Characterizing the Representer Theorem
Yaoliang Yu, Hao Cheng, Dale Schuurmans, Csaba Szepesvári · 2013
The representer theorem assures that ker-nel methods retain optimality under penal-ized empirical risk minimization. While a sufficient condition on the form of the regu-larizer 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. 1.