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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, symmetrizatio

3.3 Examples of high-dimensional distributions50 3.4 Sub-gaussian distributions in higher dimensions56 3.5 Application: Grothendieck’s inequality and semide nite programming60 3.6 Application: Maximum cut for graphs66 3.7 Kernel trick, and tightening of Grothendieck’s inequality70 3.8 Notes74 4 Random matrices 76 4.1 Preliminaries on matrices76

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