# Uncertainty-Aware Robust Learning on Noisy Graphs

arXiv: https://arxiv.org/abs/2306.08210 · HTML: https://mlsanity.com/paper/2306.08210/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [A Survey on Graph Structure Learning: Progress and Opportunities](https://mlsanity.com/paper/2103.03036/) (2021)
- [On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features](https://mlsanity.com/paper/2111.12128/) (2021)
- [Minimizing the Maximal Loss: How and Why?](https://mlsanity.com/paper/1602.01690/) (2016)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Bayesian semi-supervised learning for uncertainty-calibrated prediction of molecular properties and active learning](https://mlsanity.com/paper/1902.00925/) (2019)
- [DP-SSL: Towards Robust Semi-supervised Learning with A Few Labeled Samples](https://mlsanity.com/paper/2110.13740/) (2021)
- [Incomplete Graph Representation and Learning via Partial Graph Neural Networks](https://mlsanity.com/paper/2003.10130/) (2020)
- [Few-shot Node Classification with Extremely Weak Supervision](https://mlsanity.com/paper/2301.02708/) (2023)
- [Toward Robust Graph Semi-Supervised Learning against Extreme Data Scarcity](https://mlsanity.com/paper/2208.12422/) (2022)
- [Learning Robust Representations with Graph Denoising Policy Network](https://mlsanity.com/paper/1910.01784/) (2019)
- [Recent Advances in Reliable Deep Graph Learning: Inherent Noise, Distribution Shift, and Adversarial Attack](https://mlsanity.com/paper/2202.07114/) (2022)
- [Distributionally Robust Weighted k-Nearest Neighbors](https://mlsanity.com/paper/2006.04004/) (2020)
- [Distributionally Robust Semi-Supervised Learning Over Graphs](https://mlsanity.com/paper/2110.10582/) (2021)
- [Distributionally Robust Graphical Models](https://mlsanity.com/paper/1811.02728/) (2018)

## Built on by (most cited first, 6 of 6)

- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- ["X of Information'' Continuum: A Survey on AI-Driven Multi-dimensional Metrics for Next-Generation Networked Systems](https://mlsanity.com/paper/2507.19657/) (2025)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Global-Decision-Focused Neural ODEs for Proactive Grid Resilience Management](https://mlsanity.com/paper/2502.18321/) (2025)
- [Enhancing the Resilience of Graph Neural Networks to Topological Perturbations in Sparse Graphs](https://mlsanity.com/paper/2406.03097/) (2024)
- [Variational Graph Autoencoder for Heterogeneous Information Networks with Missing and Inaccurate Attributes](https://mlsanity.com/paper/2311.07929/) (2023)

## Abstract (arXiv)

Graph neural networks (GNNs) have excelled in various graph learning tasks, particularly node classification. However, their performance is often hampered by noisy measurements in real-world graphs, which can corrupt critical patterns in the data. To address this, we propose a novel uncertainty-aware graph learning framework inspired by distributionally robust optimization. Specifically, we use a graph neural network-based encoder to embed the node features and find the optimal node embeddings by minimizing the worst-case risk through a minimax formulation. Such an uncertainty-aware learning process leads to improved node representations and a more robust graph predictive model that effectively mitigates the impact of uncertainty arising from data noise. Our experimental results demonstrate superior predictive performance over baselines across noisy scenarios.