# Distributionally Robust Semi-Supervised Learning Over Graphs

arXiv: https://arxiv.org/abs/2110.10582 · HTML: https://mlsanity.com/paper/2110.10582/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 20 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks](https://mlsanity.com/paper/1903.10527/) (2019)
- [Adversarial Attacks and Defenses on Graphs: A Review, A Tool and Empirical Studies](https://mlsanity.com/paper/2003.00653/) (2020)
- [Real-time Power System State Estimation and Forecasting via Deep Neural Networks](https://mlsanity.com/paper/1811.06146/) (2018)
- [Data-driven Optimal Cost Selection for Distributionally Robust Optimization](https://mlsanity.com/paper/1705.07152/) (2017)

## Built on by (most cited first, 9 of 9)

- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation](https://mlsanity.com/paper/2310.14161/) (2023)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Network](https://mlsanity.com/paper/2302.00873/) (2023)
- [Bridged-GNN: Knowledge Bridge Learning for Effective Knowledge Transfer](https://mlsanity.com/paper/2308.09499/) (2023)
- [Uncertainty-Aware Robust Learning on Noisy Graphs](https://mlsanity.com/paper/2306.08210/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Addressing the Impact of Localized Training Data in Graph Neural Networks](https://mlsanity.com/paper/2307.12689/) (2023)

## Abstract (arXiv)

Semi-supervised learning (SSL) over graph-structured data emerges in many network science applications. To efficiently manage learning over graphs, variants of graph neural networks (GNNs) have been developed recently. By succinctly encoding local graph structures and features of nodes, state-of-the-art GNNs can scale linearly with the size of graph. Despite their success in practice, most of existing methods are unable to handle graphs with uncertain nodal attributes. Specifically whenever mismatches between training and testing data distribution exists, these models fail in practice. Challenges also arise due to distributional uncertainties associated with data acquired by noisy measurements. In this context, a distributionally robust learning framework is developed, where the objective is to train models that exhibit quantifiable robustness against perturbations. The data distribution is considered unknown, but lies within a Wasserstein ball centered around empirical data distribution. A robust model is obtained by minimizing the worst expected loss over this ball. However, solving the emerging functional optimization problem is challenging, if not impossible. Advocating a strong duality condition, we develop a principled method that renders the problem tractable and efficiently solvable. Experiments assess the performance of the proposed method.