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Bayesian Uncertainty Estimation for Batch Normalized Deep Networks

arXiv 1802.06455 ↗First posted 18 Feb 2018stat.MLcited by 70

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Abstract (arXiv)

We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. We further demonstrate that this finding allows us to make meaningful estimates of the model uncertainty using conventional architectures, without modifications to the network or the training procedure. Our approach is thoroughly validated by measuring the quality of uncertainty in a series of empirical experiments on different tasks. It outperforms baselines with strong statistical significance, and displays competitive performance with recent Bayesian approaches.

Key facts. Cited by 70 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Feb 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 25; 2022: 9; 2023: 14; 2024: 10; 2025: 6; 2026: 6.

70 papers.

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  1. 2023Decomposing Uncertainty for Large Language Models through Input Clarification Ensemblingcited by 113
  2. 2021Dive into Deep Learningcited by 111
  3. 2022Understanding the Generalization Benefit of Normalization Layers: Sharpness Reductioncited by 86
  4. 2022Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantificationcited by 71
  5. 2021On the Practicality of Deterministic Epistemic Uncertaintycited by 62
  6. 2023A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methodscited by 39
  7. 2021Valid prediction intervals for regression problemscited by 28
  8. 2021A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applicationscited by 24
  9. 2021Medical Image Segmentation with Limited Supervision: A Review of Deep Network Modelscited by 21
  10. 2021Classical Planning in Deep Latent Spacecited by 21
  11. 2021Multi-Class Data Description for Out-of-distribution Detectioncited by 19
  12. 2024Diffusion Model Guided Sampling with Pixel-Wise Aleatoric Uncertainty Estimationcited by 17
38 more
  1. 2023How to Fix a Broken Confidence Estimator: Evaluating Post-hoc Methods for Selective Classification with Deep Neural Networkscited by 15
  2. 2023Make Me a BNN: A Simple Strategy for Estimating Bayesian Uncertainty from Pre-trained Modelscited by 15
  3. 2024Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEscited by 14
  4. 2024A Novel Characterization of the Population Area Under the Risk Coverage Curve (AURC) and Rates of Finite Sample Estimatorscited by 13
  5. 2021Mapping oil palm density at country scale: An active learning approachcited by 12
  6. 2021Proxy-Normalizing Activations to Match Batch Normalization while Removing Batch Dependencecited by 12
  7. 2021RELAX: Representation Learning Explainabilitycited by 12
  8. 2024Epistemic Uncertainty Quantification For Pre-trained Neural Networkcited by 10
  9. 2021A Quantitative Comparison of Epistemic Uncertainty Maps Applied to Multi-Class Segmentationcited by 9
  10. 2024Explaining Predictive Uncertainty by Exposing Second-Order Effectscited by 9
  11. 2025Epistemic Uncertainty in Conformal Scores: A Unified Approachcited by 9
  12. 2021Learning Uncertainty For Safety-Oriented Semantic Segmentation In Autonomous Drivingcited by 8
  13. 2021Structured Dropout Variational Inference for Bayesian Neural Networkscited by 7
  14. 2022Scale-invariant Bayesian Neural Networks with Connectivity Tangent Kernelcited by 7
  15. 2023Effect of latent space distribution on the segmentation of images with multiple annotationscited by 7
  16. 2024Rate-In: Information-Driven Adaptive Dropout Rates for Improved Inference-Time Uncertainty Estimationcited by 7
  17. 2021Uncertainty-Aware COVID-19 Detection from Imbalanced Sound Datacited by 6
  18. 2023Uncertainty-Aware Source-Free Adaptive Image Super-Resolution with Wavelet Augmentation Transformercited by 6
  19. 2022Revisiting L1 Loss in Super-Resolution: A Probabilistic View and Beyondcited by 5
  20. 2021Active learning for reducing labeling effort in text classification taskscited by 4
  21. 2022Uncertainty categories in medical image segmentation: a study of source-related diversitycited by 4
  22. 2023Deep Gaussian Mixture Ensemblescited by 4
  23. 2024QUTE: Quantifying Uncertainty in TinyML with Early-exit-assisted ensembles for model-monitoringcited by 4
  24. 2025Torch-Uncertainty: A Deep Learning Framework for Uncertainty Quantificationcited by 4
  25. 2021Exploring Uncertainty in Deep Learning for Construction of Prediction Intervalscited by 3
  26. 2021Quantifying sources of uncertainty in drug discovery predictions with probabilistic modelscited by 3
  27. 2021Improving Generalization of Batch Whitening by Convolutional Unit Optimizationcited by 3
  28. 2022TRUST-LAPSE: An Explainable and Actionable Mistrust Scoring Framework for Model Monitoringcited by 3
  29. 2021Bridging In- and Out-of-distribution Samples for Their Better Discriminabilitycited by 2
  30. 2021Uncertainty-aware Remaining Useful Life predictorcited by 2
  31. 2021Instance Segmentation of Microscopic Foraminiferacited by 2
  32. 2021Out-of-Distribution Example Detection in Deep Neural Networks using Distance to Modelled Embeddingcited by 2
  33. 2021Training BatchNorm Only in Neural Architecture Search and Beyondcited by 2
  34. 2022Accurate Prediction and Uncertainty Estimation using Decoupled Prediction Interval Networkscited by 2
  35. 2023FG-NeRF: Flow-GAN based Probabilistic Neural Radiance Field for Independence-Assumption-Free Uncertainty Estimationcited by 2
  36. 2024Relative Difficulty Distillation for Semantic Segmentationcited by 2
  37. 2022Density Regression and Uncertainty Quantification with Bayesian Deep Noise Neural Networkscited by 1
  38. 2022Complementing Semi-Supervised Learning with Uncertainty Quantificationcited by 1

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