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. The approach is particularly valuable when researchers are interested in causal relationships within specific tiers while accounting for broader influences from other tiers without fully specifying them. Building on this, we introduce a query-specific causal discovery algorithm that takes a causal query and observational data as input and returns a graph tailored specifically to that query. Through both theoretical analysis and empirical studies, we demonstrate that our discovery algorithm can achieve exponential speedups compared to the existing method when tiered knowledge is available.