Machine Learning

A Theoretical Approach

By

  • Balas Natarajan

This is the first comprehensive introduction to computational learning theory. The author's uniform presentation of fundamental results and their applications offers AI researchers a theoretical perspective on the problems they study. The book presents tools for the analysis of probabilistic models of learning, tools that crisply classify what is and is not efficiently learnable. After a general introduction to Valiant's PAC paradigm and the important notion of the Vapnik-Chervonenkis dimension, the author explores specific topics such as finite automata and neural networks. The presentation is intended for a broad audience--the author's ability to motivate and pace discussions for beginners has been praised by reviewers. Each chapter contains numerous examples and exercises, as well as a useful summary of important results. An excellent introduction to the area, suitable either for a first course, or as a component in general machine learning and advanced AI courses. Also an important reference for AI researchers.
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Book information

  • Published: July 1991
  • Imprint: MORGAN KAUFMANN
  • ISBN: 978-1-55860-148-2


Table of Contents

Machine Learning: A Theoretical Approach
Balas K. Natarajan
  • Chapter 1 Introduction
    • 1.1 Bibliographic Notes
  • Chapter 2 Learning Concept on Countable Domains
    • 2.1 Preliminaries
    • 2.2 Sample Complexity
    • 2.3 Dimension and Learnability
    • 2.4 Learning Concepts with One-Sided Error
    • 2.5 Summary
    • 2.6 Appendix
    • 2.7 Exercises
    • 2.8 Bibliographic Notes
  • Chapter 3 Time Complexity of Concept Learning
    • 3.1 Preliminaries
    • 3.2 Polynomial-Time Learnability
    • 3.3 Occam's Razor
    • 3.4 One-Sided Error
    • 3.5 Hardness Results
    • 3.6 Summary
    • 3.7 Appendix
      • 3.7.1 Randomized Algorithms
      • 3.7.2 Chabyshev's Inequality
    • 3.8 Exercises
    • 3.9 Bibliographic Notes
  • Chapter 4 Learning Concepts on Uncoutable Domains
    • 4.1 Preliminaries
    • 4.2 Uniform Convergence and Learnability
    • 4.3 Summary
    • 4.4 Appendix
      • 4.4.1 Measurability and Probability Distributions
      • 4.4.2 Bounds for the Binomial Distribution
    • 4.5 Exercises
  • Chapter 5 Learning Functions
    • 5.1 Learning Functions on Countable Domains
      • 5.1.1 Dimension and Learnability
      • 5.1.2 Time Complexity of Function Learning
    • 5.2 Learning Functions on Uncountable Domains
    • 5.3 Summary
    • 5.4 Exercises
    • 5.5 Bibliographic Notes
  • Chapter 6 Finite Automata
    • 6.1 Preliminaries
    • 6.2 A Modified Framework
    • 6.3 Summary
    • 6.4 Exercises
    • 6.5 Bibliographic Notes
  • Chapter 7 Neural Networks
    • 7.1 Preliminaries
    • 7.2 Bounded-Precision Networks
    • 7.3 Efficiency Issues
    • 7.4 Summary
    • 7.5 Appendix
      • 7.5.1 Hyperplanes and Half-Spaces
    • 7.6 Exercises
    • 7.7 Bibliographic Notes
  • Chapter 8 Generalizing the Learning Model
    • 8.1 Preliminaries
    • 8.2 Sample Complexity
    • 8.3 Time Complexity
    • 8.4 Prediction
      • 8.4.1 Hardness Results
    • 8.5 Boosting
      • 8.5.1 Confidence Boosting
      • 8.5.2 Precision Boosting
    • 8.6 Summary
    • 8.7 Exercises
    • 8.8 Bibliographic Notes
  • Chapter 9 Conclusion
    • 9.1 The Paradigm
    • 9.2 Recent and Future Directions
    • 9.3 An AI Perspective
  • Index