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Banach-Mazur Distances and Finite-Dimensional Operator Ideals
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The article was published on 1989-05-01 and is currently open access. It has received 593 citations till now. The article focuses on the topics: Strictly singular operator & Finite-rank operator.read more
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Convex bodies : the Brunn-Minkowski theory
TL;DR: Inequalities for mixed volumes 7. Selected applications Appendix as discussed by the authors ] is a survey of mixed volumes with bounding boxes and quermass integrals, as well as a discussion of their applications.
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Rademacher and gaussian complexities: risk bounds and structural results
TL;DR: In this paper, the authors investigate the use of data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities, in a decision theoretic setting and prove general risk bounds in terms of these complexities.
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High-Dimensional Probability: An Introduction with Applications in Data Science
TL;DR: 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.
An Elementary Introduction to Modern Convex Geometry
TL;DR: In this paper, the Brunn-Minkowski inequality and its extensions are discussed and the Reverse Isoperimetric Problem is solved. But the central limit theorem and large deviation inequalities are not considered.
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Functional Analysis and Infinite-Dimensional Geometry
TL;DR: In this article, the basic concepts in Banach spaces are discussed, including weak topologies, uniform convexity, smoothness and structure, and weakly compactly generated spaces.