Learning in high-dimensional feature spaces using ANOVA-based fast matrix-vector multiplication

<p style='text-indent:20px;'>Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The matrix is typically dense and large-scale. Depending on the dimension of feature space even computation all its entries reasonable time becomes a challenging task. For cost matrix-vector product scales quadratically with dimensionality <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula>, if no customized methods applied. We propose use an ANOVA kernel, where we construct several kernels based lower-dimensional spaces for which provide fast algorithms realizing products. employ non-equispaced Fourier transform (NFFT), linear complexity fixed accuracy. Based grouping approach, then show how products can be embedded into method choosing regression conjugate gradient solver. illustrate performance our approach data sets.</p>