Foundations of Statistical Learning Theory : Empirical Infe-rence in high-dimention spaces

Posted in Science on October 13, 2008


Foundations of Statistical Learning Theory : Empirical Infe-rence in high-dimention spaces

Lecture Slides:

  • Empirical Inference Science
  • Summary
  • Contents
  • I. Inductive Inferences
  • Pattern Recognition Problem
  • Complexity Concept
  • Occam’s Razor in Physical Science
  • the Main Theorem of Vc Theory
  • Capacity Concepts: the Vc Entropy and the Growth Function
  • the Structure of the Growth Function: the Vc Dimension
  • the Main Results of the Vc Theory
  • Concept of Falsifiability
  • Vc Dimension and Popper Dimension
  • Vc and Popper Dimension: Illustration
  • Vc Bounds and Srm Principle
  • the Occam’s Razor Principle and the Srm Principle
  • the Crucial Point
  • Example 1: the Vc Dimension Is Equal to the Number of Entities (Parameters)
  • Example 2: the Vc Dimension Is Larger Than the Number of Entities (Parameters)
  • Example 3: the Vc Dimensions Is Less Than the Number of Entities (Parameters)
  • the Idea of Support Vector Machines
  • Illustration
  • Technical Details
  • More Technical Details
  • Ii. Transductive Inferences
  • Inductive and Transductive Inferences
  • What Is the Transduction Problem
  • Equivalence Classes
  • Prediction of Molecular Bioactivity
  • Selective Inference
  • the Imperative for the Complex World
  • Iii. Problems of Non-Inductive Inferences
  • What Is Wrong With Large Margin?
  • Back to Vc Entropy: the Concept of Contradiction
  • Idea of Universum
  • Inference Based on the Number of Contradictions on Universum
  • Experiments With Digit Recognition
  • Further Capacity Control: Svm+
  • Svm+: Formulation
  • Svm+: Dual Space Solution
  • One Step More: Learning Hidden Information
  • Master-Class Learning
  • Original Digits
  • Corrupted Digits
  • Master-Class Digit Recognition Learning: Technical Space
  • Master-Class Digit Recognition Learning: Holistic Space
  • Codes for Holistic Description
  • Big Picture
  • Machine Learning and Empirical Inference Science
  • Conclusion: Two Metaphors for a Simple World
  • Conclusion: Two Metaphors for a Complex World
  • What Is Empirical Inference Science About?

Author: Léon Bottou, Nec Research Coauthor: Vladimir Vapnik, University of London

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