Analyses on empirical error minimization in multiple kernel regressors

Theoretical validity of empirical error minimization in multiple kernel regressors is discussed in this paper. Generalization error of a kernel machine is usually evaluated by the induced norm of the difference between an unknown true function and an estimated one in an appropriate reproducing kernel Hilbert space. It is well known that empirical error minimization also achieves the minimum generalization error in single kernel regressors. However, it is not clarified whether or not that is true for multiple kernel regressors. Moreover, possibility of constructing the minimizer of the generalization error by a given training date set is not also clarified. In this paper, we give negative conclusions for these problems through theoretical analyses on the generalization error of multiple kernel regressors and also give an example by popular Gaussian kernels.