Query-Specific Causal Graph Pruning Under Tiered Knowledge

We present a systematic method for pruning edges from causal graphs by leveraging tiered knowledge. We characterize conditions under which edges can be removed from a causal graph while preserving the identifiability of (conditional) causal effects. This result enables causal identification on simplified graphs that are substantially smaller than the original graphs. This approach is particularly valuable when researchers are interested in causal relationships within specific tiers while controlling for broader influences from other tiers without fully specifying them. Building on this, we introduce a \emph{query-specific} causal discovery procedure that takes a causal query as an additional input and recovers a reduced graph tailored to the query from observational data. Through theoretical analysis and empirical studies, we demonstrate that our procedure can achieve exponential speedups compared to the existing method when tiered knowledge is available.