# A Recipe for Causal Graph Regression: Confounding Effects Revisited

arXiv: https://arxiv.org/abs/2507.00440 · HTML: https://mlsanity.com/paper/2507.00440/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 1 Jul 2025.

## Builds on (most cited first, 30 of 35)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Representation Learning via Invariant Causal Mechanisms](https://mlsanity.com/paper/2010.07922/) (2020)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [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)
- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [OOD-GNN: Out-of-Distribution Generalized Graph Neural Network](https://mlsanity.com/paper/2112.03806/) (2021)
- [Generalizing Graph Neural Networks on Out-Of-Distribution Graphs](https://mlsanity.com/paper/2111.10657/) (2021)
- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [No True State-of-the-Art? OOD Detection Methods are Inconsistent across Datasets](https://mlsanity.com/paper/2109.05554/) (2021)
- [Counterfactual Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.01391/) (2023)
- [Robust Causal Graph Representation Learning against Confounding Effects](https://mlsanity.com/paper/2208.08584/) (2022)
- [Deconfounding to Explanation Evaluation in Graph Neural Networks](https://mlsanity.com/paper/2201.08802/) (2022)

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

- [Peeling Context from Cause for Molecular Property Prediction](https://mlsanity.com/paper/2511.06692/) (2025)
- [Predicting Trajectories of Long COVID in Adult Women: The Critical Role of Causal Disentanglement](https://mlsanity.com/paper/2603.17722/) (2026)
- [SIR: Structured Image Representations for Explainable Robot Learning](https://mlsanity.com/paper/2606.30101/) (2026)

## Abstract (arXiv)

Through recognizing causal subgraphs, causal graph learning (CGL) has risen to be a promising approach for improving the generalizability of graph neural networks under out-of-distribution (OOD) scenarios. However, the empirical successes of CGL techniques are mostly exemplified in classification settings, while regression tasks, a more challenging setting in graph learning, are overlooked. We thus devote this work to tackling causal graph regression (CGR); to this end we reshape the processing of confounding effects in existing CGL studies, which mainly deal with classification. Specifically, we reflect on the predictive power of confounders in graph-level regression, and generalize classification-specific causal intervention techniques to regression through a lens of contrastive learning. Extensive experiments on graph OOD benchmarks validate the efficacy of our proposals for CGR. The model implementation and the code are provided on https://github.com/causal-graph/CGR.