mlsanityData to 7 Oct 2026

Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning

arXiv 2205.06342 ↗First posted 12 May 2022stat.ML cs.LG stat.COcited by 20

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Abstract (arXiv)

We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian measures on the Hilbert space of square-integrable functions in order to determine a variational posterior using a tractable optimisation criterion and avoids pathologies arising in standard variational function space inference. An exciting application of GWI is the ability to use deep neural networks in the variational parametrisation of GWI, combining their superior predictive performance with the principled uncertainty quantification analogous to that of Gaussian processes. The proposed method obtains state-of-the-art performance on several benchmark datasets.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 38 of its 77 references that are in the map. First posted on arXiv 12 May 2022.

Builds on

38 of 77 references.

References · 38

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26 more
  1. 2018Statistical Aspects of Wasserstein Distancescited by 202
  2. 2019Practical Deep Learning with Bayesian Principlescited by 158
  3. 2018Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adamcited by 131
  4. 2019Functional Variational Bayesian Neural Networkscited by 127
  5. 2021Bayesian Neural Network Priors Revisitedcited by 121
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  7. 2021Repulsive Deep Ensembles are Bayesiancited by 103
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Citing papers per year: 2022: 1; 2023: 5; 2024: 6; 2025: 4; 2026: 4.

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  1. 2023Functional Flow Matchingcited by 63
  2. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  3. 2023A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methodscited by 31
  4. 2023Variational Autoencoding Neural Operatorscited by 22
  5. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  6. 2024FSP-Laplace: Function-Space Priors for the Laplace Approximation in Bayesian Deep Learningcited by 11
  7. 2024On Divergence Measures for Training GFlowNetscited by 6
  8. 2024Spectral Convolutional Conditional Neural Processescited by 4
  9. 2024Regularized KL-Divergence for Well-Defined Function-Space Variational Inference in Bayesian neural networkscited by 3
  10. 2024Functional Stochastic Gradient MCMC for Bayesian Neural Networkscited by 2
  11. 2024Revisiting the Equivalence of Bayesian Neural Networks and Gaussian Processes: On the Importance of Learning Activationscited by 2
  12. 2025Unlearning in Diffusion models under Data Constraints: A Variational Inference Approachcited by 1
8 more
  1. 2026Laplace Approximation for Bayesian Tensor Network Kernel Machinescited by 1
  2. 2023On the meaning of uncertainty for ethical AI: philosophy and practicecited by 0
  3. 2025Variational Deep Learning via Implicit Regularizationcited by 0
  4. 2025PEdger++: Practical Edge Detection via Assembling Cross Informationcited by 0
  5. 2025Monte Carlo Functional Regularisation for Continual Learningcited by 0
  6. 2026Generalising maximum mean discrepancy: kernelised functional Bregman divergencescited by 0
  7. 2026Flow-Transformed Implicit Processes for Function-Space Variational Inferencecited by 0
  8. 2026PAPA: Online Personalized Active Preference Alignmentcited by 0