Inproceedings,
Characterizing the Representer Theorem
ICML, page 570--578. (June 2013)
Abstract
The representer theorem assures that kernel methods retain optimality
under penalized empirical risk minimization.
While a sufficient condition on the form of the regularizer guaranteeing
the representer theorem has been known since the initial development
of kernel methods, necessary conditions have only been investigated recently.
In this paper we completely characterize the necessary and sufficient
conditions on the regularizer that ensure the representer theorem holds.
The results are surprisingly simple yet broaden the conditions where the
representer theorem is known to hold.
Extension to the matrix domain is also addressed.
