# Spatial Mapping with Gaussian Processes and Nonstationary Fourier Features

arXiv: https://arxiv.org/abs/1711.05615 · HTML: https://mlsanity.com/paper/1711.05615/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2017.

## Built on by (most cited first, 16 of 16)

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- [Gauss-Legendre Features for Gaussian Process Regression](https://mlsanity.com/paper/2101.01137/) (2021)
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- [Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees](https://mlsanity.com/paper/2210.07893/) (2022)
- [Trigonometric Quadrature Fourier Features for Scalable Gaussian Process Regression](https://mlsanity.com/paper/2310.14544/) (2023)
- [Nonstationary Sparse Spectral Permanental Process](https://mlsanity.com/paper/2410.03581/) (2024)
- [Recurrent Memory for Online Interdomain Gaussian Processes](https://mlsanity.com/paper/2502.08736/) (2025)
- [Fast and Scalable Adversarial Training of Kernel SVM via Doubly Stochastic Gradients](https://mlsanity.com/paper/2107.09937/) (2021)
- [Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Prior](https://mlsanity.com/paper/2409.03149/) (2024)
- [Multi-View Oriented GPLVM: Expressiveness and Efficiency](https://mlsanity.com/paper/2502.08253/) (2025)
- [A Guide to Bayesian Optimization in Bioprocess Engineering](https://mlsanity.com/paper/2508.10642/) (2025)
- [Stein Random Feature Regression](https://mlsanity.com/paper/2406.00438/) (2024)
- [Scalable Deep Basis Kernel Gaussian Processes](https://mlsanity.com/paper/2505.18526/) (2025)
- [Regular Fourier Features for Nonstationary Gaussian Processes](https://mlsanity.com/paper/2602.23006/) (2026)
- [Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization](https://mlsanity.com/paper/2606.11255/) (2026)
- [Covariance-Boosted Gaussian Processes for Spatiotemporal Irregularities](https://mlsanity.com/paper/2607.23018/) (2026)

## Abstract (arXiv)

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order interactions. However, until recently, there has been a strong reliance on a limited class of stationary kernels such as the Matern or squared exponential, limiting the expressiveness of these modelling approaches. Recent machine learning research has focused on spectral representations to model arbitrary stationary kernels and introduced more general representations that include classes of nonstationary kernels. In this paper, we exploit the connections between Fourier feature representations, Gaussian processes and neural networks to generalise previous approaches and develop a simple and efficient framework to learn arbitrarily complex nonstationary kernel functions directly from the data, while taking care to avoid overfitting using state-of-the-art methods from deep learning. We highlight the very broad array of kernel classes that could be created within this framework. We apply this to a time series dataset and a remote sensing problem involving land surface temperature in Eastern Africa. We show that without increasing the computational or storage complexity, nonstationary kernels can be used to improve generalisation performance and provide more interpretable results.