Abstract 

The assumption that data samples are independent and identically distributed (iid) is standard in many areas of statistics and machine learning. Nevertheless, in some settings, such as social networks, infectious disease modeling, and reasoning with spatial and temporal data, this assumption is false. An extensive literature exists on making causal inferences under the iid assumption [17, 11, 26, 21], even when unobserved confounding bias may be present. But, as pointed out in [19], causal inference in non-iid contexts is challenging due to the presence of both unobserved confounding and data dependence. In this paper we develop a general theory describing when causal inferences are possible in such scenarios. We use segregated graphs [20], a generalization of latent projection mixed graphs [28], to represent causal models of this type and provide a complete algorithm for nonparametric identification in these models. We then demonstrate how statistical inference may be performed on causal parameters identified by this algorithm. In particular, we consider cases where only a single sample is available for parts of the model due to full interference, i.e., all units are pathwise dependent and neighbors’ treatments affect each others’ outcomes [24]. We apply these techniques to a synthetic data set which considers users sharing fake news articles given the structure of their social network, user activity levels, and baseline demographics and socioeconomic covariates.