Computational Learning Theory: an Introduction

Martin Anthony and Norman Biggs

Table of Contents


Ch. 1. Concepts, Hypotheses, Learning Algorithms 
1.1. Introduction 
1.2. Concepts 
1.3. Training and Learning 
1.4. Learning by Construction 
1.5. Learning by Enumeration 
Further Remarks 

Ch. 2. Boolean Formulae and Representations  
2.1. Monomial Concepts 
2.2. A Learning Algorithm for Monomials 
2.3. The Standard Notation for Boolean Functions 
2.4. Learning Disjunctions of Small Monomials 
2.5. Representations of Hypothesis Spaces 
Further Remarks 

Ch. 3. Probabilistic Learning 
3.1. An Algorithm for Learning Rays  
3.2. Probably Approximately Correct Learning 
3.3. Illustration--Learning Rays is Pac 
3.4. Exact Learning 
Further Remarks 

Ch. 4. Consistent Algorithms and Learnability 
4.1. Potential Learnability 
4.2. The Finite Case 
4.3. Decision Lists 
4.4. A Consistent Algorithm for Decision Lists 
Further Remarks 

Ch. 5. Efficient Learning--I 
5.1. Outline of Complexity Theory 
5.2. Running Time of Learning Algorithms 
5.3. An Approach to the Efficiency of Pac Learning 
5.4. The Consistency Problem 
5.5. A Hardness Result 
Further Remarks 

Ch. 6. Efficient Learning--II 
6.1. Efficiency in Terms of Confidence and Accuracy 
6.2. Pac Learning and the Consistency Problem 
6.3. The Size of a Representation 
6.4. Finding the Smallest Consistent Hypothesis 
6.5. Occam Algorithms 
6.6. Examples of Occam Algorithms 
6.7. Epac Learning 
Further Remarks 

Ch. 7. The VC Dimension 
7.1. Motivation 
7.2. The Growth Function 
7.3. The VC Dimension 
7.4. The VC Dimension of the Real Perceptron 
7.5. Sauer's Lemma 
Further Remarks 

Ch. 8. Learning and the VC Dimension 
8.1. Introduction 
8.2. VC Dimension and Potential Learnability 
8.3. Proof of the Fundamental Theorem 
8.4. Sample Complexity of Consistent Algorithms 
8.5. Lower Bounds on Sample Complexity 
8.6. Comparison of Sample Complexity Bounds 
Further Remarks 

Ch. 9. VC Dimension and Efficient Learning 
9.1. Graded Real Hypothesis Spaces 
9.2. Efficient Learning of Graded Spaces 
9.3. VC Dimension and Boolean Spaces 
9.4. Optimal Sample Complexity for Boolean Spaces 
9.5. Efficiency With Respect to Representations 
9.6. Dimension-based Occam Algorithms 
9.7. Epac Learning Again 
Further Remarks 

Ch. 10. Linear Threshold Networks 
10.1. The Boolean Perceptron 
10.2. An Incremental Algorithm 
10.3. A Finiteness Result 
10.4. Finding a Consistent Hypothesis 
10.5. Feedforward Neural Networks 
10.6. VC Dimension of Feedforward Networks 
10.7. Hardness Results for Neural Networks 
Further Remarks