# Robustness to Adversarial Perturbations in Learning from Incomplete Data

arXiv: https://arxiv.org/abs/1905.13021 · HTML: https://mlsanity.com/paper/1905.13021/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 30 of 49)

- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)
- [Improving Robustness using Generated Data](https://mlsanity.com/paper/2110.09468/) (2021)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)
- [Data Augmentation Can Improve Robustness](https://mlsanity.com/paper/2111.05328/) (2021)
- [Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?](https://mlsanity.com/paper/2104.09425/) (2021)
- [Semi-Supervised and Unsupervised Deep Visual Learning: A Survey](https://mlsanity.com/paper/2208.11296/) (2022)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [CausalAdv: Adversarial Robustness through the Lens of Causality](https://mlsanity.com/paper/2106.06196/) (2021)
- [A Unified Wasserstein Distributional Robustness Framework for Adversarial Training](https://mlsanity.com/paper/2202.13437/) (2022)
- [Exploring and Exploiting Decision Boundary Dynamics for Adversarial Robustness](https://mlsanity.com/paper/2302.03015/) (2023)
- [Assessing Fairness in the Presence of Missing Data](https://mlsanity.com/paper/2112.04899/) (2021)
- [Removing Undesirable Feature Contributions Using Out-of-Distribution Data](https://mlsanity.com/paper/2101.06639/) (2021)
- [Denoising Masked AutoEncoders Help Robust Classification](https://mlsanity.com/paper/2210.06983/) (2022)
- [Decoupled Adversarial Contrastive Learning for Self-supervised Adversarial Robustness](https://mlsanity.com/paper/2207.10899/) (2022)
- [Generalist: Decoupling Natural and Robust Generalization](https://mlsanity.com/paper/2303.13813/) (2023)
- [Understanding and Improving Ensemble Adversarial Defense](https://mlsanity.com/paper/2310.18477/) (2023)
- [A Characterization of Semi-Supervised Adversarially-Robust PAC Learnability](https://mlsanity.com/paper/2202.05420/) (2022)
- [Global-Local Regularization Via Distributional Robustness](https://mlsanity.com/paper/2203.00553/) (2022)
- [Understanding Generalization in Adversarial Training via the Bias-Variance Decomposition](https://mlsanity.com/paper/2103.09947/) (2021)
- [MixACM: Mixup-Based Robustness Transfer via Distillation of Activated Channel Maps](https://mlsanity.com/paper/2111.05073/) (2021)
- [It Is All About Data: A Survey on the Effects of Data on Adversarial Robustness](https://mlsanity.com/paper/2303.09767/) (2023)
- [Guided Interpolation for Adversarial Training](https://mlsanity.com/paper/2102.07327/) (2021)
- [NoiLIn: Improving Adversarial Training and Correcting Stereotype of Noisy Labels](https://mlsanity.com/paper/2105.14676/) (2021)
- [Robust Semi-Supervised Learning in Open Environments](https://mlsanity.com/paper/2412.18256/) (2024)
- [Conserve-Update-Revise to Cure Generalization and Robustness Trade-off in Adversarial Training](https://mlsanity.com/paper/2401.14948/) (2024)
- [Explaining Adversarial Vulnerability with a Data Sparsity Hypothesis](https://mlsanity.com/paper/2103.00778/) (2021)
- [Unlabeled Data Help: Minimax Analysis and Adversarial Robustness](https://mlsanity.com/paper/2202.06996/) (2022)
- [Adversarial Training with Complementary Labels: On the Benefit of Gradually Informative Attacks](https://mlsanity.com/paper/2211.00269/) (2022)
- [Bridged Adversarial Training](https://mlsanity.com/paper/2108.11135/) (2021)

## Abstract (arXiv)

What is the role of unlabeled data in an inference problem, when the presumed underlying distribution is adversarially perturbed? To provide a concrete answer to this question, this paper unifies two major learning frameworks: Semi-Supervised Learning (SSL) and Distributionally Robust Learning (DRL). We develop a generalization theory for our framework based on a number of novel complexity measures, such as an adversarial extension of Rademacher complexity and its semi-supervised analogue. Moreover, our analysis is able to quantify the role of unlabeled data in the generalization under a more general condition compared to the existing theoretical works in SSL. Based on our framework, we also present a hybrid of DRL and EM algorithms that has a guaranteed convergence rate. When implemented with deep neural networks, our method shows a comparable performance to those of the state-of-the-art on a number of real-world benchmark datasets.