mlsanityData to 7 Oct 2026

RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothing

arXiv 2405.08892 ↗First posted 14 May 2024cs.LGcited by 4

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Abstract (arXiv)

Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of regression. By defining robustness in regression tasks flexibly through probabilities, we demonstrate how to establish upper bounds on input data point perturbation (using the ℓ2 norm) for a user-specified probability of observing valid outputs. Furthermore, we showcase the asymptotic property of a basic averaging function in scenarios where the regression model operates without any constraint. We then derive a certified upper bound of the input perturbations when dealing with a family of regression models where the outputs are bounded. Our simulations verify the validity of the theoretical results and reveal the advantages and limitations of simple smoothing functions, i.e., averaging, in regression tasks. The code is publicly available at urlhttps://github.com/arekavandi/CertifiedRobustRegression.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 18 of its 26 references that are in the map. First posted on arXiv 14 May 2024.

Builds on

18 of 26 references.

References · 18

  1. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  2. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 462
  3. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 328
  4. 2020Visual Camera Re-Localization from RGB and RGB-D Images Using DSACcited by 176
  5. 2020Randomized Smoothing of All Shapes and Sizescited by 146
  6. 2022(Certified!!) Adversarial Robustness for Free!cited by 130
  7. 2020SoK: Certified Robustness for Deep Neural Networkscited by 100
  8. 2021Segment and Complete: Defending Object Detectors against Adversarial Patch Attacks with Robust Patch Detectioncited by 67
  9. 2019Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifierscited by 65
  10. 2020Curse of Dimensionality on Randomized Smoothing for Certifiable Robustnesscited by 56
  11. 2020Certified Defense to Image Transformations via Randomized Smoothingcited by 51
  12. 2020Detection as Regression: Certified Object Detection by Median Smoothingcited by 47
6 more
  1. 2020Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Frameworkcited by 45
  2. 2020Higher-Order Certification for Randomized Smoothingcited by 36
  3. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 18
  4. 2023RS-Del: Edit Distance Robustness Certificates for Sequence Classifiers via Randomized Deletioncited by 17
  5. 2022Reducing Certified Regression to Certified Classification for General Poisoning Attackscited by 7
  6. 2022Smoothed Embeddings for Certified Few-Shot Learningcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2026Evaluating randomized smoothing as a defense against adversarial attacks in trajectory predictioncited by 1
  2. 2025FS-IQA: Certified Feature Smoothing for Robust Image Quality Assessmentcited by 0
  3. 2026Self-Review Reinforcement Learning (SRRL) with Cross-Episode Memory and Policy Distillationcited by 0
  4. 2026Clustered Randomized Smoothing for Stochastic Prediction Functionscited by 0