Error bounds for learning the kernel
Charles Micchelli, Massimiliano Pontil, Qiang WU and Ding-Xuan Zhou
The problem of learning the kernel function has recently received considerable attention in
machine learning. Much of the work so far has focused on kernel selection criteria, particularly on minimizing a
regularized error functional over a prescribed set of kernels.
Empirical studies indicate that this approach can enhance statistical performance and is computationally feasible. In this paper, we present a theoretical analysis of its generalization error.
We establish for a wide variety of classes of kernels, such
as the set of all multivariate Gaussian kernels, that this
learning method generalizes well and, when the regularization
parameter is appropriately chosen, it is consistent. A central
role in our analysis is played by the interaction between the
sample error and the approximation error. }