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剑桥2013,Concentration Inequalities: A Nonasymptotic Theory of Independence pdf

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  • TA的每日心情
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    2016-3-19 06:18
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    [LV.4]偶尔看看III

    发表于 2015-11-19 00:07:06 | 显示全部楼层 |阅读模式
    Concentration Inequalities: A Nonasymptotic Theory of Independence pdf
    by Stephane Boucheron (Author), Gabor Lugosi (Author), Pascal Massart (Author)

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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. 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.

    Review
    The clear exposition from basic material up to recent sophisticated results and lucid writing style make the text a pleasure to read. Beginners as well as experienced scientists will prot equally from it. It will certainly become one of the standard references in the field. Hilmar Mai, Zentralblatt Math
    About the Author

    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.



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  • TA的每日心情
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    2018-11-22 08:46
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    [LV.10]以坛为家III

    发表于 2015-11-21 10:48:44 | 显示全部楼层
    loook it alllll
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  • TA的每日心情
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    2016-8-23 21:54
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    [LV.8]以坛为家I

    发表于 2015-11-21 19:50:24 | 显示全部楼层
    Thanks for sharing

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  • TA的每日心情
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    2016-7-6 23:05
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    [LV.3]偶尔看看II

    发表于 2015-11-27 20:52:02 | 显示全部楼层
    very good, thanks!!
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    发表于 2016-1-28 11:20:48 | 显示全部楼层
    多谢分享,最近读paper就想读读这本书~
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  • TA的每日心情
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    2017-12-15 11:07
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    [LV.7]常住居民III

    发表于 2016-2-13 13:44:41 | 显示全部楼层
    谢谢楼主辛苦分享!!
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  • TA的每日心情
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    2016-10-5 08:03
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    [LV.4]偶尔看看III

    发表于 2016-9-10 08:29:46 | 显示全部楼层
    谢谢                              
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    发表于 2016-10-3 10:39:07 | 显示全部楼层
    Thanks a lot.

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  • TA的每日心情
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    12 小时前
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    [LV.10]以坛为家III

    发表于 2017-2-3 17:44:37 | 显示全部楼层
    感谢楼主辛苦分享!!
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    该用户从未签到

    发表于 2019-4-19 16:18:25 | 显示全部楼层
    Thanks for sharing!
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