We consider the problem of improving kernel approximation via feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. We propose to use more efficient numerical integration technique to obtain better estimates of the integrals compared to the state-of-the-art methods. Our approach allows to use information about the integrand to enhance approximation and facilitates fast computations. We derive the convergence behavior and conduct an extensive empirical study that supports our hypothesis.
Quadrature rules for kernel approximation. The paper proposes improving the kernel approximation of random features by using quadrature rules like stochastic spherical-radial rules. The authors propose a novel version of the random feature map approach to approximately solve large-scale kernel problems. This paper shows that techniques due to Genz & Monahan (1998) can be used to achieve low kernel approximation error under the framework of random fourier feature, a new way to apply quadrature rules to improve kernel approximation.