mlsanityData to 7 Oct 2026

Adversarial Robustness Guarantees for Gaussian Processes

arXiv 2104.03180 ↗First posted 7 Apr 2021cs.LG stat.MLcited by 5

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Abstract (arXiv)

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this paper we present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations. Given a compact subset of the input space Tsubseteq ℝd, a point x^* and a GP, we provide provable guarantees of adversarial robustness of the GP by computing lower and upper bounds on its prediction range in T. We develop a branch-and-bound scheme to refine the bounds and show, for any ε > 0, that our algorithm is guaranteed to converge to values ε-close to the actual values in finitely many iterations. The algorithm is anytime and can handle both regression and classification tasks, with analytical formulation for most kernels used in practice. We evaluate our methods on a collection of synthetic and standard benchmark datasets, including SPAM, MNIST and FashionMNIST. We study the effect of approximate inference techniques on robustness and demonstrate how our method can be used for interpretability. Our empirical results suggest that the adversarial robustness of GPs increases with accurate posterior estimation.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 30 of its 49 references that are in the map. First posted on arXiv 7 Apr 2021.

Builds on

30 of 49 references.

References · 30

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18 more
  1. 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
  2. 2018Is Robustness the Cost of Accuracy? -- A Comprehensive Study on the Robustness of 18 Deep Image Classification Modelscited by 135
  3. 2018Solving Linear Programs in the Current Matrix Multiplication Timecited by 100
  4. 2018Reachability Analysis of Deep Neural Networks with Provable Guaranteescited by 93
  5. 2016Understanding Probabilistic Sparse Gaussian Process Approximationscited by 68
  6. 2018Adversarially Robust Optimization with Gaussian Processescited by 61
  7. 2017Adversarial Examples, Uncertainty, and Transfer Testing Robustness in Gaussian Process Hybrid Deep Networkscited by 48
  8. 2020Robustness of Bayesian Neural Networks to Gradient-Based Attackscited by 48
  9. 2020Probabilistic Safety for Bayesian Neural Networkscited by 41
  10. 2019Statistical Guarantees for the Robustness of Bayesian Neural Networkscited by 35
  11. 2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
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  15. 2018The Limitations of Model Uncertainty in Adversarial Settingscited by 14
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  18. 2017How Wrong Am I? - Studying Adversarial Examples and their Impact on Uncertainty in Gaussian Process Machine Learning Modelscited by 3

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Cited by year

Citing papers per year: 2022: 1; 2023: 3; 2024: 1.

5 papers.

  1. 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
  2. 2023BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programmingcited by 8
  3. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
  4. 2023Promises of Deep Kernel Learning for Control Synthesiscited by 4
  5. 2024Attacking Bayes: On the Adversarial Robustness of Bayesian Neural Networkscited by 2