The weighted controlled direct effect (WCDE) generalizes the standard controlled direct effect (CDE) by averaging over the mediator distribution, providing a robust estimate when treatment effects vary across mediator levels. This makes the WCDE especially relevant in fairness analysis, where it isolates the direct effect of an exposure on an outcome, independent of mediating pathways. This work establishes three fundamental advances for WCDE in observational studies: First, we establish necessary and sufficient conditions for the identifiability of the WCDE, clarifying when it diverges from the CDE. Next, we consider nonparametric estimation of the WCDE and derive its influence function, focusing on the class of regular and asymptotically linear estimators. Lastly, we characterize the optimal covariate adjustment set that minimizes the asymptotic variance, demonstrating how mediator-confounder interactions introduce distinct requirements compared to average treatment effect (ATE) estimation. Using synthetic and real-world data, we validate our theory numerically, showing that the proposed optimal valid adjustment set yields the lowest variance at practical sample sizes. Our results offer a principled framework for efficient estimation of direct effects in complex causal systems, with practical applications in fairness and mediation analysis.

Yet, modern machine learning pipelines offer a promising solution--provided their predictions yield correct conclusions. We focus on Prediction-Powered Causal Inferences (PPCI), i.e., estimating the treatment effect in an unlabeled target experiment, relying on training data with the same outcome annotated but potentially different treatment or effect modifiers.

We study the problem of selecting covariates for unbiased estimation of the total causal effect.Existing approaches typically rely on global causal structure learning over all variables, or on strong assumptions such as causal sufficiency - where observed variables share no latent confounders - or the pretreatment assumption, which limits covariates to those unaffected by the treatment or outcome. These requirements are often unrealistic in practice, and global learning becomes computationally prohibitive in high-dimensional settings.To address these challenges, we propose a novel local learning method for covariate selection in nonparametric causal effect estimation that avoids both the pretreatment and causal sufficiency assumptions. We first characterize a local boundary that contains at least one valid adjustment set whenever one exists for identifying the causal effect, and then develop local identification procedures to efficiently search within this boundary.We prove that the proposed method is sound and complete. Experiments on multiple synthetic datasets and two real-world datasets show that our approach achieves accurate causal effect estimation while substantially improving computational efficiency.

The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed.

The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables.

Estimating treatment effects from observational data is challenging due to two main reasons: (a) hidden confounding, and (b) covariate mismatch (control and treatment groups not having identical distributions). Long lines of works exist that address only either of these issues. To address the former, conventional techniques that require detailed knowledge in the form of causal graphs have been proposed. For the latter, covariate matching and importance weighting methods have been used. Recently, there has been progress in combining testable independencies with partial side information for tackling hidden confounding. A common framework to address both hidden confounding and selection bias is missing. We propose neural architectures that aim to learn a representation of pre-treatment covariates that is a valid adjustment and also satisfies covariate matching constraints. We combine two different neural architectures: one based on gradient matching across domains created by subsampling a suitable anchor variable that assumes causal side information, followed by the other, a covariate matching transformation. We prove that approximately invariant representations yield approximate valid adjustment sets which would enable an interval around the true causal effect. In contrast to usual sensitivity analysis, where an unknown nuisance parameter is varied, we have a testable approximation yielding a bound on the effect estimate. We also outperform various baselines with respect to ATE and PEHE errors on causal benchmarks that include IHDP, Jobs, Cattaneo, and an image-based Crowd Management dataset.