000			a
999			_c32209 _d32209
008			230921b xxu||||| |||| 00| 0 eng d
020			_a9781108415194
082			_a519.2 _bVER
100			_aVershynin, Roman
245			_aHigh-dimensional probability : an introduction with applications in data science
260			_bCambridge University Press, _c2018 _aCambridge :
300			_axiv, 284 p. ; _bill., _c27 cm
365			_b54.99 _cGBP _d109.80
490			_aCambridge series in statistical and probabilistic mathematics ; _v47
504			_aIncludes bibliographical references and index.
520			_aHigh-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.
650			_aProbabilities
650			_aRandom variables
650			_aStochastic Processes
942			_2ddc _cBK