Geometric Mutual Information for Causal Effect Estimation under Network Interference

Estimating causal effect on network data considers the situation with the presence of dependencies between individuals. To reduce complex confounding bias caused by network interference, existing methods usually adopt the same information aggregation function for covariates and treatments. However, these methods fail to exploit different geometric structures in the spaces of covariates and treatments, which are vital for information aggregation on network data. In this paper, starting from the causal effect estimation error, we propose a geometric mutual information model to learn balanced representations, so that different geometric structures involved in covariates and treatments are leveraged in representation learning and information aggregation. Specifically, we theoretically reveal that balanced representation learning on network data can be achieved by maximizing the dissimilarity between the geometric structures of covariates and treatments measured by the Gromov-Wasserstein discrepancy. To better characterize the geometry of the network data, we apply the Ricci flow to refine the graph structures for representation learning as well as information aggregation. We conduct experiments on benchmark datasets to demonstrate the effectiveness of our method.