Marginal Causal Consistency in Constraint-based Causal Learning

Maximal Ancestral Graphs (MAGs) are probabilistic graphical models that can model the distribution and causal properties of a set of variables in the presence of latent confounders. They are closed under marginalization. Invariant pairwise features of a class of Markov equivalent MAGs can be learnt from observational data sets using the FCI algorithm and its variations (such as conservative FCI and order independent FCI). We investigate the consistency of causal features (causal ancestry relations) obtained by FCI in different marginals of a single data set. In principle, the causal relationships identified by FCI on a data set D measuring a set of variables V should not conflict the output of FCI on marginal data sets including only subsets of V. In practice, however, FCI is prone to error propagation, and running FCI in different marginals results in inconsistent causal predictions. We introduce the term of marginal causal consistency to denote the consistency of causal relationships when learning marginal distributions, and investigate the marginal causal consistency of different FCI variations.Results indicate that marginal causal consistency varies for different algorithms, and is also sensitive to network density and marginal size.