Non-intuitive conditional independence facts hold in models of network data

Many social scientists and researchers across a wide range of fields focus on analyzing a single causal dependency or a conditional model of some outcome variable. However, to reason about interventions or conditional independence, it is useful to construct a joint model of a domain. Researchers in computer science, statistics, and philosophy have developed representations (e.g., Bayesian networks), theory, and learning algorithms for causal discovery of joint models from observational data. Bayesian networks are graphical models that encode joint probability distributions over a system of variables, and they can be interpreted causally under a few assumptions [7, 8]. The rules of d-separation—a set of graphical criteria—are the foundation for algorithmic derivation of the conditional independence facts implied by the structure of Bayesian networks [1]. This theory connects causal structure with conditional independence and can be leveraged to learn causal models from observational data. Accurate reasoning about conditional independence facts is the basis for constraintbased algorithms that learn the structure of Bayesian networks (e.g., PC [8]). Bayesian networks, as well as most analytic methods for causal analysis (e.g., linear regression), assume that data instances are independent and identically distributed (IID). However, many real-world systems involve multiple types of interacting entities with probabilistic dependencies among the variables on those entities. For example, citation data involve researchers collaborating on scholarly papers that cite prior work. Over the past 15 years, researchers in statistics and computer science have devised more expressive classes of directed graphical models, such as probabilistic relational models (PRMs), which remove the assumptions of IID data to model network, or relational, data [2]. Relational models more closely represent the real-world domains that many social scientists and other researchers investigate. To successfully learn causal models from observational, network data, we need a similar theory for deriving conditional independence from relational models. In this paper, we explain why d-separation does not correctly produce conditional independence facts when applied to the structure of relational models. We show that nonintuitive conditional independence facts hold in models of network data through relationally d-connecting paths that only manifest in ground graphs. We describe the abstract ground graph, a lifted representation recently introduced by Maier et al. [4], that enables a sound, complete, and computationally efficient method for deriving conditional independ-separating path elements (exists one on path) d-connecting path elements (exists all on path)