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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.

probability, and it illustrates it with only a sample of data science applications. Each chapter in this book is concluded with a Notes section, which has pointers to other texts on the matter.

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