  We investigate iterated compositions of weighted sums of Gaussian kernels and
provide an interpretation of the construction that shows some similarities with
the architectures of deep neural networks. On the theoretical side, we show
that these kernels are universal and that SVMs using these kernels are
universally consistent. We further describe a parameter optimization method for
the kernel parameters and empirically compare this method to SVMs, random
forests, a multiple kernel learning approach, and to some deep neural networks.
