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Learning from Data
Concepts, Theory, and Methods
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From Statistics to Neural Networks
This volume provides a unified approach to the study of predictive learning. It contains an up-to-date review of major issues and methods related to predictive learning in statistics, artificial neural networks (ANN), and pattern recognition. Topi...
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"The authors have succeeded in summarizing some of the recent trends and future challenges in different learning methods, including enabling technologies and some interesting practical applications." (Computing Reviews, May 22, 2008)
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Vladimir CherKassky, PhD, is Professor of Electrical and Computer Engineering at the University of Minnesota. He is internationally known for his research on neural networks and statistical learning. Filip Mulier, PhD, has worked in the software field for the last twelve years, part of which has been spent researching, developing, and applying advanced statistical and machine learning methods. He currently holds a project management position.
PREFACE. NOTATION. 1 Introduction. 1.1 Learning and Statistical Estimation. 1.2 Statistical Dependency and Causality. 1.3 Characterization of Variables. 1.4 Characterization of Uncertainty. 1.5 Predictive Learning versus Other Data Analytical Methodologies. 2 Problem Statement, Classical Approaches, and Adaptive Learning. 2.1 Formulation of the Learning Problem. 2.1.1 Objective of Learning. 2.1.2 Common Learning Tasks. 2.1.3 Scope of the Learning Problem Formulation. 2.2 Classical Approaches. 2.2.1 Density Estimation. 2.2.2 Classification. 2.2.3 Regression. 2.2.4 Solving Problems with Finite Data. 2.2.5 Nonparametric Methods. 2.2.6 Stochastic Approximation. 2.3 Adaptive Learning: Concepts and Inductive Principles. 2.3.1 Philosophy, Major Concepts, and Issues. 2.3.2 A Priori Knowledge and Model Complexity. 2.3.3 Inductive Principles. 2.3.4 Alternative Learning Formulations. 2.4 Summary. 3 Regularization Framework. 3.1 Curse and Complexity of Dimensionality. 3.2 Function Approximation and Characterization of Complexity. 3.3 Penalization. 3.3.1 Parametric Penalties. 3.3.2 Nonparametric Penalties. 3.4 Model Selection (Complexity Control). 3.4.1 Analytical Model Selection Criteria. 3.4.2 Model Selection via Resampling. 3.4.3 Bias-Variance Tradeoff. 3.4.4 Example of Model Selection. 3.4.5 Function Approximation versus Predictive Learning. 3.5 Summary. 4 Statistical Learning Theory. 4.1 Conditions for Consistency and Convergence of ERM. 4.2 Growth Function and VC Dimension. 4.2.1 VC Dimension for Classification and Regression Problems. 4.2.2 Examples of Calculating VC Dimension. 4.3 Bounds on the Generalization. 4.3.1 Classification. 4.3.2 Regression. 4.3.3 Generalization Bounds and Sampling Theorem. 4.4 Structural Risk Minimization. 4.4.1 Dictionary Representation. 4.4.2 Feature Selection. 4.4.3 Penalization Formulation. 4.4.4 Input Preprocessing. 4.4.5 Initial Conditions for Training Algorithm. 4.5 Comparisons of Model Selection for Regression. 4.5.1 Model Selection for Linear Estimators. 4.5.2 Model Selection for k-Nearest-Neighbor Regression. 4.5.3 Model Selection for Linear Subset Regression. 4.5.4 Discussion. 4.6 Measuring the VC Dimension. 4.7 VC Dimension, Occam's Razor, and Popper's Falsifiability. 4.8 Summary and Discussion. 5 Nonlinear Optimization Strategies. 5.1 Stochastic Approximation Methods. 5.1.1 Linear Parameter Estimation. 5.1.2 Backpropagation Training of MLP Networks. 5.2 Iterative Methods. 5.2.1 EM Methods for Density Estimation. 5.2.2 Generalized Inverse Training of MLP Networks. 5.3 Greedy Optimization. 5.3.1 Neural Network Construction Algorithms. 5.3.2 Classification and Regression Trees. 5.4 Feature Selection, Optimization, and Statistical Learning Theory. 5.5 Summary. 6 Methods for Data Reduction and Dimensionality Reduction. 6.1 Vector Quantization and Clustering. 6.1.1 Optimal Source Coding in Vector Quantization. 6.1.2 Generalized Lloyd Algorithm. 6.1.3 Clustering. 6.1.4 EM Algorithm for VQ and Clustering. 6.1.5 Fuzzy Clustering. 6.2 Dimensionality Reduction: Statistical Methods. 6.2.1 Linear Principal Components. 6.2.2 Principal Curves and Surfaces. 6.2.3 Multidimensional Scaling. 6.3 Dimensionality Reduction: Neural Network Methods. 6.3.1 Discrete Principal Curves and Self-Organizing Map Algorithm. 6.3.2 Statistical Interpretation of the SOM Method. 6.3.3 Flow-Through Version of the SOM and Learning Rate Schedules. 6.3.4 SOM Applications and Modifications. 6.3.5 Self-Supervised MLP. 6.4 Methods for Multivariate Data Analysis. 6.4.1 Factor Analysis. 6.4.2 Independent Component Analysis. 6.5 Summary. 7 Methods for Regression. 7.1 Taxonomy: Dictionary versus Kernel Representation. 7.2 Linear Estimators. 7.2.1 Estimation of Linear Models and Equivalence of Representations. 7.2.2 Analytic Form of Cross-Validation. 7.2.3 Estimating Complexity of Penalized Linear Models. 7.2.4 Nonadaptive Methods. 7.3 Adaptive Dictionary Methods. 7.3.1 Additive Methods and Projection Pursuit Regression. 7.3.2 Multilayer Per