Elementary Introduction to Statistical Learning Theory.
Title:
Elementary Introduction to Statistical Learning Theory.
Author:
Kulkarni, Sanjeev.
ISBN:
9781118023433
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (235 pages)
Series:
Wiley Series in Probability and Statistics ; v.853
Wiley Series in Probability and Statistics
Contents:
An Elementary Introduction to Statistical Learning Theory -- Contents -- Preface -- 1 Introduction: Classification, Learning, Features, and Applications -- 1.1 Scope -- 1.2 Why Machine Learning? -- 1.3 Some Applications -- 1.3.1 Image Recognition -- 1.3.2 Speech Recognition -- 1.3.3 Medical Diagnosis -- 1.3.4 Statistical Arbitrage -- 1.4 Measurements, Features, and Feature Vectors -- 1.5 The Need for Probability -- 1.6 Supervised Learning -- 1.7 Summary -- 1.8 Appendix: Induction -- 1.9 Questions -- 1.10 References -- 2 Probability -- 2.1 Probability of Some Basic Events -- 2.2 Probabilities of Compound Events -- 2.3 Conditional Probability -- 2.4 Drawing Without Replacement -- 2.5 A Classic Birthday Problem -- 2.6 Random Variables -- 2.7 Expected Value -- 2.8 Variance -- 2.9 Summary -- 2.10 Appendix: Interpretations of Probability -- 2.11 Questions -- 2.12 References -- 3 Probability Densities -- 3.1 An Example in Two Dimensions -- 3.2 Random Numbers in [0,1] -- 3.3 Density Functions -- 3.4 Probability Densities in Higher Dimensions -- 3.5 Joint and Conditional Densities -- 3.6 Expected Value and Variance -- 3.7 Laws of Large Numbers -- 3.8 Summary -- 3.9 Appendix: Measurability -- 3.10 Questions -- 3.11 References -- 4 The Pattern Recognition Problem -- 4.1 A Simple Example -- 4.2 Decision Rules -- 4.3 Success Criterion -- 4.4 The Best Classifier: Bayes Decision Rule -- 4.5 Continuous Features and Densities -- 4.6 Summary -- 4.7 Appendix: Uncountably Many -- 4.8 Questions -- 4.9 References -- 5 The Optimal Bayes Decision Rule -- 5.1 Bayes Theorem -- 5.2 Bayes Decision Rule -- 5.3 Optimality and Some Comments -- 5.4 An Example -- 5.5 Bayes Theorem and Decision Rule with Densities -- 5.6 Summary -- 5.7 Appendix: Defining Conditional Probability -- 5.8 Questions -- 5.9 References -- 6 Learning from Examples.
6.1 Lack of Knowledge of Distributions -- 6.2 Training Data -- 6.3 Assumptions on the Training Data -- 6.4 A Brute Force Approach to Learning -- 6.5 Curse of Dimensionality, Inductive Bias, and No Free Lunch -- 6.6 Summary -- 6.7 Appendix: What Sort of Learning? -- 6.8 Questions -- 6.9 References -- 7 The Nearest Neighbor Rule -- 7.1 The Nearest Neighbor Rule -- 7.2 Performance of the Nearest Neighbor Rule -- 7.3 Intuition and Proof Sketch of Performance -- 7.4 Using more Neighbors -- 7.5 Summary -- 7.6 Appendix: When People use Nearest Neighbor Reasoning -- 7.6.1 Who Is a Bachelor? -- 7.6.2 Legal Reasoning -- 7.6.3 Moral Reasoning -- 7.7 Questions -- 7.8 References -- 8 Kernel Rules -- 8.1 Motivation -- 8.2 A Variation on Nearest Neighbor Rules -- 8.3 Kernel Rules -- 8.4 Universal Consistency of Kernel Rules -- 8.5 Potential Functions -- 8.6 More General Kernels -- 8.7 Summary -- 8.8 Appendix: Kernels, Similarity, and Features -- 8.9 Questions -- 8.10 References -- 9 Neural Networks: Perceptrons -- 9.1 Multilayer Feedforward Networks -- 9.2 Neural Networks for Learning and Classification -- 9.3 Perceptrons -- 9.3.1 Threshold -- 9.4 Learning Rule for Perceptrons -- 9.5 Representational Capabilities of Perceptrons -- 9.6 Summary -- 9.7 Appendix: Models of Mind -- 9.8 Questions -- 9.9 References -- 10 Multilayer Networks -- 10.1 Representation Capabilities of Multilayer Networks -- 10.2 Learning and Sigmoidal Outputs -- 10.3 Training Error and Weight Space -- 10.4 Error Minimization by Gradient Descent -- 10.5 Backpropagation -- 10.6 Derivation of Backpropagation Equations -- 10.6.1 Derivation for a Single Unit -- 10.6.2 Derivation for a Network -- 10.7 Summary -- 10.8 Appendix: Gradient Descent and Reasoning toward Reflective Equilibrium -- 10.9 Questions -- 10.10 References -- 11 PAC Learning -- 11.1 Class of Decision Rules.
11.2 Best Rule from a Class -- 11.3 Probably Approximately Correct Criterion -- 11.4 PAC Learning -- 11.5 Summary -- 11.6 Appendix: Identifying Indiscernibles -- 11.7 Questions -- 11.8 References -- 12 VC Dimension -- 12.1 Approximation and Estimation Errors -- 12.2 Shattering -- 12.3 VC Dimension -- 12.4 Learning Result -- 12.5 Some Examples -- 12.6 Application to Neural Nets -- 12.7 Summary -- 12.8 Appendix: VC Dimension and Popper Dimension -- 12.9 Questions -- 12.10 References -- 13 Infinite VC Dimension -- 13.1 A Hierarchy of Classes and Modified PAC Criterion -- 13.2 Misfit Versus Complexity Trade-Off -- 13.3 Learning Results -- 13.4 Inductive Bias and Simplicity -- 13.5 Summary -- 13.6 Appendix: Uniform Convergence and Universal Consistency -- 13.7 Questions -- 13.8 References -- 14 The Function Estimation Problem -- 14.1 Estimation -- 14.2 Success Criterion -- 14.3 Best Estimator: Regression Function -- 14.4 Learning in Function Estimation -- 14.5 Summary -- 14.6 Appendix: Regression Toward the Mean -- 14.7 Questions -- 14.8 References -- 15 Learning Function Estimation -- 15.1 Review of the Function Estimation/Regression Problem -- 15.2 Nearest Neighbor Rules -- 15.3 Kernel Methods -- 15.4 Neural Network Learning -- 15.5 Estimation with a Fixed Class of Functions -- 15.6 Shattering, Pseudo-Dimension, and Learning -- 15.7 Conclusion -- 15.8 Appendix: Accuracy, Precision, Bias, and Variance in Estimation -- 15.9 Questions -- 15.10 References -- 16 Simplicity -- 16.1 Simplicity in Science -- 16.1.1 Explicit Appeals to Simplicity -- 16.1.2 Is the World Simple? -- 16.1.3 Mistaken Appeals to Simplicity -- 16.1.4 Implicit Appeals to Simplicity -- 16.2 Ordering Hypotheses -- 16.2.1 Two Kinds of Simplicity Orderings -- 16.3 Two Examples -- 16.3.1 Curve Fitting -- 16.3.2 Enumerative Induction -- 16.4 Simplicity as Simplicity of Representation.
16.4.1 Fix on a Particular System of Representation? -- 16.4.2 Are Fewer Parameters Simpler? -- 16.5 Pragmatic Theory of Simplicity -- 16.6 Simplicity and Global Indeterminacy -- 16.7 Summary -- 16.8 Appendix: Basic Science and Statistical Learning Theory -- 16.9 Questions -- 16.10 References -- 17 Support Vector Machines -- 17.1 Mapping the Feature Vectors -- 17.2 Maximizing the Margin -- 17.3 Optimization and Support Vectors -- 17.4 Implementation and Connection to Kernel Methods -- 17.5 Details of the Optimization Problem -- 17.5.1 Rewriting Separation Conditions -- 17.5.2 Equation for Margin -- 17.5.3 Slack Variables for Nonseparable Examples -- 17.5.4 Reformulation and Solution of Optimization -- 17.6 Summary -- 17.7 Appendix: Computation -- 17.8 Questions -- 17.9 References -- 18 Boosting -- 18.1 Weak Learning Rules -- 18.2 Combining Classifiers -- 18.3 Distribution on the Training Examples -- 18.4 The Adaboost Algorithm -- 18.5 Performance on Training Data -- 18.6 Generalization Performance -- 18.7 Summary -- 18.8 Appendix: Ensemble Methods -- 18.9 Questions -- 18.10 References -- Bibliography -- Author Index -- Subject Index.
Abstract:
A thought-provoking look at statistical learning theory and its role in understanding human learning and inductive reasoning A joint endeavor from leading researchers in the fields of philosophy and electrical engineering, An Elementary Introduction to Statistical Learning Theory is a comprehensive and accessible primer on the rapidly evolving fields of statistical pattern recognition and statistical learning theory. Explaining these areas at a level and in a way that is not often found in other books on the topic, the authors present the basic theory behind contemporary machine learning and uniquely utilize its foundations as a framework for philosophical thinking about inductive inference. Promoting the fundamental goal of statistical learning, knowing what is achievable and what is not, this book demonstrates the value of a systematic methodology when used along with the needed techniques for evaluating the performance of a learning system. First, an introduction to machine learning is presented that includes brief discussions of applications such as image recognition, speech recognition, medical diagnostics, and statistical arbitrage. To enhance accessibility, two chapters on relevant aspects of probability theory are provided. Subsequent chapters feature coverage of topics such as the pattern recognition problem, optimal Bayes decision rule, the nearest neighbor rule, kernel rules, neural networks, support vector machines, and boosting. Appendices throughout the book explore the relationship between the discussed material and related topics from mathematics, philosophy, psychology, and statistics, drawing insightful connections between problems in these areas and statistical learning theory. All chapters conclude with a summary section, a set of practice questions, and a reference sections that supplies historical notes and additional
resources for further study. An Elementary Introduction to Statistical Learning Theory is an excellent book for courses on statistical learning theory, pattern recognition, and machine learning at the upper-undergraduate and graduate levels. It also serves as an introductory reference for researchers and practitioners in the fields of engineering, computer science, philosophy, and cognitive science that would like to further their knowledge of the topic.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Genre:
Added Author:
Electronic Access:
Click to View