Conditional Independences and Causal Relations implied by Sets of Equations

The discovery of causal relations is a fundamental objective in many scientific endeavours. The process of the scientific method usually involves a conjecture, such as a causal graph or a set of equations, that explains observed phenomena. In practice, such a graph structure can be learned automatically from conditional independences in observational data via the PC/FCI algorithms (Spirtes, Glymour, and Scheines, 2000; Zhang, 2008). The crucial assumption in causal discovery is that directed edges in this learned graph express causal relations between variables. However, an immediate concern is whether directed graphs actually can simultaneously encode the causal semantics and the conditional independence constraints of a system.