# Harmonizable mixture kernels with variational Fourier features

arXiv: https://arxiv.org/abs/1810.04416 · HTML: https://mlsanity.com/paper/1810.04416/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2018.

## Built on by (most cited first, 8 of 8)

- [On Learning the Transformer Kernel](https://mlsanity.com/paper/2110.08323/) (2021)
- [Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures](https://mlsanity.com/paper/2202.09233/) (2022)
- [Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey](https://mlsanity.com/paper/2103.10134/) (2021)
- [Shallow and Deep Nonparametric Convolutions for Gaussian Processes](https://mlsanity.com/paper/2206.08972/) (2022)
- [Adaptive RKHS Fourier Features for Compositional Gaussian Process Models](https://mlsanity.com/paper/2407.01856/) (2024)
- [Stein Random Feature Regression](https://mlsanity.com/paper/2406.00438/) (2024)
- [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)

## Abstract (arXiv)

The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatment of non-stationary kernels, HMK supports harmonizable covariances, a wide subset of kernels including all stationary and many non-stationary covariances. We also propose variational Fourier features, an inter-domain sparse GP inference framework that offers a representative set of 'inducing frequencies'. We show that harmonizable mixture kernels interpolate between local patterns, and that variational Fourier features offers a robust kernel learning framework for the new kernel family.