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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.

and Hilbert spaces and linear operators. Knowledge of measure theory is not essential but would be helpful. A word on exercises Exercises are integrated into the text. The reader can do them immediately to check his or her understanding of the material just presented, and to prepare better for later developments.

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