# Fast Evaluation of Additive Kernels: Feature Arrangement, Fourier Methods, and Kernel Derivatives

arXiv: https://arxiv.org/abs/2404.17344 · HTML: https://mlsanity.com/paper/2404.17344/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 88 references that are in the map.
- First posted on arXiv 26 Apr 2024.

## Builds on (most cited first, 7 of 7)

- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [Survey on Feature Selection](https://mlsanity.com/paper/1510.02892/) (2015)
- [Learning in High-Dimensional Feature Spaces Using ANOVA-Based Fast Matrix-Vector Multiplication](https://mlsanity.com/paper/2111.10140/) (2021)
- [A Preconditioned Interior Point Method for Support Vector Machines Using an ANOVA-Decomposition and NFFT-Based Matrix-Vector Products](https://mlsanity.com/paper/2312.00538/) (2023)

## Built on by (most cited first, 1 of 1)

- [Preconditioned Additive Gaussian Processes with Fourier Acceleration](https://mlsanity.com/paper/2504.00480/) (2025)

## Abstract (arXiv)

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel matrices typically deteriorate in their performance if the feature vectors reside in higher-dimensional feature spaces. We here present a technique based on the non-equispaced fast Fourier transform (NFFT) with rigorous error analysis. We show that this approach is also well suited to allow the approximation of the matrix that arises when the kernel is differentiated with respect to the kernel hyperparameters; a problem often found in the training phase of methods such as Gaussian processes. We also provide an error analysis for this case. We illustrate the performance of the additive kernel scheme with fast matrix vector products on a number of data sets. Our code is available at https://github.com/wagnertheresa/NFFTAddKer