  Random Fourier features provide a way to tackle large-scale machine learning
problems with kernel methods. Their slow Monte Carlo convergence rate has
motivated the research of deterministic Fourier features whose approximation
error can decrease exponentially in the number of basis functions. However, due
to their tensor product extension to multiple dimensions, these methods suffer
heavily from the curse of dimensionality, limiting their applicability to one,
two or three-dimensional scenarios. In our approach we overcome said curse of
dimensionality by exploiting the tensor product structure of deterministic
Fourier features, which enables us to represent the model parameters as a
low-rank tensor decomposition. We derive a monotonically converging block
coordinate descent algorithm with linear complexity in both the sample size and
the dimensionality of the inputs for a regularized squared loss function,
allowing to learn a parsimonious model in decomposed form using deterministic
Fourier features. We demonstrate by means of numerical experiments how our
low-rank tensor approach obtains the same performance of the corresponding
nonparametric model, consistently outperforming random Fourier features.
