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

arXiv: https://arxiv.org/abs/2405.08892 · HTML: https://mlsanity.com/paper/2405.08892/

## Key facts

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

## Builds on (most cited first, 18 of 18)

- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Visual Camera Re-Localization from RGB and RGB-D Images Using DSAC](https://mlsanity.com/paper/2002.12324/) (2020)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [(Certified!!) Adversarial Robustness for Free!](https://mlsanity.com/paper/2206.10550/) (2022)
- [SoK: Certified Robustness for Deep Neural Networks](https://mlsanity.com/paper/2009.04131/) (2020)
- [Segment and Complete: Defending Object Detectors against Adversarial Patch Attacks with Robust Patch Detection](https://mlsanity.com/paper/2112.04532/) (2021)
- [Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifiers](https://mlsanity.com/paper/1906.04948/) (2019)
- [Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness](https://mlsanity.com/paper/2002.03239/) (2020)
- [Certified Defense to Image Transformations via Randomized Smoothing](https://mlsanity.com/paper/2002.12463/) (2020)
- [Detection as Regression: Certified Object Detection by Median Smoothing](https://mlsanity.com/paper/2007.03730/) (2020)
- [Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework](https://mlsanity.com/paper/2002.09169/) (2020)
- [Higher-Order Certification for Randomized Smoothing](https://mlsanity.com/paper/2010.06651/) (2020)
- [CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networks](https://mlsanity.com/paper/2109.10696/) (2021)
- [RS-Del: Edit Distance Robustness Certificates for Sequence Classifiers via Randomized Deletion](https://mlsanity.com/paper/2302.01757/) (2023)
- [Reducing Certified Regression to Certified Classification for General Poisoning Attacks](https://mlsanity.com/paper/2208.13904/) (2022)
- [Smoothed Embeddings for Certified Few-Shot Learning](https://mlsanity.com/paper/2202.01186/) (2022)

## Built on by (most cited first, 4 of 4)

- [Evaluating randomized smoothing as a defense against adversarial attacks in trajectory prediction](https://mlsanity.com/paper/2603.10821/) (2026)
- [FS-IQA: Certified Feature Smoothing for Robust Image Quality Assessment](https://mlsanity.com/paper/2508.05516/) (2025)
- [Self-Review Reinforcement Learning (SRRL) with Cross-Episode Memory and Policy Distillation](https://mlsanity.com/paper/2607.05541/) (2026)
- [Clustered Randomized Smoothing for Stochastic Prediction Functions](https://mlsanity.com/paper/2608.12037/) (2026)

## 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.