Model Selection in Kernel Methods Based on a Spectral Analysis of Label Information

We propose a novel method for addressing the model selection problem in the context of kernel methods. In contrast to existing methods which rely on hold-out testing or try to compensate for the optimism of the generalization error, our method is based on a structural analysis of the label information using the eigenstructure of the kernel matrix. In this setting, the label vector can be transformed into a representation in which the smooth information is easily discernible from the noise. This permits to estimate a cut-off dimension such that the leading coefficients in that representation contains the learnable information, discarding the noise. Based on this cut-off dimension, the regularization parameter is estimated for kernel ridge regression.