Tractable Function-Space Variational Inference in Bayesian Neural Networks
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Abstract (arXiv)
Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a prior distribution over the network parameters, infer an approximate posterior distribution, and use it to make stochastic predictions. However, explicit inference over neural network parameters makes it difficult to incorporate meaningful prior information about the data-generating process into the model. In this paper, we pursue an alternative approach. Recognizing that the primary object of interest in most settings is the distribution over functions induced by the posterior distribution over neural network parameters, we frame Bayesian inference in neural networks explicitly as inferring a posterior distribution over functions and propose a scalable function-space variational inference method that allows incorporating prior information and results in reliable predictive uncertainty estimates. We show that the proposed method leads to state-of-the-art uncertainty estimation and predictive performance on a range of prediction tasks and demonstrate that it performs well on a challenging safety-critical medical diagnosis task in which reliable uncertainty estimation is essential.
Key facts. Cited by 41 papers in the map (data through 14 Oct 2026). Builds on 26 of its 62 references that are in the map. First posted on arXiv 28 Dec 2023.
Builds on
26 of 62 references.
References · 26
- 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
- 2013Playing Atari with Deep Reinforcement Learningcited by 3,274
- 2016Concrete Problems in AI Safetycited by 1,642
- 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,287
- 2019A Simple Baseline for Bayesian Uncertainty in Deep Learningcited by 560
- 2015Weight Uncertainty in Neural Networkscited by 554
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- 2019Practical Deep Learning with Bayesian Principlescited by 158
- 2019Functional Variational Bayesian Neural Networkscited by 127
- 2019Functional Regularisation for Continual Learning with Gaussian Processescited by 123
- 2020Continual Deep Learning by Functional Regularisation of Memorable Pastcited by 105
- 2018Measuring and regularizing networks in function spacecited by 99
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- 2019A Systematic Comparison of Bayesian Deep Learning Robustness in Diabetic Retinopathy Taskscited by 62
- 2015On Sparse variational methods and the Kullback-Leibler divergence between stochastic processescited by 57
- 2022Benchmarking Bayesian Deep Learning on Diabetic Retinopathy Detection Taskscited by 49
- 2020Global inducing point variational posteriors for Bayesian neural networks and deep Gaussian processescited by 43
- 2018Variational Implicit Processescited by 41
- 2019Function Space Particle Optimization for Bayesian Neural Networkscited by 41
- 2020Understanding Variational Inference in Function-Spacecited by 40
- 2019Radial Bayesian Neural Networks: Beyond Discrete Support In Large-Scale Bayesian Deep Learningcited by 37
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- 2020Improving predictions of Bayesian neural nets via local linearizationcited by 7
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Citing papers per year: 2024: 18; 2025: 11; 2026: 12.
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- 2026Possibilistic Predictive Uncertainty for Deep Learning1 May 2026
- 2026Data-Driven Priors for Uncertainty-Aware Risk Prediction of Clinical Deterioration using Multimodal Data9 Mar 2026
- 2026Function-Space Empirical Bayes Regularisation with Student's t Priors25 Feb 2026
- 2026On the Equivalence of Random Network Distillation, Deep Ensembles, and Bayesian Inference23 Feb 2026
- 2026Diffusion-Inspired Reconfiguration of Transformers for Uncertainty Calibration9 Feb 2026
- 2026Bayesian PINNs for uncertainty-aware inverse problems (BPINN-IP)4 Feb 2026
- 2026Function-Space Empirical Bayes Regularisation with Large Vision-Language Model Priors3 Feb 2026
- 2026Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective1 Feb 2026
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- 2025From Overfitting to Reliability: Introducing the Hierarchical Approximate Bayesian Neural Network15 Dec 2025
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- 2025Maxitive Donsker-Varadhan Formulation for Possibilistic Variational Inference26 Nov 2025
- 2025Few-Shot Multimodal Medical Imaging: A Theoretical Framework3 Nov 2025
- 2025Out-of-Distribution Detection Methods Answer the Wrong Questions2 Jul 2025
- 2025Position: The Future of Bayesian Prediction Is Prior-Fitted29 May 2025
- 2025Variational Deep Learning via Implicit Regularization26 May 2025
- 2025Feature Preserving Shrinkage on Bayesian Neural Networks via the R2D2 Prior23 May 2025
- 2025Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'8 May 2025
- 2025Uncertainty Quantification for Machine Learning in Healthcare: A Survey4 May 2025
- 2025Contextual Similarity Distillation: Ensemble Uncertainties with a Single Model14 Mar 2025
- 2024Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensembles20 Dec 2024
- 2024Functional Stochastic Gradient MCMC for Bayesian Neural Networks25 Sep 2024
- 2024Low-Budget Simulation-Based Inference with Bayesian Neural Networks27 Aug 2024
- 2024Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks10 Aug 2024
- 2024FSP-Laplace: Function-Space Priors for the Laplace Approximation in Bayesian Deep Learning18 Jul 2024
- 2024Context-Guided Diffusion for Out-of-Distribution Molecular and Protein Design16 Jul 2024
- 2024BayTTA: Uncertainty-aware medical image classification with optimized test-time augmentation using Bayesian model averaging25 Jun 2024
- 2024Generative vs. Discriminative modeling under the lens of uncertainty quantification13 Jun 2024
- 2024On Uniform, Bayesian, and PAC-Bayesian Deep Ensembles8 Jun 2024
- 2024One-Shot Federated Learning with Bayesian Pseudocoresets4 Jun 2024
- 2024R'enyi Neural Processes25 May 2024
- 2024Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification23 May 2024
- 2024Attacking Bayes: On the Adversarial Robustness of Bayesian Neural Networks27 Apr 2024
- 2024Spectral Convolutional Conditional Neural Processes19 Apr 2024
- 2024Posterior Uncertainty Quantification in Neural Networks using Data Augmentation18 Mar 2024
- 2024Deep Exploration with PAC-Bayes5 Feb 2024
- 2024Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI1 Feb 2024
- 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks10 Jan 2024
- 2024Deep Exploration with PAC-Bayescited by 4
- 2024Deep Exploration with PAC-Bayes5 Feb 2024
- 2024Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AIcited by 62
- 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Taskscited by 26
- 2025Position: The Future of Bayesian Prediction Is Prior-Fittedcited by 20
- 2025Uncertainty Quantification for Machine Learning in Healthcare: A Surveycited by 14
- 2025Out-of-Distribution Detection Methods Answer the Wrong Questionscited by 14
- 2024Credal Wrapper of Model Averaging for Uncertainty Estimation in Classificationcited by 13
- 2024FSP-Laplace: Function-Space Priors for the Laplace Approximation in Bayesian Deep Learningcited by 11
- 2024Posterior Uncertainty Quantification in Neural Networks using Data Augmentationcited by 9
- 2024Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensemblescited by 8
- 2025Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'cited by 8
- 2024Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networkscited by 6
- 2024BayTTA: Uncertainty-aware medical image classification with optimized test-time augmentation using Bayesian model averagingcited by 5
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- 2026Equivariant Covariance Tensors: Guaranteed SPD Uncertainty for Tensor-Valued Geometric Learning25 Aug 2026
- 2026Flow-Transformed Implicit Processes for Function-Space Variational Inference1 Jun 2026
- 2026A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification11 May 2026
- 2026Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation11 May 2026
- 2026Possibilistic Predictive Uncertainty for Deep Learning1 May 2026
- 2026Data-Driven Priors for Uncertainty-Aware Risk Prediction of Clinical Deterioration using Multimodal Data9 Mar 2026
- 2026Function-Space Empirical Bayes Regularisation with Student's t Priors25 Feb 2026
- 2026On the Equivalence of Random Network Distillation, Deep Ensembles, and Bayesian Inference23 Feb 2026
- 2026Diffusion-Inspired Reconfiguration of Transformers for Uncertainty Calibration9 Feb 2026
- 2026Bayesian PINNs for uncertainty-aware inverse problems (BPINN-IP)4 Feb 2026
- 2026Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective1 Feb 2026
- 2025From Overfitting to Reliability: Introducing the Hierarchical Approximate Bayesian Neural Network15 Dec 2025
12 newest of 37 All 37 (JSON)