Book

This monograph presents a mathematical theory of concentration inequalities for functions of independent random variables. The basic phenomenon under investigation is that if a function of many independent random variables does not depend too much on any of them then it is concentrated around its expected value. This book offers a host of inequalities to quantify this statement. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities, transportation arguments, to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are presented. The book offers a self-contained introduction to concentration inequalities, including a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed. Special attention is paid to applications to the supremum of empirical processes.\n\n Keywords: concentration inequalities, entropy method, concentration of measure, isoperimetric problems, empirical processes, transportation method, influences
2013

Publications

About adaptive coding on countable alphabets: max-stableenvelope classes

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About adaptive coding on countable alphabets

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Concentration inequalities

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Adaptive compression against a countable alphabet

Concentration inequalities for order statistics

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Sharp threshold for percolation on expanders

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A high-dimensional Wilks phenomenon

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Coding on countably infinite alphabets

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On concentration of self-bounding functions

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Error exponents for AR order testing

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Moment inequalities for functions of independent randomvariables

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Theory of classification: a survey of some recent advances

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Concentration Inequalities

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Concentration inequalities using the entropy method

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Introduction to Statistical Learning Theory

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Bins and balls: large deviations of the empirical occupancyprocess

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Model Selection and Error Estimation

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On a square packing problem

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On the independence number of random interval graphs

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Problèmes d'informatique fondamentale. Voyages au pays de l'informatique fondamentale au gré de problm̀es de concours.

A sharp concentration inequality with applications

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About priority encoding transmission

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Loss patterns and loss resilient codes over the Internet

Model Selection and Error Estimation

On the fluctuations of the giant component

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Coding exponents for some Markov channels

Codage à Protections Inégales et Diffusion

An urn model from learning theory

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Noise Injection: Theoretical Prospects

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De la représentation à la validation~: lagénéralisation dans les réseaux de neurones

Control of complexity in learning with perturbed inputs

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Sur les traces de l'apprentissage

Algorithmique parallèle

Message Passing Architectures

Apprentissage et calculs

Learnability in the presence of noise

Bruit et apprentissage

Apprentissage et calculs

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Learnability in the Presence of Noise

Teaching

I am a teaching instructor for the following courses at Université Paris-Diderot and at ENS Ulm:

With David Gérard-Varet, I share the responsibility of :

Master I de Mathématiques et Applications

Skills

R

90%

Statistics

100%

Python

90%

Concentration theory

100%

Databases

100%

Extreme values

100%

Experience

 
 
 
 
 
September 2004 – Present
Paris

Professor

University Paris-Diderot

Taught statistics, probability, numerical analysis, algorithms and databases.
 
 
 
 
 
November 1990 – August 2004
Orsay, Paris Area

Researcher

CNRS/Université Paris-Sud

Themes include:

  • Statistical Learning
  • Telecommunications
  • Random graphs
  • Information theory
 
 
 
 
 
January 1989 – October 1990
Marcoussis, Paris Area

Engineer

Alcatel-Alsthom

R and D, on OOL, Telecommunications, Multi-Agents systems Responsibilities include:

  • Analysing
  • Modelling
  • Coding