Quadrature-based features for kernel approximation

Marina Munkhoeva, Yermek Kapushev, Evgeny Burnaev, Ivan Oseledets

Abstract: 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.

TL;DR: Quadrature rules for kernel approximation.

Keywords: kernel methods, low-rank approximation, quadrature rules, random features

Code: [ maremun/quffka](https://github.com/maremun/quffka) + [ 1 community implementation](https://paperswithcode.com/paper/?openreview=H1U_af-0-)

Data: [CIFAR-100](https://paperswithcode.com/dataset/cifar-100)

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:1802.03832/code)