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Concentration inequalities : a nonasymptotic theory of independence /

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Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomen...

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Bibliographic Details
Main Authors: Boucheron, Stéphane (Author), Lugosi, Gábor (Author), Massart, Pascal (Author)
Format: Book
Language:English
Published: Oxford, United Kingdom : Oxford University Press, 2013.
Edition:First edition.
Subjects:
Concentration functions.
Inequalities (Mathematics)
Measure theory.
Table of Contents:
  • Foreword
  • 1. Introduction
  • 2. Basic Inequalities
  • 3. Bounding the Variance
  • 4. Basic Information Inequalities
  • 5. Logarithmic Sobolev Inequalities
  • 6. The Entropy Method
  • 7. Concentration and Isoperimetry
  • 8. The Transportation Method
  • 9. Influences and Threshold Phenomena
  • 10. Isoperimetry on the Hypercube and Gaussian Spaces
  • 11. The Variance of Suprema of Empirical Processes
  • 12. Suprema of Empirical Processes: Exponential Inequalities
  • 13. The Expected Value of Suprema of Empirical Processes
  • 14. [Fi]-Entropies
  • 15. Moment Inequalities.