Causal discovery becomes especially challenging when the possibility of latent confounding and/or selection bias is not assumed away. For this task, ancestral graph models are particularly useful in that they can represent the presence of latent confounding and selection effect, without explicitly invoking unobserved variables. Based on the machinery of ancestral graphs, there is a provably sound causal discovery algorithm, known as the FCI algorithm, that allows the possibility of latent confounders and selection bias. However, the orientation rules used in (...) the algorithm are not complete. In this paper, we provide additional orientation rules, augmented by which the FCI algorithm is shown to be complete, in the sense that it can, under standard assumptions, discover all aspects of the causal structure that are uniquely determined by facts of probabilistic dependence and independence. The result is useful for developing any causal discovery and reasoning system based on ancestral graph models. (shrink)

Using Gebharter’s representation, we consider aspects of the problem of discovering the structure of unmeasured submechanisms when the variables in those submechanisms have not been measured. Exploiting an early insight of Sober’s, we provide a correct algorithm for identifying latent, endogenous structure—submechanisms—for a restricted class of structures. The algorithm can be merged with other methods for discovering causal relations among unmeasured variables, and feedback relations between measured variables and unobserved causes can sometimes be learned.