Discussion of "Learning Equivalence Classes of Acyclic Models with Latent and Selection Variables from Multiple Datasets with Overlapping Variables"

In automated causal discovery, the constraint-based approach seeks to learn an (equivalence) class of causal structures (with possibly latent variables and/or selection variables) that are compatible (according to some assumptions, usually the causal Markov and faithfulness assumptions) with the conditional dependence and independence relations found in data. In the paper under discussion, Tillman and Spirtes (T&S) develop a constraint-based algorithm for learning causal structures from multiple, overlapping datasets. The basic setup of the problem is this: the variables of interest are not all measured at once in a single study. Instead there are several studies, each measuring a subset, which produce multiple datasets with overlapping variables. Assuming there is a common structure over the variables of interest (with possibly latent confounding variables and selection variables) that generated all the datasets, T&S’s algorithm is designed to discover features of that structure by learning the features shared by all the causal structures that are compatible with all the datasets .