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High-Dimensional Probability

High-Dimensional ProbabilityAn Introduction with Applications in Data ScienceRoman VershyninUniversity of California, IrvineJune 9, 2020 ~rvershyn/ContentsPrefaceviAppetizer: using Probability to cover a geometric set11 Preliminaries on random quantities associated with random classical of sums of independent random concentration inequalities? s s : degrees of random Hoeffding s and Khintchine s s vectors in high of the matrices and principal component of High-Dimensional distributions in higher : Grothendieck s inequality and semidefinite : Maximum cut for trick, and tightening of Grothendieck s on , covering numbers and packing : error correcting bounds on random sub-gaussian : community detection in bounds on sub-gaussian : covariance estimation and without of Lipschitz functions on the on other metric measure : Johnson-Lindenstrauss Bernstein s : community detection in sparse : covariance estimation for general forms, symmetrization and of anisotropic random matrices with : matrix concepts and s bounds on Gaussian s minoration dimension, stable rank, and Gaussian projections of s : empirical.

metrization tricks, chaining and comparison techniques for stochastic processes, combinatorial reasoning based on the VC dimension, and a lot more. High-dimensional probability provides vital theoretical tools for applications in data science. This book integrates theory with applications for covariance

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