Fast Summation of Radial Kernels via QMC Slicing
Johannes Hertrich Tim Jahn Michael Quellmalz
The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing,  which relies on random projections to one-dimensional subspaces and fast Fourier summation. We prove bounds for the slicing error and propose a quasi-Monte Carlo (QMC) approach for selecting the projections based on spherical quadrature rules. Numerical examples demonstrate that our QMC-slicing approach significantly outperforms existing methods like (QMC-)random Fourier features, orthogonal Fourier features or non-QMC slicing  on standard test datasets.
fast kernel summation, slicing, quasi-Monte Carlo, non-equispaced fast Fourier transforms, random Fourier features