# Preconditioned Additive Gaussian Processes with Fourier Acceleration

arXiv: https://arxiv.org/abs/2504.00480 · HTML: https://mlsanity.com/paper/2504.00480/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Preconditioning for Scalable Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2107.00243/) (2021)
- [Variable Selection Consistency of Gaussian Process Regression](https://mlsanity.com/paper/1912.05738/) (2019)
- [Leveraging Locality and Robustness to Achieve Massively Scalable Gaussian Process Regression](https://mlsanity.com/paper/2306.14731/) (2023)
- [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)
- [Data-Driven Linear Complexity Low-Rank Approximation of General Kernel Matrices: A Geometric Approach](https://mlsanity.com/paper/2212.12674/) (2022)
- [Posterior Covariance Structures in Gaussian Processes](https://mlsanity.com/paper/2408.07379/) (2024)
- [HiGP: A high-performance Python package for Gaussian Process](https://mlsanity.com/paper/2503.02259/) (2025)
- [Fast Evaluation of Additive Kernels: Feature Arrangement, Fourier Methods, and Kernel Derivatives](https://mlsanity.com/paper/2404.17344/) (2024)

## Abstract (arXiv)

Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant computational challenges. This paper introduces a matrix-free method that utilizes the Non-equispaced Fast Fourier Transform (NFFT) to achieve nearly linear complexity in the multiplication of kernel matrices and their derivatives with vectors for a predetermined accuracy level. To address high-dimensional problems, we propose an additive kernel approach. Each sub-kernel in this approach captures lower-order feature interactions, allowing for the efficient application of the NFFT method and potentially increasing accuracy across various real-world datasets. Additionally, we implement a preconditioning strategy that accelerates hyperparameter tuning, further improving the efficiency and effectiveness of GPs.