# Causal invariant geographic network representations with feature and structural distribution shifts

arXiv: https://arxiv.org/abs/2503.19382 · HTML: https://mlsanity.com/paper/2503.19382/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 90 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Builds on (most cited first, 30 of 52)

- [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)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Generative Causal Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.06643/) (2021)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [OSMnx: New Methods for Acquiring, Constructing, Analyzing, and Visualizing Complex Street Networks](https://mlsanity.com/paper/1611.01890/) (2016)
- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [OoD-Bench: Quantifying and Understanding Two Dimensions of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.03721/) (2021)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)

## Built on by (most cited first, 3 of 3)

- [GeoAgentBench: A Dynamic Execution Benchmark for Tool-Augmented Agents in Spatial Analysis](https://mlsanity.com/paper/2604.13888/) (2026)
- [Causal Neighbourhood Learning for Invariant Graph Representations](https://mlsanity.com/paper/2602.17934/) (2026)
- [A Counterfactual Graph Approach to Oppositional Narrative Analysis](https://mlsanity.com/paper/2603.06135/) (2026)

## Abstract (arXiv)

The existing methods learn geographic network representations through deep graph neural networks (GNNs) based on the i.i.d. assumption. However, the spatial heterogeneity and temporal dynamics of geographic data make the out-of-distribution (OOD) generalisation problem particularly salient. The latter are particularly sensitive to distribution shifts (feature and structural shifts) between testing and training data and are the main causes of the OOD generalisation problem. Spurious correlations are present between invariant and background representations due to selection biases and environmental effects, resulting in the model extremes being more likely to learn background representations. The existing approaches focus on background representation changes that are determined by shifts in the feature distributions of nodes in the training and test data while ignoring changes in the proportional distributions of heterogeneous and homogeneous neighbour nodes, which we refer to as structural distribution shifts. We propose a feature-structure mixed invariant representation learning (FSM-IRL) model that accounts for both feature distribution shifts and structural distribution shifts. To address structural distribution shifts, we introduce a sampling method based on causal attention, encouraging the model to identify nodes possessing strong causal relationships with labels or nodes that are more similar to the target node. Inspired by the Hilbert-Schmidt independence criterion, we implement a reweighting strategy to maximise the orthogonality of the node representations, thereby mitigating the spurious correlations among the node representations and suppressing the learning of background representations. Our experiments demonstrate that FSM-IRL exhibits strong learning capabilities on both geographic and social network datasets in OOD scenarios.