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Understanding Probabilistic Sparse Gaussian Process Approximations

arXiv 1606.04820 ↗First posted 15 Jun 2016stat.MLcited by 68

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Abstract (arXiv)

Good sparse approximations are essential for practical inference in Gaussian Processes as the computational cost of exact methods is prohibitive for large datasets. The Fully Independent Training Conditional (FITC) and the Variational Free Energy (VFE) approximations are two recent popular methods. Despite superficial similarities, these approximations have surprisingly different theoretical properties and behave differently in practice. We thoroughly investigate the two methods for regression both analytically and through illustrative examples, and draw conclusions to guide practical application.

Key facts. Cited by 68 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Jun 2016.

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Citing papers per year: 2021: 24; 2022: 8; 2023: 8; 2024: 16; 2025: 8; 2026: 4.

68 papers.

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  1. 2021How Powerful are Performance Predictors in Neural Architecture Search?cited by 88
  2. 2021Spatio-Temporal Variational Gaussian Processescited by 32
  3. 2021Meta-Learning Reliable Priors in the Function Spacecited by 23
  4. 2021Conditioning Sparse Variational Gaussian Processes for Online Decision-makingcited by 23
  5. 2022Posterior and Computational Uncertainty in Gaussian Processescited by 23
  6. 2021Tighter Bounds on the Log Marginal Likelihood of Gaussian Process Regression Using Conjugate Gradientscited by 20
  7. 2021Kernel Interpolation for Scalable Online Gaussian Processescited by 18
  8. 2021Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processescited by 17
  9. 2023Learning a Depth Covariance Functioncited by 16
  10. 2021Bias-Free Scalable Gaussian Processes via Randomized Truncationscited by 15
  11. 2023Grokking Beyond Neural Networks: An Empirical Exploration with Model Complexitycited by 13
  12. 2024Surprisingly Strong Performance Prediction with Neural Graph Featurescited by 11
38 more
  1. 2022Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priorscited by 9
  2. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  3. 2021Adaptive Inducing Points Selection For Gaussian Processescited by 8
  4. 2022Variational Nearest Neighbor Gaussian Processcited by 8
  5. 2024Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inferencecited by 8
  6. 2023Free-Form Variational Inference for Gaussian Process State-Space Modelscited by 7
  7. 2021Hierarchical Inducing Point Gaussian Process for Inter-domain Observationscited by 6
  8. 2021Scalable Cross Validation Losses for Gaussian Process Modelscited by 6
  9. 2021Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modellingcited by 6
  10. 2021Bridging the reality gap in quantum devices with physics-aware machine learningcited by 6
  11. 2021Adversarial Robustness Guarantees for Gaussian Processescited by 5
  12. 2021Input Dependent Sparse Gaussian Processescited by 5
  13. 2022Revisiting Active Sets for Gaussian Process Decoderscited by 5
  14. 2023Learning Choice Functions with Gaussian Processescited by 5
  15. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 5
  16. 2021Deep Gaussian Processes for Biogeophysical Parameter Retrieval and Model Inversioncited by 4
  17. 2022Fully Bayesian inference for latent variable Gaussian process modelscited by 4
  18. 2024Multi-fidelity Gaussian process surrogate modeling for regression problems in physicscited by 4
  19. 2025Scalable Gaussian Processes with Latent Kronecker Structurecited by 4
  20. 2021Gaussian Processes with Differential Privacycited by 3
  21. 2021Gaussian Process Inference Using Mini-batch Stochastic Gradient Descent: Convergence Guarantees and Empirical Benefitscited by 3
  22. 2022Memory Safe Computations with XLA Compilercited by 3
  23. 2022Learning Multiscale Non-stationary Causal Structurescited by 3
  24. 2024Latent mixed-effect models for high-dimensional longitudinal datacited by 3
  25. 2021Healing Products of Gaussian Processescited by 2
  26. 2021Uncertainty-aware Remaining Useful Life predictorcited by 2
  27. 2021Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guaranteescited by 2
  28. 2021Training BatchNorm Only in Neural Architecture Search and Beyondcited by 2
  29. 2023Multi-Response Heteroscedastic Gaussian Process Models and Their Inferencecited by 2
  30. 2023Deep evidential fusion with uncertainty quantification and contextual discounting for multimodal medical image segmentationcited by 2
  31. 2024Recommendations for Baselines and Benchmarking Approximate Gaussian Processescited by 2
  32. 2024Noise-Aware Differentially Private Regression via Meta-Learningcited by 2
  33. 2025Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Predictioncited by 2
  34. 2025Sparse Gaussian Neural Processescited by 2
  35. 2023Efficient Sensor Placement from Regression with Sparse Gaussian Processes in Continuous and Discrete Spacescited by 1
  36. 2024Adjusting Model Size in Continual Gaussian Processes: How Big is Big Enough?cited by 1
  37. 2024Amortized Variational Inference for Deep Gaussian Processescited by 1
  38. 2024MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learningcited by 1

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