# Explaining and Adapting Graph Conditional Shift

arXiv: https://arxiv.org/abs/2306.03256 · HTML: https://mlsanity.com/paper/2306.03256/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Central Moment Discrepancy (CMD) for Domain-Invariant Representation Learning](https://mlsanity.com/paper/1702.08811/) (2017)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization](https://mlsanity.com/paper/2009.05204/) (2020)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization](https://mlsanity.com/paper/2102.06966/) (2021)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [DANE: Domain Adaptive Network Embedding](https://mlsanity.com/paper/1906.00684/) (2019)
- [Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networks](https://mlsanity.com/paper/2210.01906/) (2022)
- [Graph Domain Adaptation: A Generative View](https://mlsanity.com/paper/2106.07482/) (2021)

## Built on by (most cited first, 14 of 14)

- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [Rethinking Propagation for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2402.05660/) (2024)
- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [Pairwise Alignment Improves Graph Domain Adaptation](https://mlsanity.com/paper/2403.01092/) (2024)
- [Subgraph Pooling: Tackling Negative Transfer on Graphs](https://mlsanity.com/paper/2402.08907/) (2024)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Graph Domain Adaptation: Challenges, Progress and Prospects](https://mlsanity.com/paper/2402.00904/) (2024)
- [Nested Graph Pseudo-Label Refinement for Noisy Label Domain Adaptation Learning](https://mlsanity.com/paper/2508.00716/) (2025)
- [Beyond Generalization: A Survey of Out-Of-Distribution Adaptation on Graphs](https://mlsanity.com/paper/2402.11153/) (2024)
- [Deceptive Fairness Attacks on Graphs via Meta Learning](https://mlsanity.com/paper/2310.15653/) (2023)
- [Structural Alignment Improves Graph Test-Time Adaptation](https://mlsanity.com/paper/2502.18334/) (2025)
- [Conditional Shift-Robust Conformal Prediction for Graph Neural Network](https://mlsanity.com/paper/2405.11968/) (2024)
- [Enhancing Node-Level Graph Domain Adaptation by Alleviating Local Dependency](https://mlsanity.com/paper/2512.13149/) (2025)
- [Domain Adaptive Unfolded Graph Neural Networks](https://mlsanity.com/paper/2411.13137/) (2024)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have shown remarkable performance on graph-structured data. However, recent empirical studies suggest that GNNs are very susceptible to distribution shift. There is still significant ambiguity about why graph-based models seem more vulnerable to these shifts. In this work we provide a thorough theoretical analysis on it by quantifying the magnitude of conditional shift between the input features and the output label. Our findings show that both graph heterophily and model architecture exacerbate conditional shifts, leading to performance degradation. To address this, we propose an approach that involves estimating and minimizing the conditional shift for unsupervised domain adaptation on graphs. In our controlled synthetic experiments, our algorithm demonstrates robustness towards distribution shift, resulting in up to 10% absolute ROC AUC improvement versus the second-best algorithm. Furthermore, comprehensive experiments on both node classification and graph classification show its robust performance under various distribution shifts.