Discussion of "learning equivalence classes of acyclic models with latent and selection variables from multiple datasets with overlapping variables"

Learning equivalence classes of acyclic models with latent and selection variables from multiple datasets with overlapping variables is discussed. The problem of inferring the presence of latent variables, their relation to the observables, and the relation among themselves, is considered. A different approach for identifying causal structures, one that results in much simpler equivalence classes, is provided. It is found that the computational cost is much higher than the procedure implemented, but if datasets are individually of modest dimensionality, it might be doable in practice. From the point of view of search algorithms for optimizing structure, much of the machinery of combinatorial optimization could optimize the penalized composite likelihood score by enforcing constraints such that the independence models over different subsets of variables agree on the overlapping sets.