Geometric Parameters in Learning Theory

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