Fast Summation of Radial Kernels via QMC Slicing

Understand

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.