Causal Inference with Non-IID Data using Linear Graphical Models
Authors: Chi Zhang, Karthika Mohan, Judea Pearl

Traditional causal inference techniques assume data are independent and identically distributed (IID) and thus  ignores interactions among units. However, a unit’s treatment may affect another unit's outcome (interference), a unit’s treatment may be correlated with another unit’s outcome, or a unit’s treatment and outcome may be spuriously correlated through another unit. To capture such nuances, we model the data generating process using causal graphs and conduct a systematic analysis of the bias caused by different types of interactions when computing causal effects. We derive theorems to detect and quantify the interaction bias, and derive conditions under which it is safe to ignore interactions. Put differently, we present conditions under which causal effects can be computed with negligible bias by assuming that samples are IID. Furthermore, we develop a method to eliminate bias in cases where blindly assuming IID is expected to yield a significantly biased estimate. Finally, we test the coverage and performance of our methods through simulations.