Causal Discovery: When Conditional Independence Can Recover a Causal Graph and When It Cannot

Correlation alone cannot reveal causation, but causal discovery aims to recover the causal graph behind observational data. The approach assumes data are generated from a directed acyclic graph in which each variable depends on its direct causes plus independent noise. Chains, forks and colliders each produce distinct patterns of conditional independence, which allow some edge directions to be inferred. The method relies on assumptions such as the causal Markov condition, faithfulness and causal sufficiency, meaning no hidden common causes. When these hold, the recovered structure is informative, but if they fail the output may be an unreliable causal graph.