Dormant Independence

The construction of causal graphs from non-experimental data rests on a set of constraints that the graph structure imposes on all probability distributions compatible with the graph. These constraints are of two types: conditional independencies and algebraic constraints, first noted by Verma. While conditional independencies are well studied and frequently used in causal induction algorithms, Verma constraints are still poorly understood, and rarely applied. In this paper we examine a special subset of Verma constraints which are easy to understand, easy to identify and easy to apply; they arise from “dormant independencies,” namely, conditional independencies that hold in interventional distributions. We give a complete algorithm for determining if a dormant independence between two sets of variables is entailed by the causal graph, such that this independence is identifiable, in other words if it resides in an interventional distribution that can be predicted without resorting to interventions. We further show the usefulness of dormant independencies in model testing and induction by giving an algorithm that uses constraints entailed by dormant independencies to prune extraneous edges from a given causal graph.