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Sparse Gaussian Processes with Spherical Harmonic Features

arXiv 2006.16649 ↗First posted 30 Jun 2020stat.ML cs.LGcited by 43

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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.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jun 2020.

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Citing papers per year: 2021: 13; 2022: 6; 2023: 7; 2024: 13; 2025: 2; 2026: 2.

43 papers.

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  1. 2022A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awarenesscited by 49
  2. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  3. 2021Deep Neural Networks as Point Estimates for Deep Gaussian Processescited by 26
  4. 2021SigGPDE: Scaling Sparse Gaussian Processes on Sequential Datacited by 22
  5. 2021Uniform Generalization Bounds for Overparameterized Neural Networkscited by 21
  6. 2022Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learningcited by 20
  7. 2021Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelscited by 19
  8. 2022Additive Gaussian Processes Revisitedcited by 19
  9. 2021Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processescited by 17
  10. 2023Variational Linearized Laplace Approximation for Bayesian Deep Learningcited by 17
  11. 2021Large-Scale Learning with Fourier Features and Tensor Decompositionscited by 14
  12. 2021Sparse Algorithms for Markovian Gaussian Processescited by 10
31 more
  1. 2024The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphscited by 10
  2. 2021Scalable Variational Gaussian Processes via Harmonic Kernel Decompositioncited by 8
  3. 2022Deep Variational Implicit Processescited by 8
  4. 2024Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variatescited by 8
  5. 2024Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inferencecited by 8
  6. 2021Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processescited by 7
  7. 2023Quantized Fourier and Polynomial Features for more Expressive Tensor Network Modelscited by 6
  8. 2022Log-Linear-Time Gaussian Processes Using Binary Tree Kernelscited by 4
  9. 2023Actually Sparse Variational Gaussian Processescited by 4
  10. 2021Variational Gaussian Processes: A Functional Analysis Viewcited by 3
  11. 2023Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processescited by 3
  12. 2024On Uncertainty Quantification for Near-Bayes Optimal Algorithmscited by 3
  13. 2024Early learning of the optimal constant solution in neural networks and humanscited by 3
  14. 2022Self-supervised learning with rotation-invariant kernelscited by 2
  15. 2023Sparse Gaussian Processes with Spherical Harmonic Features Revisitedcited by 2
  16. 2024Multi-layer random features and the approximation power of neural networkscited by 2
  17. 2024Residual Deep Gaussian Processes on Manifoldscited by 2
  18. 2024Fixed-Mean Gaussian Processes for Post-hoc Bayesian Deep Learningcited by 2
  19. 2021Conditional Deep Gaussian Processes: empirical Bayes hyperdata learningcited by 1
  20. 2023Spherical Inducing Features for Orthogonally-Decoupled Gaussian Processescited by 1
  21. 2024Efficient Visibility Approximation for Game AI using Neural Omnidirectional Distance Fieldscited by 1
  22. 2024Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?cited by 1
  23. 2025Repulsive Monte Carlo on the sphere for the sliced Wasserstein distancecited by 1
  24. 2026The Wristband Gaussian Loss: Deterministic, Composable Latents via a Sphere-Interval Decompositioncited by 1
  25. 2021Spectrum Gaussian Processes Based On Tunable Basis Functionscited by 0
  26. 2023Deep Transformed Gaussian Processescited by 0
  27. 2024Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regressioncited by 0
  28. 2024Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matricescited by 0
  29. 2024Review of Recent Advances in Gaussian Process Regression Methodscited by 0
  30. 2025Scalable Deep Basis Kernel Gaussian Processescited by 0
  31. 2026On Basis Function Selection for Sparse Gaussian Process Regressioncited by 0