Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairs
Causal discovery is crucial for causal inference in observational studies: it can enable the identification of valid adjustment sets (VAS) for unbiased effect estimation. However, global causal discovery is notoriously hard in the nonparametric setting, with exponential time and sample complexity in the worst case. To address this, we propose local discovery by partitioning (LDP), a novel nonparametric local discovery algorithm that is tailored for downstream inference tasks while avoiding the pretreatment assumption. LDP is a constraint-based procedure that partitions variables into subsets defined solely by their causal relation to an exposure-outcome pair. Further, LDP returns a VAS for the exposure-outcome pair under causal insufficiency and mild sufficient conditions. Total independence tests is worst-case quadratic in variable count. Asymptotic theoretical guarantees are numerically validated on synthetic graphs. Adjustment sets from LDP yield less biased and more precise average treatment effect estimates than baseline discovery algorithms, with LDP outperforming on confounder recall, runtime, and test count for VAS discovery. Further, LDP ran at least 1300x faster than baselines on a benchmark.
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