mlsanityData to 7 Oct 2026

Variational Implicit Processes

arXiv 1806.02390 ↗First posted 6 Jun 2018stat.ML cs.LGcited by 41

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Abstract (arXiv)

We introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions, with examples including data simulators, Bayesian neural networks and non-linear transformations of stochastic processes. A novel and efficient approximate inference algorithm for IPs, namely the variational implicit processes (VIPs), is derived using generalised wake-sleep updates. This method returns simple update equations and allows scalable hyper-parameter learning with stochastic optimization. Experiments show that VIPs return better uncertainty estimates and lower errors over existing inference methods for challenging models such as Bayesian neural networks, and Gaussian processes.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jun 2018.

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Citing papers per year: 2021: 9; 2022: 7; 2023: 9; 2024: 7; 2025: 5; 2026: 4.

41 papers.

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  1. 2021Bayesian Neural Network Priors Revisitedcited by 121
  2. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  3. 2022Do Bayesian Neural Networks Need To Be Fully Stochastic?cited by 63
  4. 2023Tractable Function-Space Variational Inference in Bayesian Neural Networkscited by 41
  5. 2021The Gaussian Neural Processcited by 34
  6. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  7. 2023A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methodscited by 31
  8. 2021Meta-Learning Reliable Priors in the Function Spacecited by 23
  9. 2021The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learningcited by 23
  10. 2022The Neural Process Family: Survey, Applications and Perspectivescited by 23
  11. 2022Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learningcited by 20
  12. 2023Function-Space Regularization in Neural Networks: A Probabilistic Perspectivecited by 20
29 more
  1. 2021Sparse Uncertainty Representation in Deep Learning with Inducing Weightscited by 16
  2. 2024Sparse Inducing Points in Deep Gaussian Processes: Enhancing Modeling with Denoising Diffusion Variational Inferencecited by 16
  3. 2021Function-space Inference with Sparse Implicit Processescited by 13
  4. 2022Deep Variational Implicit Processescited by 8
  5. 2022On the detrimental effect of invariances in the likelihood for variational inferencecited by 8
  6. 2021A variational approximate posterior for the deep Wishart processcited by 6
  7. 2023Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processescited by 6
  8. 2022Energy-Based Models for Functional Data using Path Measure Tiltingcited by 5
  9. 2024Spectral Convolutional Conditional Neural Processescited by 4
  10. 2023Adaptive Conditional Quantile Neural Processescited by 3
  11. 2024Nonparametric Automatic Differentiation Variational Inference with Spline Approximationcited by 3
  12. 2024On Uncertainty Quantification for Near-Bayes Optimal Algorithmscited by 3
  13. 2024Regularized KL-Divergence for Well-Defined Function-Space Variational Inference in Bayesian neural networkscited by 3
  14. 2023Function Space Bayesian Pseudocoreset for Bayesian Neural Networkscited by 2
  15. 2025Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systemscited by 2
  16. 2021Conditional Deep Gaussian Processes: empirical Bayes hyperdata learningcited by 1
  17. 2022Correcting Model Bias with Sparse Implicit Processescited by 1
  18. 2023Variational Elliptical Processescited by 1
  19. 2024R'enyi Neural Processescited by 1
  20. 2024Flexible Bayesian Last Layer Models Using Implicit Priors and Diffusion Posterior Samplingcited by 1
  21. 2025Bayesian Computation in Deep Learningcited by 1
  22. 2025Unlearning in Diffusion models under Data Constraints: A Variational Inference Approachcited by 1
  23. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  24. 2023Function-Space Regularization for Deep Bayesian Classificationcited by 0
  25. 2025Revisiting Unbiased Implicit Variational Inferencecited by 0
  26. 2025Active Learning for Manifold Gaussian Process Regressioncited by 0
  27. 2026Function-Space Empirical Bayes Regularisation with Large Vision-Language Model Priorscited by 0
  28. 2026Function-Space Empirical Bayes Regularisation with Student's t Priorscited by 0
  29. 2026Flow-Transformed Implicit Processes for Function-Space Variational Inferencecited by 0