Local Covariate Selection for Average Causal Effect Estimation without Pretreatment and Causal Sufficiency Assumptions

Causal effect estimation is a fundamental task in many scientific fields. Selecting appropriate covariates for adjustment is crucial for obtaining unbiased causal effects. However, most existing methods either rely on learning the global causal structure, assume the absence of latent variables, or impose the pretreatment assumption-restricts covariates to those unaffected by the treatment or outcome. These assumptions are often unrealistic in real-world scenarios, and global structure learning can be computationally intensive and inefficient. To address these challenges, we first characterize the local existence boundary of adjustment sets for causal effect estimation. Based on this characterization, we develop a novel local learning method for covariate selection in nonparametric causal effect estimation. This method accommodates the presence of latent variables and eliminates the need for the pretreatment assumption. We prove that the proposed method is both sound and complete under standard assumptions. Its effectiveness is validated through extensive experiments on both synthetic and real-world datasets.