Concentration Inequalities A Nonasymptotic Theory of Independence

Stephane Boucheron, Laboratoire de Probabilites et Modeles Aleatoires, Universite Paris-Diderot,Gabor Lugosi, ICREA Research Professor, Pompeu Fabra University,Pascal Massart, Laboratoire de Mathematiques, Universite Paris Sud and Institut Universitaire de France

Stephane Boucheron is a Professor in the Applied Mathematics and Statistics Department at Universite Paris-Diderot, France.


Gabor Lugosi is ICREA Research Professor in the Department of Economics at the Pompeu Fabra University in Barcelona, Spain.


Pascal Massart is a Professor in the Department of Mathematics at Universite de Paris-Sud, France.

Foreword, Michel Ledoux
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. Φ-entropies
15. Moment inequalities