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• W2288884963 abstract "Let A be an isotropic, sub-gaussian m × n matrix. We prove that the process $$Z_{x},:=,left |Axright |_{2} -sqrt{m}left |xright |_{2}$$ has sub-gaussian increments, that is, $$|Z_{x} - Z_{y}|_{psi _{2}} leq C|x - y|_{2}$$ for any $$x,y in mathbb{R}^{n}$$ . Using this, we show that for any bounded set $$T subseteq mathbb{R}^{n}$$ , the deviation of ∥ Ax ∥ 2 around its mean is uniformly bounded by the Gaussian complexity of T. We also prove a local version of this theorem, which allows for unbounded sets. These theorems have various applications, some of which are reviewed in this paper. In particular, we give a new result regarding model selection in the constrained linear model." @default.
• W2288884963 created "2016-06-24" @default.
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• W2288884963 date "2017-01-01" @default.
• W2288884963 modified "2023-09-23" @default.
• W2288884963 title "A Simple Tool for Bounding the Deviation of Random Matrices on Geometric Sets" @default.
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• W2288884963 doi "https://doi.org/10.1007/978-3-319-45282-1_18" @default.
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