mlsanityData to 7 Oct 2026

Marginalising over Stationary Kernels with Bayesian Quadrature

arXiv 2106.07452 ↗First posted 14 Jun 2021stat.ML cs.LGcited by 4

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Abstract (arXiv)

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive for larger datasets. We propose a Bayesian Quadrature scheme to make this marginalisation more efficient and thereby more practical. Through use of the maximum mean discrepancies between distributions, we define a kernel over kernels that captures invariances between Spectral Mixture (SM) Kernels. Kernel samples are selected by generalising an information-theoretic acquisition function for warped Bayesian Quadrature. We show that our framework achieves more accurate predictions with better calibrated uncertainty than state-of-the-art baselines, especially when given limited (wall-clock) time budgets.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 26 of its 56 references that are in the map. First posted on arXiv 14 Jun 2021.

Builds on

26 of 56 references.

References · 26

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2018Computational Optimal Transportcited by 765
  3. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
  4. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  5. 2013Gaussian Process Kernels for Pattern Discovery and Extrapolationcited by 131
  6. 2013Structure Discovery in Nonparametric Regression through Compositional Kernel Searchcited by 86
  7. 2016Variational Fourier features for Gaussian processescited by 85
  8. 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
  9. 2017Non-Stationary Spectral Kernelscited by 38
  10. 2016Preconditioning Kernel Matricescited by 32
  11. 2014Sampling for Inference in Probabilistic Models with Fast Bayesian Quadraturecited by 31
  12. 2014Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernelscited by 30
14 more
  1. 2017Fast Information-theoretic Bayesian Optimisationcited by 19
  2. 2015Generalized Spectral Kernelscited by 17
  3. 2019Active Multi-Information Source Bayesian Quadraturecited by 17
  4. 2019Function-Space Distributions over Kernelscited by 17
  5. 2018Bayesian Quadrature for Multiple Related Integralscited by 15
  6. 2017A Gaussian Process Regression Model for Distribution Inputscited by 12
  7. 2018Improving Quadrature for Constrained Integrandscited by 12
  8. 2015Improving the Gaussian Process Sparse Spectrum Approximation by Representing Uncertainty in Frequency Inputscited by 11
  9. 2015Bayesian Nonparametric Kernel-Learningcited by 10
  10. 2018Scalable L'evy Process Priors for Spectral Kernel Learningcited by 7
  11. 2018Bayesian Nonparametric Spectral Estimationcited by 6
  12. 2019Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regressioncited by 6
  13. 2019Automated Model Selection with Bayesian Quadraturecited by 5
  14. 2017Integral Transforms from Finite Data: An Application of Gaussian Process Regression to Fourier Analysiscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 0; 2024: 1; 2025: 0; 2026: 1.

4 papers.

  1. 2022Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombinationcited by 20
  2. 2022Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measurescited by 7
  3. 2026Bayesian Quadraturecited by 1
  4. 2024Stein Random Feature Regressioncited by 0