# Debiased Graph Neural Networks with Agnostic Label Selection Bias

arXiv: https://arxiv.org/abs/2201.07708 · HTML: https://mlsanity.com/paper/2201.07708/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 105 references that are in the map.
- First posted on arXiv 19 Jan 2022.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)

## Built on by (most cited first, 25 of 25)

- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [Deep Graph Anomaly Detection: A Survey and New Perspectives](https://mlsanity.com/paper/2409.09957/) (2024)
- [Alleviating Structural Distribution Shift in Graph Anomaly Detection](https://mlsanity.com/paper/2401.14155/) (2024)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Causality and Independence Enhancement for Biased Node Classification](https://mlsanity.com/paper/2310.09586/) (2023)
- [Predicting the Silent Majority on Graphs: Knowledge Transferable Graph Neural Network](https://mlsanity.com/paper/2302.00873/) (2023)
- [Graph Fairness Learning under Distribution Shifts](https://mlsanity.com/paper/2401.16784/) (2024)
- [Learning Invariant Representations of Graph Neural Networks via Cluster Generalization](https://mlsanity.com/paper/2403.03599/) (2024)
- [Graph Out-of-Distribution Generalization with Controllable Data Augmentation](https://mlsanity.com/paper/2308.08344/) (2023)
- [Graph Contrastive Invariant Learning from the Causal Perspective](https://mlsanity.com/paper/2401.12564/) (2024)
- [Directed Acyclic Graph Structure Learning from Dynamic Graphs](https://mlsanity.com/paper/2211.17029/) (2022)
- [When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlook](https://mlsanity.com/paper/2312.12477/) (2023)
- [Topology-Aware Dynamic Reweighting for Distribution Shifts on Graph](https://mlsanity.com/paper/2406.01066/) (2024)
- [A Survey of Out-of-distribution Generalization for Graph Machine Learning from a Causal View](https://mlsanity.com/paper/2409.09858/) (2024)
- [Causal invariant geographic network representations with feature and structural distribution shifts](https://mlsanity.com/paper/2503.19382/) (2025)
- [Deep Stable Multi-Interest Learning for Out-of-distribution Sequential Recommendation](https://mlsanity.com/paper/2304.05615/) (2023)
- [DeCaf: A Causal Decoupling Framework for OOD Generalization on Node Classification](https://mlsanity.com/paper/2410.20295/) (2024)
- [Mitigating Message Imbalance in Fraud Detection with Dual-View Graph Representation Learning](https://mlsanity.com/paper/2507.06469/) (2025)
- [Evolving Graph Learning for Out-of-Distribution Generalization in Non-stationary Environments](https://mlsanity.com/paper/2511.02354/) (2025)
- [FRGNN: Mitigating the Impact of Distribution Shift on Graph Neural Networks via Test-Time Feature Reconstruction](https://mlsanity.com/paper/2308.09259/) (2023)
- [Towards Human-like Perception: Learning Structural Causal Model in Heterogeneous Graph](https://mlsanity.com/paper/2312.05757/) (2023)
- [IENE: Identifying and Extrapolating the Node Environment for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2406.00764/) (2024)
- [Contextual Representation Anchor Network to Alleviate Selection Bias in Few-Shot Drug Discovery](https://mlsanity.com/paper/2410.20711/) (2024)

## Abstract (arXiv)

Most existing Graph Neural Networks (GNNs) are proposed without considering the selection bias in data, i.e., the inconsistent distribution between the training set with test set. In reality, the test data is not even available during the training process, making selection bias agnostic. Training GNNs with biased selected nodes leads to significant parameter estimation bias and greatly impacts the generalization ability on test nodes. In this paper, we first present an experimental investigation, which clearly shows that the selection bias drastically hinders the generalization ability of GNNs, and theoretically prove that the selection bias will cause the biased estimation on GNN parameters. Then to remove the bias in GNN estimation, we propose a novel Debiased Graph Neural Networks (DGNN) with a differentiated decorrelation regularizer. The differentiated decorrelation regularizer estimates a sample weight for each labeled node such that the spurious correlation of learned embeddings could be eliminated. We analyze the regularizer in causal view and it motivates us to differentiate the weights of the variables based on their contribution on the confounding bias. Then, these sample weights are used for reweighting GNNs to eliminate the estimation bias, thus help to improve the stability of prediction on unknown test nodes. Comprehensive experiments are conducted on several challenging graph datasets with two kinds of label selection biases. The results well verify that our proposed model outperforms the state-of-the-art methods and DGNN is a flexible framework to enhance existing GNNs.