Sciweavers

CORR
2008
Springer

When is there a representer theorem? Vector versus matrix regularizers

13 years 12 months ago
When is there a representer theorem? Vector versus matrix regularizers
We consider a general class of regularization methods which learn a vector of parameters on the basis of linear measurements. It is well known that if the regularizer is a nondecreasing function of the L2 norm, then the learned vector is a linear combination of the input data. This result, known as the representer theorem, lies at the basis of kernel-based methods in machine learning. In this paper, we prove the necessity of the above condition, in the case of differentiable regularizers. We further extend our analysis to regularization methods which learn a matrix, a problem which is motivated by the application to multi-task learning. In this context, we study a more general representer theorem, which holds for a larger class of regularizers. We provide a necessary and sufficient condition characterizing this class of matrix regularizers and we highlight some concrete examples of practical importance. Our analysis uses basic principles from matrix theory, especially the useful notio...
Andreas Argyriou, Charles A. Micchelli, Massimilia
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Andreas Argyriou, Charles A. Micchelli, Massimiliano Pontil
Comments (0)