mlsanityData to 7 Oct 2026

Statistical Guarantees for the Robustness of Bayesian Neural Networks

arXiv 1903.01980 ↗First posted 5 Mar 2019cs.LG cs.CV stat.MLcited by 35

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Abstract (arXiv)

We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i.e., with a priori error and confidence bounds. We provide experimental comparison for several approximate BNN inference techniques on image classification tasks associated to MNIST and a two-class subset of the GTSRB dataset. Our results enable quantification of uncertainty of BNN predictions in adversarial settings.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Mar 2019.

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Citing papers per year: 2021: 12; 2022: 3; 2023: 10; 2024: 5; 2025: 2; 2026: 3.

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  1. 2023Making Substitute Models More Bayesian Can Enhance Transferability of Adversarial Examplescited by 32
  2. 2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
  3. 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
  4. 2021Towards Practical Robustness Analysis for DNNs based on PAC-Model Learningcited by 12
  5. 2021Structured Stochastic Gradient MCMCcited by 12
  6. 2021Infinite Time Horizon Safety of Bayesian Neural Networkscited by 12
  7. 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
  8. 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
  9. 2021Certification of Iterative Predictions in Bayesian Neural Networkscited by 8
  10. 2023BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programmingcited by 8
  11. 2023TrajPAC: Towards Robustness Verification of Pedestrian Trajectory Prediction Modelscited by 8
  12. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
23 more
  1. 2021Adversarial Robustness Guarantees for Gaussian Processescited by 5
  2. 2021Evaluating the Robustness of Bayesian Neural Networks Against Different Types of Attackscited by 5
  3. 2024Tight Verification of Probabilistic Robustness in Bayesian Neural Networkscited by 5
  4. 2021Robustness of Bayesian Neural Networks to White-Box Adversarial Attackscited by 4
  5. 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 4
  6. 2024Solving Probabilistic Verification Problems of Neural Networks using Branch and Boundcited by 4
  7. 2021The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networkscited by 3
  8. 2023Individual Fairness in Bayesian Neural Networkscited by 3
  9. 2023Improving Transferability of Adversarial Examples via Bayesian Attackscited by 3
  10. 2026Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformerscited by 3
  11. 2021Fast Falsification of Neural Networks using Property Directed Testingcited by 2
  12. 2021PopSkipJump: Decision-Based Attack for Probabilistic Classifierscited by 2
  13. 2023Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networkscited by 2
  14. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 2
  15. 2022Probabilistic Inverse Modeling: An Application in Hydrologycited by 1
  16. 2025Learning Beyond Euclid: Curvature-Adaptive Generalization for Neural Networks on Manifoldscited by 1
  17. 2022Robustness of Control Design via Bayesian Learningcited by 0
  18. 2023Uncertainty Quantification in Inverse Models in Hydrologycited by 0
  19. 2024Patch Synthesis for Property Repair of Deep Neural Networkscited by 0
  20. 2024Risk-Averse Certification of Bayesian Neural Networkscited by 0
  21. 2025Support is All You Need for Certified VAE Trainingcited by 0
  22. 2026Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generationcited by 0
  23. 2026Certified Uncertainty Propagation in One-Shot Federated Bayesian Models via Posterior Event Transportcited by 0