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An Elementary Introduction to Statistical Learning Theory Book

An Elementary Introduction to Statistical Learning Theory
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An Elementary Introduction to Statistical Learning Theory, 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 Intro, An Elementary Introduction to Statistical Learning Theory
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  • An Elementary Introduction to Statistical Learning Theory
  • Written by author Sanjeev Kulkarni
  • Published by Wiley, John & Sons, Incorporated, 8/2/2011
  • 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 Intro
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Authors

Preface.

1. Introduction: Classification, Learning, Features, Applications.

1.1 Scope.

1.2 Why Machine Learning?

1.3 Some Applications.

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.

7.7 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 Feed Forward Networks.

9.2 Neural Networks for Learning and Classification.

9.3 Perceptrons.

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.

10.7 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 Tradeoff.

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 Networks 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.

16.2 Ordering Hypotheses.

16.3 Two Examples.

16.4 Simplicity as Simplicity of Representation.

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.

17.6 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. 


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An Elementary Introduction to Statistical Learning Theory, A thought-provoking look at statistical learning theory and its role in understanding human learning and inductive reasoning
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An Elementary Introduction to Statistical Learning Theory, A thought-provoking look at statistical learning theory and its role in understanding human learning and inductive reasoning
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An Elementary Introduction to Statistical Learning Theory

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An Elementary Introduction to Statistical Learning Theory, 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, <i>An Elementary Intro, An Elementary Introduction to Statistical Learning Theory

An Elementary Introduction to Statistical Learning Theory

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