High-dimensional probability offers insight into the behavior of
random vectors, random matrices, random subspaces, and objects used
to quantify uncertainty in high dimensions. Drawing on ideas from
probability, analysis, and geometry, it lends itself to
applications in mathematics, statistics, theoretical computer
science, signal processing, optimization, and more. It is the first
to integrate theory, key tools, and modern applications of
high-dimensional probability. Concentration inequalities form the
core, and it covers both classical results such as Hoeffding's and
Chernoff's inequalities and modern developments such as the matrix
Bernstein's inequality. It then introduces the powerful methods
based on stochastic processes, including such tools as Slepian's,
Sudakov's, and Dudley's inequalities, as well as generic chaining
and bounds based on VC dimension. A broad range of illustrations is
embedded throughout, including classical and modern results for
covariance estimation, clustering, networks, semidefinite
programming, coding, dimension reduction, matrix completion,
machine learning, compressed sensing, and sparse regression.
General
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