Learning from Good and Bad Data

I Identification in the Limit from Indifferent Teachers.- 1 The Identification Problem.- 1.1 Learning from Indifferent Teachers.- 1.2 A Working Assumption.- 1.3 Convergence.- 1.4 A General Strategy.- 1.5 Examples from Existing Research.- 1.6 Basic Definitions.- 1.7 A General Algorithm.- 1.8 Additional Comments.- 2 Identification by Refinement.- 2.1 Order Homomorphisms.- 2.2 Refinements.- 2.2.1 Introduction.- 2.2.2 Upward and Downward Refinements.- 2.2.3 Summary.- 2.3 Identification by Refinement.- 2.4 Conclusion.- 3 How to Work With Refinements.- 3.1 Introduction.- 3.2 Three Useful Properties.- 3.3 Normal Forms and Monotonic Operations.- 3.4 Universal Refinements.- 3.4.1 Abstract Formulation.- 3.4.2 A Refinement for Clause-Form Sentences.- 3.4.3 Inductive Bias.- 3.5 Conclusions.- 3.6 Appendix to Chapter 3.- 3.6.1 Summary of Logic Notation and Terminology.- 3.6.2 Proof of Theorem 3.32.- 3.6.3 Refinement Properties of Figure 3.2.- II Probabilistic Identification from Random Examples.- 4 Probabilistic Approximate Identification.- 4.1 Probabilistic Identification in the Limit.- 4.2 The Model of Valiant.- 4.2.1 Pac-Identification.- 4.2.2 Identifying Normal-Form Expressions.- 4.2.3 Related Results about Valiant’s Model.- 4.3 Using the Partial Order.- 4.4 Summary.- 5 Identification from Noisy Examples.- 5.1 Introduction.- 5.2 Prior Research Results.- 5.3 The Classification Noise Process.- 5.4 Pac-Identification.- 5.4.1 Finite Classes.- 5.4.2 Infinite Classes.- 5.4.3 Estimating the Noise Rate ?.- 5.5 Probabilistic Identification in the Limit.- 5.6 Identifying Normal-Form Expressions.- 5.7 Other Models of Noise.- 5.8 Appendix to Chapter 5.- 6 Conclusions.