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.

翻译：本研究提出，因果推断为捕捉图神经网络中的异质消息传递提供了一种有前景的途径。通过利用因果效应分析，我们能够基于节点间非对称的依赖关系识别异质边。学习得到的因果结构能够提供更精确的节点间关系。为降低计算复杂度，我们在图学习中引入了基于干预的因果推断方法。我们首先将图上的因果分析形式化为一个结构学习模型，并在贝叶斯框架内定义优化问题，从而简化了分析过程。随后，我们提出将优化目标分解为基于因果关系的**一致性惩罚项**与**结构修正项**，并进行了理论分析。我们通过条件熵对该目标进行估计，并阐释了条件熵如何量化图的异质性。基于此，我们提出了CausalMP——一种用于异质图学习的因果消息传递发现网络，该网络能够迭代地学习输入图的显式因果结构。我们在异质图与同质图设置下进行了大量实验。结果表明，我们的模型在链接预测任务上取得了优越的性能。在不同基础模型上，基于因果结构的训练也能提升节点分类任务中的表征质量。