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.

Assumptions about equality of effects are commonly made in causal inference tasks. For example, the well-known “difference-in-differences” method assumes that confounding remains constant across time periods. Similarly, it is not unreasonable to assume that causal effects apply equally to units undergoing interference. Finally, sensitivity analysis often hypothesizes equality among existing and unaccounted for confounders. Despite the ubiquity of these “equality constraints,” modern identification methods have not leveraged their presence in a systematic way. In this paper, we develop a novel graphical criterion that extends the well-known method of generalized instrumental sets to exploit such additional constraints for causal identification in linear models. We further demonstrate how it solves many diverse problems found in the literature in a general way, including difference-in-differences, interference, as well as benchmarking in sensitivity analysis.

Modern causal analysis involves two major tasks, discovery and identification. The first aims to learn a causal structure compatible with the available data, the second leverages that structure to estimate causal effects. Rather than performing the two tasks in tandem, as is usually done in the literature, we propose a symbiotic approach in which the two are performed simultaneously for mutual benefit; information gained through identification helps causal discovery and vice versa. This approach enables the usage of Verma constraints, which remain dormant in constraint-based methods of discovery, and permit us to learn more complete structures, hence identify a larger set of causal effects than previously achievable with standard methods.