Approximation properties of certain operator-induced norms on Hilbert spaces
Statistics Theory
2011-06-01 v1 Machine Learning
Statistics Theory
Abstract
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproducing kernel Hilbert spaces (RKHS). Our results have implications to the analysis of M-estimators in models based on finite-dimensional linear approximation of functions, and also to some related packing problems.
Keywords
Cite
@article{arxiv.1105.6351,
title = {Approximation properties of certain operator-induced norms on Hilbert spaces},
author = {Arash A. Amini and Martin J. Wainwright},
journal= {arXiv preprint arXiv:1105.6351},
year = {2011}
}