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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.
Abbas Mehrabian, Holger Rauhut, and Hao Xing who o ered substantial feedback that lead to signi cant improvements. The issues that are found after publication have been corrected in the electronic version. Please feel free to send me any further feedback. Irvine, California June 9, …
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