Outcome-adapted Automatic Debiased Machine Learning

Parameters of interest in causal inference, such as treatment or policy effects, can often be expressed as linear functionals of an outcome regression function. Automatic debiased machine learning (AutoDML) is a unified framework for obtaining asymptotically normal estimators of such parameters, which requires estimation of both a regression function and a Riesz representer. Existing AutoDML neural network architectures, such as RieszNet and MADNet, use a shared intermediate covariate representation. However, it remains unclear whether this shared representation should be predictive of the Riesz representer or the outcome. We show that a shared representation of the covariates that preserves predictive power of the outcome while discarding information about the Riesz representer is asymptotically more efficient than the baseline AutoDML estimator that uses all covariates. Motivated by these results, we propose the outcome-adapted AutoDML estimator and establish its asymptotic behavior in a sample splitting framework. We provide a neural network implementation of the estimator that learns a sparse representation of the covariates that is predictive of the outcome but not predictive of the Riesz representer. We demonstrate the efficiency gains of our estimator over existing alternatives on synthetic data and achieve state-of-the-art estimation accuracy on the semi-synthetic IHDP benchmark dataset.

Proximal Mediation Analysis with Hidden Recanting Witnesses

Mediation analysis is essential for decomposing the causal effect of a treatment into direct and indirect pathways. However, many practical settings rely on the stringent assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori. Such a requirement is often untenable, especially when these variables remain unobservable due to measurement difficulties or privacy constraints. In this paper, we leverage proximal causal inference to develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses. Building on this, we develop a semiparametric inference framework that derives the efficient influence function and proposes a proximal multiply robust estimator, which remains consistent if at least one set of nuisance models is correctly specified. When all nuisance models are correctly specified and converge at appropriate rates, the estimator is asymptotically normal and achieves the semiparametric efficiency bound. We provide a minimax optimization-based debiased machine learning procedure for point estimation and constructing valid confidence intervals. The performance of the proposed methods is demonstrated by simulation studies and a real data application.