Cooperative Causal GraphSAGE

GraphSAGE is a widely used graph neural network. The introduction of causal inference has improved its robust performance and named as Causal GraphSAGE. However, Causal GraphSAGE focuses on measuring causal weighting among individual nodes, but neglecting the cooperative relationships among sampling nodes as a whole. To address this issue, this paper proposes Cooperative Causal GraphSAGE (CoCa-GraphSAGE), which combines cooperative game theory with Causal GraphSAGE. Initially, a cooperative causal structure model is constructed in the case of cooperation based on the graph structure. Subsequently, Cooperative Causal sampling (CoCa-sampling) algorithm is proposed, employing the Shapley values to calculate the cooperative contribution based on causal weights of the nodes sets. CoCa-sampling guides the selection of nodes with significant cooperative causal effects during the neighborhood sampling process, thus integrating the selected neighborhood features under cooperative relationships, which takes the sampled nodes as a whole and generates more stable target node embeddings. Experiments on publicly available datasets show that the proposed method has comparable classification performance to the compared methods and outperforms under perturbations, demonstrating the robustness improvement by CoCa-sampling.