Reasoning about Independence in Probabilistic Models of Relational Data

Bayesian networks leverage conditional independence to compactly encode joint probability distributions. Many learning algorithms exploit the constraints implied by observed conditional independencies to learn the structure of Bayesian networks. The rules of d-separation provide a theoretical and algorithmic framework for deriving conditional independence facts from model structure. However, this theory only applies to Bayesian networks. Many real-world systems, such as social or economic systems, are characterized by interacting heterogeneous entities and probabilistic dependencies that cross the boundaries of entities. Consequently, researchers have developed extensions to Bayesian networks that can represent these relational dependencies. We show that the theory of d-separation inaccurately infers conditional independence when applied directly to the structure of probabilistic models of relational data. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.