Local Causal Discovery for Statistically Efficient Causal Inference
Mátyás Schubert, Tom Claassen, Sara Magliacane
TL;DR
LOAD addresses the problem of estimating the causal effect between a pair of variables when the full causal graph is unknown, balancing the scalability of local causal discovery with the statistical optimality of global approaches. It introduces a principled pipeline that first infers the target relation using local Markov-blanket information, then tests identifiability via a local amenability criterion, and finally computes the optimal adjustment set by identifying mediators and their parents when identifiability holds. The method is proven sound and complete for identifying causal effects from local information and is shown to achieve accuracy comparable to global methods while dramatically reducing CI tests and improving scalability in large graphs. Empirical results on synthetic and realistic networks demonstrate that LOAD often outperforms local methods in adjustment-set quality and approaches global methods in causal-estimation performance, with favorable computational trade-offs.
Abstract
Causal discovery methods can identify valid adjustment sets for causal effect estimation for a pair of target variables, even when the underlying causal graph is unknown. Global causal discovery methods focus on learning the whole causal graph and therefore enable the recovery of optimal adjustment sets, i.e., sets with the lowest asymptotic variance, but they quickly become computationally prohibitive as the number of variables grows. Local causal discovery methods offer a more scalable alternative by focusing on the local neighborhood of the target variables, but are restricted to statistically suboptimal adjustment sets. In this work, we propose Local Optimal Adjustments Discovery (LOAD), a sound and complete causal discovery approach that combines the computational efficiency of local methods with the statistical optimality of global methods. First, LOAD identifies the causal relation between the targets and tests if the causal effect is identifiable by using only local information. If it is identifiable, it then finds the optimal adjustment set by leveraging local causal discovery to infer the mediators and their parents. Otherwise, it returns the locally valid parent adjustment sets based on the learned local structure. In our experiments on synthetic and realistic data LOAD outperforms global methods in scalability, while providing more accurate effect estimation than local methods.