mlsanityData to 7 Oct 2026

MCMC for Variationally Sparse Gaussian Processes

arXiv 1506.04000 ↗First posted 12 Jun 2015stat.MLcited by 44

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Abstract (arXiv)

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate covariance function parameter posteriors. This paper simultaneously addresses these, using a variational approximation to the posterior which is sparse in support of the function but otherwise free-form. The result is a Hybrid Monte-Carlo sampling scheme which allows for a non-Gaussian approximation over the function values and covariance parameters simultaneously, with efficient computations based on inducing-point sparse GPs. Code to replicate each experiment in this paper will be available shortly.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Jun 2015.

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Citing papers per year: 2021: 11; 2022: 10; 2023: 6; 2024: 5; 2025: 8; 2026: 4.

44 papers.

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  1. 2021The Promises and Pitfalls of Deep Kernel Learningcited by 81
  2. 2021Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processescited by 17
  3. 2021Variational multiple shooting for Bayesian ODEs with Gaussian processescited by 15
  4. 2022Safe Active Learning for Multi-Output Gaussian Processescited by 13
  5. 2021SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processescited by 9
  6. 2022Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priorscited by 9
  7. 2023Fully Bayesian Autoencoders with Latent Sparse Gaussian Processescited by 9
  8. 2024Improving sample efficiency of high dimensional Bayesian optimization with MCMCcited by 9
  9. 2022Variational Nearest Neighbor Gaussian Processcited by 8
  10. 2021Fast and Scalable Spike and Slab Variable Selection in High-Dimensional Gaussian Processescited by 7
  11. 2023Free-Form Variational Inference for Gaussian Process State-Space Modelscited by 7
  12. 2021Hierarchical Inducing Point Gaussian Process for Inter-domain Observationscited by 6
32 more
  1. 2022Semi-Parametric Inducing Point Networks and Neural Processescited by 6
  2. 2023Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processescited by 6
  3. 2025Koopman-Equivariant Gaussian Processescited by 6
  4. 2021Input Dependent Sparse Gaussian Processescited by 5
  5. 2022Gaussian Processes for Missing Value Imputationcited by 5
  6. 2022Sparse Gaussian Process Hyperparameters: Optimize or Integrate?cited by 4
  7. 2023Actually Sparse Variational Gaussian Processescited by 4
  8. 2024Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equationscited by 4
  9. 2021Calibrated simplex-mapping classificationcited by 3
  10. 2025Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modellingcited by 3
  11. 2025Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecastingcited by 3
  12. 2023Gradient and Uncertainty Enhanced Sequential Sampling for Global Fitcited by 2
  13. 2025Recurrent Memory for Online Interdomain Gaussian Processescited by 2
  14. 2021On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approachcited by 1
  15. 2021Nonlinear Hawkes Process with Gaussian Process Self Effectscited by 1
  16. 2021Geometry-Aware Hierarchical Bayesian Learning on Manifoldscited by 1
  17. 2022Modelling calibration uncertainty in networks of environmental sensorscited by 1
  18. 2022Learning Physics between Digital Twins with Low-Fidelity Models and Physics-Informed Gaussian Processescited by 1
  19. 2023Spherical Inducing Features for Orthogonally-Decoupled Gaussian Processescited by 1
  20. 2024Hyperbolic Secant representation of the logistic function: Application to probabilistic Multiple Instance Learning for CT intracranial hemorrhage detectioncited by 1
  21. 2025Flow-Induced Diagonal Gaussian Processescited by 1
  22. 2026Safe Reinforcement Learning via Recovery-based Shielding with Gaussian Process Dynamics Modelscited by 1
  23. 2022A Bayesian Approach To Graph Partitioningcited by 0
  24. 2022Virgo: Scalable Unsupervised Classification of Cosmological Shock Wavescited by 0
  25. 2024Active Learning of Molecular Data for Task-Specific Objectivescited by 0
  26. 2024Gearing Gaussian process modeling and sequential design towards stochastic simulatorscited by 0
  27. 2025Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functionscited by 0
  28. 2025Surrogate Graph Partitioning for Spatial Predictioncited by 0
  29. 2025Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process modelscited by 0
  30. 2026Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classificationcited by 0
  31. 2026Inverse-Free Sparse Variational Gaussian Processescited by 0
  32. 2026Sequential sparse Gaussian process quantile regressioncited by 0