Telling Peer Direct Effects from Indirect Effects in Observational Network Data

Estimating causal effects is crucial for decision-makers in many applications, but it is particularly challenging with observational network data due to peer interactions. Some algorithms have been proposed to estimate causal effects involving network data, particularly peer effects, but they often fail to tell apart diverse 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 the identification conditions of these causal effects. To differentiate these effects, we leverage causal mediation analysis and tailor it specifically for network data. Furthermore, given the inherent challenges of accurately estimating effects in networked environments, we propose to incorporate attention mechanisms to capture the varying influences of different neighbors and to explore high-order neighbor effects using multi-layer graph neural networks (GNNs). Additionally, we employ the Hilbert-Schmidt Independence Criterion (HSIC) to further enhance the model’s robustness and accuracy. Extensive experiments on two semi-synthetic datasets derived from real-world networks and on a dataset from a recommendation system confirm the effectiveness of our approach. Our findings have the potential to improve intervention strategies in networked systems, particularly in social networks and public health.

People in networks—such as friends, classmates, or online connections—can influence us in two ways: their actions affect us directly, and their resulting outcomes affect us indirectly. Unfortunately, standard observational data cannot separate these two paths of influence. We propose gDIS, an approach that learns which connections matter most, automatically combines information across the network, and uses a statistical check to avoid misleading correlations. We tested gDIS on two semi-synthetic social networks and a dataset from a recommendation system, and it distinguished direct and indirect influences more accurately than existing methods. By clearly separating these pathways, our method can help health officials decide who to vaccinate first and marketers choose early adopters, leading to more efficient intervention strategies.