# Sparse Gaussian Processes with Spherical Harmonic Features

arXiv: https://arxiv.org/abs/2006.16649 · HTML: https://mlsanity.com/paper/2006.16649/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2020.

## Built on by (most cited first, 30 of 43)

- [A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness](https://mlsanity.com/paper/2205.00403/) (2022)
- [Universal Approximation Theorems for Differentiable Geometric Deep Learning](https://mlsanity.com/paper/2101.05390/) (2021)
- [Deep Neural Networks as Point Estimates for Deep Gaussian Processes](https://mlsanity.com/paper/2105.04504/) (2021)
- [SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data](https://mlsanity.com/paper/2105.04211/) (2021)
- [Uniform Generalization Bounds for Overparameterized Neural Networks](https://mlsanity.com/paper/2109.06099/) (2021)
- [Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning](https://mlsanity.com/paper/2205.06342/) (2022)
- [Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels](https://mlsanity.com/paper/2110.14423/) (2021)
- [Additive Gaussian Processes Revisited](https://mlsanity.com/paper/2206.09861/) (2022)
- [Variational Linearized Laplace Approximation for Bayesian Deep Learning](https://mlsanity.com/paper/2302.12565/) (2023)
- [Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2106.01121/) (2021)
- [Large-Scale Learning with Fourier Features and Tensor Decompositions](https://mlsanity.com/paper/2109.01545/) (2021)
- [The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphs](https://mlsanity.com/paper/2407.08086/) (2024)
- [Sparse Algorithms for Markovian Gaussian Processes](https://mlsanity.com/paper/2103.10710/) (2021)
- [Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference](https://mlsanity.com/paper/2411.01036/) (2024)
- [Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition](https://mlsanity.com/paper/2106.05992/) (2021)
- [Deep Variational Implicit Processes](https://mlsanity.com/paper/2206.06720/) (2022)
- [Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variates](https://mlsanity.com/paper/2402.01493/) (2024)
- [Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes](https://mlsanity.com/paper/2106.10210/) (2021)
- [Quantized Fourier and Polynomial Features for more Expressive Tensor Network Models](https://mlsanity.com/paper/2309.05436/) (2023)
- [Log-Linear-Time Gaussian Processes Using Binary Tree Kernels](https://mlsanity.com/paper/2210.01633/) (2022)
- [Actually Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2304.05091/) (2023)
- [Variational Gaussian Processes: A Functional Analysis View](https://mlsanity.com/paper/2110.12798/) (2021)
- [Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes](https://mlsanity.com/paper/2308.14142/) (2023)
- [On Uncertainty Quantification for Near-Bayes Optimal Algorithms](https://mlsanity.com/paper/2403.19381/) (2024)
- [Early learning of the optimal constant solution in neural networks and humans](https://mlsanity.com/paper/2406.17467/) (2024)
- [Self-supervised learning with rotation-invariant kernels](https://mlsanity.com/paper/2208.00789/) (2022)
- [Sparse Gaussian Processes with Spherical Harmonic Features Revisited](https://mlsanity.com/paper/2303.15948/) (2023)
- [Multi-layer random features and the approximation power of neural networks](https://mlsanity.com/paper/2404.17461/) (2024)
- [Residual Deep Gaussian Processes on Manifolds](https://mlsanity.com/paper/2411.00161/) (2024)
- [Fixed-Mean Gaussian Processes for Post-hoc Bayesian Deep Learning](https://mlsanity.com/paper/2412.04177/) (2024)

## Abstract (arXiv)

We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier features, but it does not suffer from the curse of dimensionality, and leads to diagonal covariance matrices between inducing variables. This enables a speed-up in inference, because it bypasses the need to invert large covariance matrices. Our experiments show that our model is able to fit a regression model for a dataset with 6 million entries two orders of magnitude faster compared to standard sparse GPs, while retaining state of the art accuracy. We also demonstrate competitive performance on classification with non-conjugate likelihoods.