Identifiability in Causal Bayesian Networks: A Sound and Complete Algorithm

This paper addresses the problem of identifying causal effects from nonexperimental data in a causal Bayesian network, i.e., a directed acyclic graph that represents causal relationships. The identifiability question asks whether it is possible to compute the probability of some set of (effect) variables given intervention on another set of (intervention) variables, in the presence of non-observable (i.e., hidden or latent) variables. It is well known that the answer to the question depends on the structure of the causal Bayesian network, the set of observable variables, the set of effect variables, and the set of intervention variables. Our work is based on the work of Tian, Pearl, Huang, and Valtorta (Tian & Pearl 2002a; 2002b; 2003; Huang & Valtorta 2006a) and extends it. We show that the identify algorithm that Tian and Pearl define and prove sound for semi-Markovian models can be transfered to general causal graphs and is not only sound, but also complete. This result effectively solves the identifiability question for causal Bayesian networks that Pearl posed in 1995 (Pearl 1995), by providing a sound and complete algorithm for identifiability.