Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairs

This work addresses the problem of automated covariate selection under limited prior knowledge. Given an exposure-outcome pair {X,Y} and a variable set Z of unknown causal structure, the Local Discovery by Partitioning (LDP) algorithm partitions Z into subsets defined by their relation to {X,Y}. We enumerate eight exhaustive and mutually exclusive partitions of any arbitrary Z and leverage this taxonomy to differentiate confounders from other variable types. LDP is motivated by valid adjustment set identification, but avoids the pretreatment assumption commonly made by automated covariate selection methods. We provide theoretical guarantees that LDP returns a valid adjustment set for any Z that meets sufficient graphical conditions. Under stronger conditions, we prove that partition labels are asymptotically correct. Total independence tests is worst-case quadratic in |Z|, with sub-quadratic runtimes observed empirically. We numerically validate our theoretical guarantees on synthetic and semi-synthetic graphs. Adjustment sets from LDP yield less biased and more precise average treatment effect estimates than baselines, with LDP outperforming on confounder recall, test count, and runtime for valid adjustment set discovery.