Improving constraint-based discovery with robust propagation and reliable LLM priors

Learning causal structure from observational data is central to scientific modeling and decision-making. Constraint-based methods aim to recover conditional independence (CI) relations in a causal directed acyclic graph (DAG). Classical approaches such as PC and subsequent methods orient v-structures first and then propagate edge directions from these seeds, assuming perfect CI tests and exhaustive search of separating subsets -- assumptions often violated in practice, leading to cascading errors in the final graph. Recent work has explored using large language models (LLMs) as experts, prompting sets of nodes for edge directions, and could augment edge orientation when assumptions are not met. However, such methods implicitly assume perfect experts, which is unrealistic for hallucination-prone LLMs. We propose MosaCD, a causal discovery method that propagates edges from a high-confidence set of seeds derived from both CI tests and LLM annotations. To filter hallucinations, we introduce shuffled queries that exploit LLMs' positional bias, retaining only high-confidence seeds. We then apply a novel confidence-down propagation strategy that orients the most reliable edges first, and can be integrated with any skeleton-based discovery method. Across multiple real-world graphs, MosaCD achieves higher accuracy in final graph construction than existing constraint-based methods, largely due to the improved reliability of initial seeds and robust propagation strategies.