Approximation properties of certain operator-induced norms on Hilbert spaces |
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Authors: | Arash A Amini Martin J Wainwright |
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Institution: | 1. Department of Statistics, UC Berkeley, Berkeley, CA 94720, United States;2. Department of Electrical Engineering and Computer Sciences, UC Berkeley, Berkeley, CA 94720, United States |
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Abstract: | We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the norm, and study their approximation properties over Hilbert subspaces of . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in a reproducing kernel Hilbert space (RKHS). Our results have implications to the analysis of -estimators in models based on finite-dimensional linear approximation of functions, and also to some related packing problems. |
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