# Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition

arXiv: https://arxiv.org/abs/2106.05992 · HTML: https://mlsanity.com/paper/2106.05992/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 25 of 25)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Rates of Convergence for Sparse Variational Gaussian Process Regression](https://mlsanity.com/paper/1903.03571/) (2019)
- [Learning Invariances using the Marginal Likelihood](https://mlsanity.com/paper/1808.05563/) (2018)
- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [Sparse Gaussian Processes with Spherical Harmonic Features](https://mlsanity.com/paper/2006.16649/) (2020)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition](https://mlsanity.com/paper/1710.07324/) (2017)
- [Thoughts on Massively Scalable Gaussian Processes](https://mlsanity.com/paper/1511.01870/) (2015)
- [Gaussian Quadrature for Kernel Features](https://mlsanity.com/paper/1709.02605/) (2017)
- [Variational Inference for Gaussian Process Models with Linear Complexity](https://mlsanity.com/paper/1711.10127/) (2017)
- [Deep convolutional Gaussian processes](https://mlsanity.com/paper/1810.03052/) (2018)
- [Orthogonally Decoupled Variational Gaussian Processes](https://mlsanity.com/paper/1809.08820/) (2018)
- [Generalized Spectral Kernels](https://mlsanity.com/paper/1506.02236/) (2015)
- [Function-Space Distributions over Kernels](https://mlsanity.com/paper/1910.13565/) (2019)
- [Scalable Gaussian Processes with Grid-Structured Eigenfunctions (GP-GRIEF)](https://mlsanity.com/paper/1807.02125/) (2018)
- [Variational Orthogonal Features](https://mlsanity.com/paper/2006.13170/) (2020)

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

- [Calibrating Transformers via Sparse Gaussian Processes](https://mlsanity.com/paper/2303.02444/) (2023)
- [Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inference](https://mlsanity.com/paper/2407.17033/) (2024)
- [When are Iterative Gaussian Processes Reliably Accurate?](https://mlsanity.com/paper/2112.15246/) (2021)
- [Tighter sparse variational Gaussian processes](https://mlsanity.com/paper/2502.04750/) (2025)
- [Nonnegative spatial factorization](https://mlsanity.com/paper/2110.06122/) (2021)
- [Sparse Gaussian Processes with Spherical Harmonic Features Revisited](https://mlsanity.com/paper/2303.15948/) (2023)
- [New Bounds for Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2502.08730/) (2025)
- [Spherical Inducing Features for Orthogonally-Decoupled Gaussian Processes](https://mlsanity.com/paper/2304.14034/) (2023)

## Abstract (arXiv)

We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to decompose a kernel as a sum of orthogonal kernels. Our variational approximation exploits this orthogonality to enable a large number of inducing points at a low computational cost. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections, and it significantly outperforms standard variational methods in scalability and accuracy. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.