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Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users

arXiv 2007.06823 ↗First posted 14 Jul 2020cs.LG stat.MLcited by 336

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Abstract (arXiv)

Modern deep learning methods constitute incredibly powerful tools to tackle a myriad of challenging problems. However, since deep learning methods operate as black boxes, the uncertainty associated with their predictions is often challenging to quantify. Bayesian statistics offer a formalism to understand and quantify the uncertainty associated with deep neural network predictions. This tutorial provides an overview of the relevant literature and a complete toolset to design, implement, train, use and evaluate Bayesian Neural Networks, i.e. Stochastic Artificial Neural Networks trained using Bayesian methods.

Key facts. Cited by 336 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Jul 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 27; 2022: 52; 2023: 68; 2024: 76; 2025: 79; 2026: 34.

336 papers.

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  1. 2024A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directionscited by 115
  2. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  3. 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 78
  4. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  5. 2022Personalized Federated Learning via Variational Bayesian Inferencecited by 68
  6. 2022Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysiscited by 62
  7. 2023Credal Bayesian Deep Learningcited by 45
  8. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  9. 2023A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methodscited by 39
  10. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 36
  11. 2025No Answer Needed: Predicting LLM Answer Accuracy from Question-Only Linear Probescited by 35
  12. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
38 more
  1. 2021Deep Ensembles from a Bayesian Perspectivecited by 27
  2. 2022Augmenting Softmax Information for Selective Classification with Out-of-Distribution Datacited by 27
  3. 2023Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorialcited by 27
  4. 2022Implicit Full Waveform Inversion with Deep Neural Representationcited by 26
  5. 2023A Large-Scale Study of Probabilistic Calibration in Neural Network Regressioncited by 26
  6. 2023A Primer on Bayesian Neural Networks: Review and Debatescited by 26
  7. 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Taskscited by 26
  8. 2021A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applicationscited by 24
  9. 2022Uncertainty Quantification for Traffic Forecasting: A Unified Approachcited by 22
  10. 2022Bayesian Learning for Neural Networks: an algorithmic surveycited by 22
  11. 2023Bayesian Federated Learning: A Surveycited by 22
  12. 2021PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physicscited by 21
  13. 2024The Empirical Impact of Neural Parameter Symmetries, or Lack Thereofcited by 21
  14. 2024Gaussian Stochastic Weight Averaging for Bayesian Low-Rank Adaptation of Large Language Modelscited by 20
  15. 2025Generative Uncertainty in Diffusion Modelscited by 20
  16. 2023Random-Set Neural Networks (RS-NN)cited by 19
  17. 2021Deep Learning Methods for Daily Wildfire Danger Forecastingcited by 17
  18. 2024Modeling uncertainty for Gaussian Splattingcited by 17
  19. 2022Autoinverse: Uncertainty Aware Inversion of Neural Networkscited by 16
  20. 2022Epistemic Deep Learningcited by 15
  21. 2022On double-descent in uncertainty quantification in overparametrized modelscited by 15
  22. 2023DUDES: Deep Uncertainty Distillation using Ensembles for Semantic Segmentationcited by 15
  23. 2023Improving Neural Additive Models with Bayesian Principlescited by 15
  24. 2023Bayesian Renormalizationcited by 13
  25. 2024Credal Wrapper of Model Averaging for Uncertainty Estimation in Classificationcited by 13
  26. 2021Structured Stochastic Gradient MCMCcited by 12
  27. 2021Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Datacited by 12
  28. 2022Uncertainty estimation of pedestrian future trajectory using Bayesian approximationcited by 12
  29. 2022Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Datacited by 12
  30. 2022A General Framework for quantifying Aleatoric and Epistemic uncertainty in Graph Neural Networkscited by 12
  31. 2023Wasserstein Generative Regressioncited by 12
  32. 2024Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Modelscited by 12
  33. 2021Fail-Safe Execution of Deep Learning based Systems through Uncertainty Monitoringcited by 11
  34. 2021The Peril of Popular Deep Learning Uncertainty Estimation Methodscited by 11
  35. 2022Explainable Artificial Intelligence for Bayesian Neural Networks: Towards trustworthy predictions of ocean dynamicscited by 11
  36. 2022Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equationscited by 11
  37. 2023Improved uncertainty quantification for neural networks with Bayesian last layercited by 11
  38. 2023UMat: Uncertainty-Aware Single Image High Resolution Material Capturecited by 11

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