Fast Summation of Radial Kernels via QMC Slicing

Johannes Hertrich, Tim Jahn, Michael Quellmalz

Keywords: fast kernel summation, slicing, quasi-Monte Carlo, non-equispaced fast Fourier transforms, random Fourier features

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.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 3626