  One of the main computational bottlenecks when working with kernel based
learning is dealing with the large and typically dense kernel matrix.
Techniques dealing with fast approximations of the matrix vector product for
these kernel matrices typically deteriorate in their performance if the feature
vectors reside in higher-dimensional feature spaces. We here present a
technique based on the non-equispaced fast Fourier transform (NFFT) with
rigorous error analysis. We show that this approach is also well suited to
allow the approximation of the matrix that arises when the kernel is
differentiated with respect to the kernel hyperparameters; a problem often
found in the training phase of methods such as Gaussian processes. We also
provide an error analysis for this case. We illustrate the performance of the
additive kernel scheme with fast matrix vector products on a number of data
sets. Our code is available at https://github.com/wagnertheresa/NFFTAddKer
