simple PLS ..........................................523 9.7.2 PLS Procedures .......................................524 9.7.3 Properties of PLS ......................................526 9.8 Supervised Dimension Reduction: Sufficient Dimensions in Regression ................................................527 9.9 Visualization I: Basic Plots ....................................531 9.9.1 Elementary Visualization ................................534 9.9.2 Projections ............................................541 9.9.3 Time Dependence ......................................543 9.10 Visualization II: Transformations ...............................546 9.10.1 Chernoff Faces ........................................546 9.10.2 Multidimensional Scaling ...............................547 9.10.3 Self-Organizing Maps ..................................553 9.11 Exercises ...................................................560 10 Variable Selection ................................................569 10.1 Concepts from Linear Regression ...............................570 10.1.1 Subset Selection .......................................572 10.1.2 Variable Ranking ......................................575 10.1.3 Overview .............................................577 10.2 Traditional Criteria ...........................................578 10.2.1 Akaiké Information Criterion (AIC) .......................580 10.2.2 Bayesian Information Criterion (BIC) .....................583 10.2.3 Choices of Information Criteria ..........................585 10.2.4 Cross Validation .......................................587 10.3 Shrinkage Methods ...........................................599 10.3.1 Shrinkage Methods for Linear Models .....................601 10.3.2 Grouping in Variable Selection ...........................615 10.3.3 Least Angle Regression .................................617 10.3.4 Shrinkage Methods for Model Classes .....................620 10.3.5 Cautionary Notes ......................................631 10.4 Bayes Variable Selection ......................................632 10.4.1 Prior Specification .....................................635 10.4.2 Posterior Calculation and Exploration .....................643 xjv Contents 10.4.3 Evaluating Evidence ....................................647 10.4.4 Connections Between Bayesian and Frequentisi Methods .....650 10.5 Computational Comparisons ...................................653 10.5.1 The η > ρ Case ........................................653 10.5.2 When ρ > η ...........................................665 10.6 Notes .......................................................667 10.6.1 Code for Generating Data in Section 10.5..................667 10.7 Exercises ...................................................671 11 Multiple Testing .................................................679 11.1 Analyzing the Hypothesis Testing Problem .......................681 11.1.1 A Paradigmatic Setting .................................681 11.1.2 Counts for Multiple Tests ...............................684 11.1.3 Measures of Error in Multiple Testing .....................685 11.1.4 Aspects of Error Control ................................687 11.2 Controlling the Familywise Error Rate ...........................690 11.2.1 One-Step Adjustments ..................................690 11.2.2 Stepwise p-Value Adjustments ...........................693 11.3 PCER and PFER .............................................695 11.3.1 Null Domination .......................................696 11.3.2 Two Procedures .......................................697 11.3.3 Controlling the Type I Error Rate .........................702 11.3.4 Adjusted p-Values for PFER/PCER .......................706 11.4 Controlling the False Discovery Rate ............................707 11.4.1 FDR and other Measures of Error .........................709 11.4.2 The Benjamini-Hochberg Procedure ......................710 11.4.3 A BH Theorem for a Dependent Setting ...................711 11.4.4 Variations on BH ......................................713 11.5 Controlling the Positive False Discovery Rate .....................719 11.5.1 Bayesian Interpretations ................................719 11.5.2 Aspects of Implementation ..............................723 11.6 Bayesian Multiple Testing .....................................727 11.6.1 Fully Bayes: Hierarchical ...............................728 11.6.2 Fully Bayes: Decision theory ............................731 Contents xv 11.7 Notes.......................................................736 11.7.1 Proof of the Benjamini-Hochberg Theorem ................736 11.7.2 Proof of the Benjamini- Yekutieli Theorem .................739 References ...........................................................743 Index ...............................................................773
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spellingShingle	Clarke, Bertrand 1963- Fokoué, Ernest Zhang, Hao Helen Principles and theory for data mining and machine learning Data mining Machine learning Statistical methods Data Mining (DE-588)4428654-5 gnd Maschinelles Lernen (DE-588)4193754-5 gnd
subject_GND	(DE-588)4428654-5 (DE-588)4193754-5
title	Principles and theory for data mining and machine learning
title_auth	Principles and theory for data mining and machine learning
title_exact_search	Principles and theory for data mining and machine learning
title_full	Principles and theory for data mining and machine learning Bertrand Clarke, Ernest Fokoué, Hao Helen Zhang
title_fullStr	Principles and theory for data mining and machine learning Bertrand Clarke, Ernest Fokoué, Hao Helen Zhang
title_full_unstemmed	Principles and theory for data mining and machine learning Bertrand Clarke, Ernest Fokoué, Hao Helen Zhang
title_short	Principles and theory for data mining and machine learning
title_sort	principles and theory for data mining and machine learning
topic	Data mining Machine learning Statistical methods Data Mining (DE-588)4428654-5 gnd Maschinelles Lernen (DE-588)4193754-5 gnd
topic_facet	Data mining Machine learning Statistical methods Data Mining Maschinelles Lernen
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017660324&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT clarkebertrand principlesandtheoryfordataminingandmachinelearning AT fokoueernest principlesandtheoryfordataminingandmachinelearning AT zhanghaohelen principlesandtheoryfordataminingandmachinelearning

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