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Quality of Uncertainty Quantification for Bayesian Neural Network Inference

arXiv 1906.09686 ↗First posted 24 Jun 2019cs.LG stat.MLcited by 58

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Abstract (arXiv)

Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive uncertainty estimates for 10 common inference methods on both regression and classification tasks. Our experiments demonstrate that commonly used metrics (e.g. test log-likelihood) can be misleading. Our experiments also indicate that inference innovations designed to capture structure in the posterior do not necessarily produce high quality posterior approximations.

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Jun 2019.

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Citing papers per year: 2021: 15; 2022: 12; 2023: 12; 2024: 10; 2025: 5; 2026: 4.

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2021A Survey of Uncertainty in Deep Neural Networkscited by 675
2021What Are Bayesian Neural Network Posteriors Really Like?cited by 307
2022CARD: Classification and Regression Diffusion Modelscited by 102
2021Priors in Bayesian Deep Learning: A Reviewcited by 101
2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
2023Uncertainty in Natural Language Generation: From Theory to Applicationscited by 61
2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operatorscited by 33
2021Deep Ensembles from a Bayesian Perspectivecited by 27
2023Beyond Deep Ensembles: A Large-Scale Evaluation of Bayesian Deep Learning under Distribution Shiftcited by 20
2021Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurementscited by 11
2021Learning-to-defer for sequential medical decision-making under uncertaintycited by 10
2021Post-hoc loss-calibration for Bayesian neural networkscited by 9

38 more

2024A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learningcited by 9
2022Are you using test log-likelihood correctly?cited by 8
2024Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noisecited by 8
2024Randomized Physics-Informed Neural Networks for Bayesian Data Assimilationcited by 7
2022Structure and Distribution Metric for Quantifying the Quality of Uncertainty: Assessing Gaussian Processes, Deep Neural Nets, and Deep Neural Operators for Regressioncited by 5
2022What is Flagged in Uncertainty Quantification? Latent Density Models for Uncertainty Categorizationcited by 5
2022Dual Accuracy-Quality-Driven Neural Network for Prediction Interval Generationcited by 5
2021Bayesian Autoencoders: Analysing and Fixing the Bernoulli likelihood for Out-of-Distribution Detectioncited by 4
2021A framework for benchmarking uncertainty in deep regressioncited by 4
2022Bayesian autoencoders with uncertainty quantification: Towards trustworthy anomaly detectioncited by 4
2024Multi-fidelity Gaussian process surrogate modeling for regression problems in physicscited by 4
2025E-PINNs: Epistemic Physics-Informed Neural Networkscited by 4
2021Uncertainty Characteristics Curves: A Systematic Assessment of Prediction Intervalscited by 3
2022Benchmarking Bayesian neural networks and evaluation metrics for regression taskscited by 3
2022Uncertainty Calibration in Bayesian Neural Networks via Distance-Aware Priorscited by 3
2023Randomized Physics-Informed Machine Learning for Uncertainty Quantification in High-Dimensional Inverse Problemscited by 3
2024DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecastingcited by 3
2025Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusioncited by 3
2026Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensemblescited by 3
2022SLOVA: Uncertainty Estimation Using Single Label One-Vs-All Classifiercited by 2
2023High Accuracy Uncertainty-Aware Interatomic Force Modeling with Equivariant Bayesian Neural Networkscited by 2
2024On the Calibration of Epistemic Uncertainty: Principles, Paradoxes and Conflictual Losscited by 2
2024Enhanced BPINN Training Convergence in Solving General and Multi-scale Elliptic PDEs with Noisecited by 2
2021Decision Theoretic Bootstrappingcited by 1
2021Estimating the Uncertainty of Neural Network Forecasts for Influenza Prevalence Using Web Search Activitycited by 1
2022Masked Bayesian Neural Networks : Computation and Optimalitycited by 1
2023Variational Bayesian Neural Networks via Resolution of Singularitiescited by 1
2023Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustnesscited by 1
2024Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Modelscited by 1
2024SoftCVI: Contrastive variational inference with self-generated soft labelscited by 1
2025Damper-B-PINN: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Vehicle State Estimationcited by 1
2026DBPnet: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Wheel Load Estimationcited by 1
2021Generative Particle Variational Inference via Estimation of Functional Gradientscited by 0
2021Understanding Uncertainty in Bayesian Deep Learningcited by 0
2021Coalitional Bayesian Autoencoders -- Towards explainable unsupervised deep learningcited by 0
2022Convergence Analysis for Training Stochastic Neural Networks via Stochastic Gradient Descentcited by 0
2023Human Limits in Machine Learning: Prediction of Plant Phenotypes Using Soil Microbiome Datacited by 0
2023Continuous Time Evidential Distributions for Irregular Time Seriescited by 0

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