Fast Summation of Radial Kernels via QMC Slicing

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.

@article{hertrich2025_2410.01316,
  title={ Fast Summation of Radial Kernels via QMC Slicing },
  author={ Johannes Hertrich and Tim Jahn and Michael Quellmalz },
  journal={arXiv preprint arXiv:2410.01316},
  year={ 2025 }
}