Fast Summation of Radial Kernels via QMC Slicing
Numerical Analysis
2025-02-25 v2 Machine Learning
Numerical Analysis
Computation
Machine Learning
Abstract
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.
Cite
@article{arxiv.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}
}
Comments
Published as a conference paper at ICLR 2025