High-Dimensional Probability

High-dimensional probability offers insight into the behavior of random vectors random matrices random subspaces and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability analysis and geometry it lends itself to applications in mathematics statistics theoretical computer science signal processing optimization and more. It is the first to integrate theory key tools and modern applications of high-dimensional probability. Concentration inequalities form the core and it covers both classical results such as Hoeffding''s and Chernoff''s inequalities and modern developments such as the matrix Bernstein''s inequality. It then introduces the powerful methods based on stochastic processes including such tools as Slepian''s Sudakov''s and Dudley''s inequalities as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout including classical and modern results for covariance estimation clustering networks semidefinite programming coding dimension reduction matrix completion machine learning compressed sensing and sparse regression.