Conditions and Assumptions for Constraint-based Causal Structure Learning

This paper formalizes constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. More importantly, we provide clear and testable assumptions, as an alternative to faithfulness, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. We provide these definitions and results 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.