Conditions and Assumptions for Constraint-based Causal Structure Learning

The paper formalizes constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We define a "generic" structure learning algorithm, which provides conditions that, under the faithfulness assumption, the output of all known exact algorithms in the literature must satisfy, and which outputs graphs that are Markov equivalent to the causal graph. More importantly, we provide clear assumptions, weaker than faithfulness, under which the same generic algorithm outputs Markov equivalent graphs to the causal graph. We provide the theory for the general class of models under the assumption that the distribution is Markovian to the true causal graph, and we specialize the definitions and results for structural causal models.