mlsanityData to 7 Oct 2026

Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming

arXiv 2004.11408 ↗First posted 23 Apr 2020stat.CO stat.MEcited by 28

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Abstract (arXiv)

Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially when estimated with fully Bayesian methods such as Markov chain Monte Carlo. In this paper, we focus on a low-rank approximate Bayesian Gaussian processes, based on a basis function approximation via Laplace eigenfunctions for stationary covariance functions. The main contribution of this paper is a detailed analysis of the performance, and practical recommendations for how to select the number of basis functions and the boundary factor. Intuitive visualizations and recommendations, make it easier for users to improve approximation accuracy and computational performance. We also propose diagnostics for checking that the number of basis functions and the boundary factor are adequate given the data. The approach is simple and exhibits an attractive computational complexity due to its linear structure, and it is easy to implement in probabilistic programming frameworks. Several illustrative examples of the performance and applicability of the method in the probabilistic programming language Stan are presented together with the underlying Stan model code.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Apr 2020.

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Citing papers per year: 2021: 5; 2022: 1; 2023: 2; 2024: 7; 2025: 5; 2026: 8.

28 papers.

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  1. 2021Pathfinder: Parallel quasi-Newton variational inferencecited by 26
  2. 2021No-Regret Algorithms for Time-Varying Bayesian Optimizationcited by 19
  3. 2023Random Exploration in Bayesian Optimization: Order-Optimal Regret and Computational Efficiencycited by 16
  4. 2025Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimizationcited by 13
  5. 2024The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphscited by 10
  6. 2024Epsilon-Greedy Thompson Sampling to Bayesian Optimizationcited by 8
  7. 2021Efficient Exploration in Binary and Preferential Bayesian Optimizationcited by 5
  8. 2022A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of termscited by 5
  9. 2024Dynamic Online Ensembles of Basis Expansionscited by 5
  10. 2024Quantum-Assisted Hilbert-Space Gaussian Process Regressioncited by 4
  11. 2025Differentially Private Kernelized Contextual Banditscited by 3
  12. 2025Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimizationcited by 3
16 more
  1. 2021Contextual Bayesian optimization with binary outputscited by 1
  2. 2024Explainable Learning with Gaussian Processescited by 1
  3. 2025Bayesian Inference and Learning in Nonlinear Dynamical Systems: A Framework for Incorporating Explicit and Implicit Prior Knowledgecited by 1
  4. 2025Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processescited by 1
  5. 2026Nearly-Optimal Algorithm for Adversarial Kernelized Banditscited by 1
  6. 2021Scalable mixed-domain Gaussian process modeling and model reduction for longitudinal datacited by 0
  7. 2023Push: Concurrent Probabilistic Programming for Bayesian Deep Learningcited by 0
  8. 2024Towards Multilevel Modelling of Train Passing Events on the Staffordshire Bridgecited by 0
  9. 2024Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matricescited by 0
  10. 2026Pareto-Optimal Anytime Algorithms via Bayesian Racingcited by 0
  11. 2026Time-adaptive infinite-dimensional Gaussian process regression on manifoldscited by 0
  12. 2026Fast and Provably Accurate Sequential Designs using Hilbert Space Gaussian Processescited by 0
  13. 2026Differentiable latent structure discovery for interpretable forecasting in clinical time seriescited by 0
  14. 2026Sharper Guarantees for Misspecified Kernelized Bandit Optimizationcited by 0
  15. 2026Modeling Temporal scRNA-seq Data with Latent Gaussian Process and Optimal Transportcited by 0
  16. 2026On Basis Function Selection for Sparse Gaussian Process Regressioncited by 0