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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-gauss

We begin our study of high-dimensional probability with an elegant argument that showcases the usefulness of probabilistic reasoning in geometry. Recall that a convex combination of points z 1;:::;z m 2Rn is a linear combi-nation with coe cients that are non-negative and sum to 1, i.e. it is a sum of the form Xm i=1 iz i where i 0 and Xm i=1 i ...

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