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Doubly Stochastic Variational Inference for Deep Gaussian Processes

arXiv 1705.08933 ↗First posted 24 May 2017stat.MLcited by 143

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Abstract (arXiv)

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs, but inference in these models has proved challenging. Existing approaches to inference in DGP models assume approximate posteriors that force independence between the layers, and do not work well in practice. We present a doubly stochastic variational inference algorithm, which does not force independence between layers. With our method of inference we demonstrate that a DGP model can be used effectively on data ranging in size from hundreds to a billion points. We provide strong empirical evidence that our inference scheme for DGPs works well in practice in both classification and regression.

Key facts. Cited by 143 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 May 2017.

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Citing papers per year: 2021: 35; 2022: 26; 2023: 27; 2024: 24; 2025: 20; 2026: 11.

143 papers.

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  1. 2021Self-Attention Between Datapoints: Going Beyond Individual Input-Output Pairs in Deep Learningcited by 113
  2. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  3. 2021The Promises and Pitfalls of Deep Kernel Learningcited by 81
  4. 2022A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awarenesscited by 49
  5. 2023Safe Exploration in Reinforcement Learning: A Generalized Formulation and Algorithmscited by 28
  6. 2023Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorialcited by 27
  7. 2021Deep Neural Networks as Point Estimates for Deep Gaussian Processescited by 26
  8. 2021The Limitations of Large Width in Neural Networks: A Deep Gaussian Process Perspectivecited by 21
  9. 2023Calibrating Transformers via Sparse Gaussian Processescited by 21
  10. 2023Variational Linearized Laplace Approximation for Bayesian Deep Learningcited by 18
  11. 2025Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMscited by 17
  12. 2021Sparse Uncertainty Representation in Deep Learning with Inducing Weightscited by 16
38 more
  1. 2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inferencecited by 16
  2. 2021How to Evaluate Uncertainty Estimates in Machine Learning for Regression?cited by 15
  3. 2021A theory of representation learning gives a deep generalisation of kernel methodscited by 15
  4. 2022Statistical Deep Learning for Spatial and Spatio-Temporal Datacited by 15
  5. 2022Multi-fidelity Hierarchical Neural Processescited by 15
  6. 2025Stochastic Process Learning via Operator Flow Matchingcited by 14
  7. 2021GPflux: A Library for Deep Gaussian Processescited by 13
  8. 2021Deep Gaussian Processes: A Surveycited by 13
  9. 2024Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modelingcited by 13
  10. 2021Deep Gaussian Process Emulation using Stochastic Imputationcited by 11
  11. 2021Triangulation candidates for Bayesian optimizationcited by 11
  12. 2023Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlowcited by 11
  13. 2024Stopping Bayesian Optimization with Probabilistic Regret Boundscited by 11
  14. 2021SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processescited by 9
  15. 2023Fully Bayesian Autoencoders with Latent Sparse Gaussian Processescited by 9
  16. 2024Universal Functional Regression with Neural Operator Flowscited by 9
  17. 2021Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulationscited by 8
  18. 2021Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Featurescited by 8
  19. 2021Scalable Variational Gaussian Processes via Harmonic Kernel Decompositioncited by 8
  20. 2022Deep Variational Implicit Processescited by 8
  21. 2023A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processescited by 8
  22. 2023Sparse Variational Student-t Processescited by 8
  23. 2022Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classificationcited by 7
  24. 2022Nonparametric Factor Trajectory Learning for Dynamic Tensor Decompositioncited by 7
  25. 2023Free-Form Variational Inference for Gaussian Process State-Space Modelscited by 7
  26. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  27. 2021A variational approximate posterior for the deep Wishart processcited by 6
  28. 2023Guided Deep Kernel Learningcited by 6
  29. 2023Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processescited by 6
  30. 2023Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processescited by 6
  31. 2024Multi-Fidelity Methods for Optimization: A Surveycited by 6
  32. 2021Input Dependent Sparse Gaussian Processescited by 5
  33. 2021A Sparse Expansion For Deep Gaussian Processescited by 5
  34. 2022Generalised Gaussian Process Latent Variable Models (GPLVM) with Stochastic Variational Inferencecited by 5
  35. 2022Gaussian Processes for Missing Value Imputationcited by 5
  36. 2022Hybrid Transfer in Deep Reinforcement Learning for Ads Allocationcited by 5
  37. 2023Active Learning of Piecewise Gaussian Process Surrogatescited by 5
  38. 2023Towards Flexibility and Interpretability of Gaussian Process State-Space Modelcited by 5

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