1. Introduction. - 1. 1 The Components of a Learning Paradigm. - 1. 2 Parametric Hypothesis Spaces. - 1. 3 Technical Contents and Major Contributions. - 2. Generalization Error For Neural Nets. - 2. 1 Introduction. - 2. 2 Definitions and Statement of the Problem. - 2. 3 Stating the Problem for Radial Basis Functions. - 2. 4 Main Result. - 2. 5 Remarks. - 2. 6 Implications of the Theorem in Practice: Putting In the Numbers. - 2. 7 Conclusion. - 2-A Notations. - 2-B A Useful Decomposition of the Expected Risk. - 2-C A Useful Inequality. - 2-D Proof of the Main Theorem. - 3. Active Learning. - 3. 1 A General Framework For Active Approximation. - 3. 2 Example 1: A Class of Monotonically Increasing Bounded Functions. - 3. 3 Example 2: A Class of Functions with Bounded First Derivative. - 3. 4 Conclusions Extensions and Open Problems. - 3. 5 A Simple Example. - 3. 6 Generalizations. - 4. Language Learning. - 4. 1 Language Learning and The Poverty of Stimulus. - 4. 2 Constrained Grammars-Principles and Parameters. - 4. 3 Learning in the Principles and Parameters Framework. - 4. 4 Formal Analysis of the Triggering Learning Algorithm. - 4. 5 Characterizing Convergence Times for the Markov Chain Model. - 4. 6 Exploring Other Points. - 4. 7 Batch Learning Upper and Lower Bounds: An Aside. - 4. 8 Conclusions Open Questions and Future Directions. - 4-A Unembedded Sentences For Parametric Grammars. - 4-B Memoryless Algorithms and Markov Chains. - 4-C Proof of Learnability Theorem. - 4-D Formal Proof. - 5. Language Change. - 5. 1 Introduction. - 5. 2 Language Change in Parametric Systems. - 5. 3 Example 1: A Three Parameter System. - 5. 4 Example 2: The Case of Modern French:. - 5. 5 Conclusions. - 6. Conclusions. - 6. 1 Emergent Themes. - 6. 2 Extensions. - 6. 3 A Concluding Note. - References. Language: English