# Heterophilic Graph Neural Networks Optimization with Causal Message-passing

arXiv: https://arxiv.org/abs/2411.13821 · HTML: https://mlsanity.com/paper/2411.13821/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 21 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [SimGRACE: A Simple Framework for Graph Contrastive Learning without Data Augmentation](https://mlsanity.com/paper/2202.03104/) (2022)
- [All in One: Multi-task Prompting for Graph Neural Networks](https://mlsanity.com/paper/2307.01504/) (2023)
- [Generative Causal Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.06643/) (2021)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [Learning from Counterfactual Links for Link Prediction](https://mlsanity.com/paper/2106.02172/) (2021)
- [Graph Prompt Learning: A Comprehensive Survey and Beyond](https://mlsanity.com/paper/2311.16534/) (2023)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [Linkless Link Prediction via Relational Distillation](https://mlsanity.com/paper/2210.05801/) (2022)
- [EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks](https://mlsanity.com/paper/2205.13892/) (2022)
- [Label-Wise Graph Convolutional Network for Heterophilic Graphs](https://mlsanity.com/paper/2110.08128/) (2021)
- [Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learning](https://mlsanity.com/paper/2206.12933/) (2022)
- [Link Prediction on Heterophilic Graphs via Disentangled Representation Learning](https://mlsanity.com/paper/2208.01820/) (2022)
- [Knowledge Graph Completion with Counterfactual Augmentation](https://mlsanity.com/paper/2302.13083/) (2023)
- [Deep Insights into Noisy Pseudo Labeling on Graph Data](https://mlsanity.com/paper/2310.01634/) (2023)
- [Causal Lifting and Link Prediction](https://mlsanity.com/paper/2302.01198/) (2023)
- [On Local Aggregation in Heterophilic Graphs](https://mlsanity.com/paper/2106.03213/) (2021)

## Built on by (most cited first, 4 of 4)

- [G-Refer: Graph Retrieval-Augmented Large Language Model for Explainable Recommendation](https://mlsanity.com/paper/2502.12586/) (2025)
- [Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization](https://mlsanity.com/paper/2508.00357/) (2025)
- [Graph-based Fake Account Detection: A Survey](https://mlsanity.com/paper/2507.06541/) (2025)
- [Separated Contrastive Learning for Matching in Cross-domain Recommendation with Curriculum Scheduling](https://mlsanity.com/paper/2502.16239/) (2025)

## Abstract (arXiv)

In this work, we discover that causal inference provides a promising approach to capture heterophilic message-passing in Graph Neural Network (GNN). By leveraging cause-effect analysis, we can discern heterophilic edges based on asymmetric node dependency. The learned causal structure offers more accurate relationships among nodes. To reduce the computational complexity, we introduce intervention-based causal inference in graph learning. We first simplify causal analysis on graphs by formulating it as a structural learning model and define the optimization problem within the Bayesian scheme. We then present an analysis of decomposing the optimization target into a consistency penalty and a structure modification based on cause-effect relations. We then estimate this target by conditional entropy and present insights into how conditional entropy quantifies the heterophily. Accordingly, we propose CausalMP, a causal message-passing discovery network for heterophilic graph learning, that iteratively learns the explicit causal structure of input graphs. We conduct extensive experiments in both heterophilic and homophilic graph settings. The result demonstrates that the our model achieves superior link prediction performance. Training on causal structure can also enhance node representation in classification task across different base models.