Geometric Parameters in Learning Theory

Chapter
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 1850)

Abstract

  • 1. Introduction

  • 2. Glivenko-Cantelli Classes and Learnability

    • 2.1. The Classical Approach

    • 2.2. Talagrand’s Inequality for Empirical Processes

  • 3. Uniform Measures of Complexity

    • 3.1. Metric Entropy and the Combinatorial Dimension

    • 3.2. Random Averages and the Combinatorial Dimension

    • 3.3. Phase Transitions in GC Classes

    • 3.4. Concentration of the Combinatorial Dimension

  • 4. Learning Sample Complexity and Error Bounds

    • 4.1. Error Bounds

    • 4.2. Comparing Structures

  • 5. Estimating the Localized Averages

    • 5.1. L2 Localized Averages

    • 5.2. Data Dependent Bounds

    • 5.3. Geometric Interpretation

  • 6. Bernstein Type of L p Loss Classes

  • 7. Classes of Linear Functionals

  • 8. Concluding Remarks

  • References

Mathematics Subject Classification (2000):

46-06 46B07 52-06 60-06 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Research School of Information Sciences and EngineeringAustralian National UniversityCanberraAustralia

Personalised recommendations