Estimating causal effects is crucial for decision-makers in many applications, but it is particularly challenging with observational network data due to peer interactions. Many algorithms have been proposed to estimate causal effects involving network data, particularly peer effects, but they often overlook the variety of peer effects. To address this issue, we propose a general setting which considers both peer direct effects and peer indirect effects, and the effect of an individual's own treatment, and provide identification conditions of these causal effects and proofs. To estimate these causal effects, we utilize attention mechanisms to distinguish the influences of different neighbors and explore high-order neighbor effects through multi-layer graph neural networks (GNNs). Additionally, to control the dependency between node features and representations, we incorporate the Hilbert-Schmidt Independence Criterion (HSIC) into the GNN, fully utilizing the structural information of the graph, to enhance the robustness and accuracy of the model. Extensive experiments on two semi-synthetic datasets confirm the effectiveness of our approach. Our theoretical findings have the potential to improve intervention strategies in networked systems, with applications in areas such as social networks and epidemiology.

翻译：在许多应用中，因果效应的估计对决策者至关重要，但由于同伴交互的存在，这在观测网络数据中尤为困难。已有许多算法被提出来估计涉及网络数据（尤其是同伴效应）的因果效应，但它们往往忽略了同伴效应的多样性。为解决这一问题，我们提出了一个通用框架，同时考虑同伴直接效应、同伴间接效应以及个体自身处理的影响，并提供了这些因果效应的识别条件与证明。为估计这些因果效应，我们利用注意力机制区分不同邻居的影响，并通过多层图神经网络（GNNs）探索高阶邻居效应。此外，为控制节点特征与表示之间的依赖性，我们将希尔伯特-施密特独立性准则（HSIC）融入GNN中，充分利用图的结构信息，以增强模型的鲁棒性与准确性。在两个半合成数据集上的大量实验验证了我们方法的有效性。我们的理论发现有望改进网络系统中的干预策略，可应用于社交网络与流行病学等领域。