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Concentration Inequalities : A Nonasymptotic Theory of Independence

ISBN: 9780199535255 | 0199535256
Format: Hardcover
Publisher: Oxford University Press, USA
Pub. Date: 3/22/2013

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SummaryTable of Contents
Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with highprobability, it is close to its expected value. This book offers a host o... MORE

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 proc... MORE


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