Causal Effect Estimation under Networked Interference without Networked Unconfoundedness Assumption

Estimating causal effects under networked interference from observational data is a crucial yet challenging problem. Most existing methods mainly rely on the networked unconfoundedness assumption, which guarantees the identification of networked effects. However, this assumption is often violated due to the latent confounders inherent in observational data, thereby hindering the identification of networked effects. To address this issue, we leverage the rich interaction patterns between units in networks, which provide valuable information for recovering these latent confounders. Building on this insight, we develop a confounder recovery framework that explicitly characterizes three categories of latent confounders in networked settings: those affecting only the unit, those affecting only the unit’s neighbors, and those influencing both. Based on this framework, we design a networked effect estimator using identifiable representation learning techniques. From a theoretical standpoint, we prove the identifiability of all three types of latent confounders and, by leveraging the recovered confounders, establish a formal identification result for networked effects. Extensive experiments validate our theoretical findings and demonstrate the effectiveness of the proposed method.

💡 Research Summary

**
The paper tackles the challenging problem of causal effect estimation under networked interference when the standard “networked unconfoundedness” assumption (which requires that all confounders be observed) does not hold. The authors observe that the interaction patterns inherent in a network provide auxiliary information that can be exploited to recover latent confounders. They formalize three distinct categories of latent confounders: (i) u_i affecting only the focal unit, (ii) u_n affecting only the unit’s neighbors, and (iii) u_c affecting both the unit and its neighbors. By decomposing the overall latent confounder vector U into these three components, they construct a causal graph (Figure 2) that makes explicit how each type influences treatment assignments (individual treatment t_i and neighborhood exposure z_i) and outcomes Y_i.

The core theoretical contribution is twofold. First, under a weaker “latent networked unconfoundedness” assumption (Assumption 5) and assuming the network is sufficiently rich, they prove that the three latent confounder types are identifiable from the observed data (X, T, Z) together with the network adjacency matrix. The proof leverages the fact that the distribution of neighbor treatments, conditioned on observed proxies, contains signatures of the hidden variables because the interference mechanism (summarized by a known exposure function g) couples the treatments of neighboring units. Second, once the latent confounders are recovered, they show that the average main effect (AME), average spillover effect (ASE), and average total effect (ATE) become identifiable without requiring the full unconfoundedness assumption. The identification formulas are expressed in terms of the conditional expectation µ(t, z, x, x_N) = E