The representer theorem for Hilbert spaces: a necessary and sufficient condition
Functional Analysis
2012-07-18 v3 Machine Learning
Abstract
A family of regularization functionals is said to admit a linear representer theorem if every member of the family admits minimizers that lie in a fixed finite dimensional subspace. A recent characterization states that a general class of regularization functionals with differentiable regularizer admits a linear representer theorem if and only if the regularization term is a non-decreasing function of the norm. In this report, we improve over such result by replacing the differentiability assumption with lower semi-continuity and deriving a proof that is independent of the dimensionality of the space.
Keywords
Cite
@article{arxiv.1205.1928,
title = {The representer theorem for Hilbert spaces: a necessary and sufficient condition},
author = {Francesco Dinuzzo and Bernhard Schölkopf},
journal= {arXiv preprint arXiv:1205.1928},
year = {2012}
}