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- Concentration inequalities. A nonasymptotic theory of independence
- Concentration inequalities : a nonasymptotic theory of independence
- Math - Topics in Probability
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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 high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in an accessible way by covering the key developments and applications in the field. The authors describe the interplay between the probabilistic structure independence and a variety of tools ranging from functional inequalities to transportation arguments to information theory.

## Concentration inequalities. A nonasymptotic theory of independence

Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented. A self-contained introduction to concentration inequalities, it includes 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 whilst special attention is paid to applications to the supremum of empirical processes.

Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.

Flowing text, Original pages. Web, Tablet, Phone, eReader. It syncs automatically with your account and allows you to read online or offline wherever you are.

Please follow the detailed Help center instructions to transfer the files to supported eReaders. Concentration Inequalities and Model Selection: Since the impressive works of Talagrand, concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics.

They also turn out to be essential tools to develop a non-asymptotic theory in statistics, exactly as the central limit theorem and large deviations are known to play a central part in the asymptotic theory.

## Concentration inequalities : a nonasymptotic theory of independence

An overview of a non-asymptotic theory for model selection is given here and some selected applications to variable selection, change points detection and statistical learning are discussed. This volume reflects the content of the course given by P. It is mostly self-contained and accessible to graduate students.

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- CS 281B / Stat 241B, Spring 2014:?

The language has grown in popularity in recent years, both in teaching and in industry. Scroll down for a more detailed list of topics. Contact the instructor, Eric Blais , with any other question.

## Math - Topics in Probability

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### About the author

Variance and concentration Efron-Stein inequality. Entropy method Information theory inequalities. Isoperimetry Isoperimetric inequalities on the hypercube and Gaussian spaces. Influence of variables Inequalities on the influence of variables.

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