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Concentration Inequalities - A Nonasymptotic Theory of Independence (Hardcover, New)
Loot Price: R5,148
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Concentration Inequalities - A Nonasymptotic Theory of Independence (Hardcover, New)
Expected to ship within 12 - 17 working days
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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.
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