Numerical Methods for Kernel Slicing

Abstract

Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear complexity, provided that the kernel can be sliced and its Fourier coefficients are known. To obtain these coefficients, we view the slicing relation as an inverse problem and present two algorithms for their recovery. Extensive numerical experiments demonstrate the speed and accuracy of our methods.