PUATE: Semiparametric Efficient Average Treatment Effect Estimation from Treated (Positive) and Unlabeled Units

The estimation of average treatment effects (ATEs), defined as the difference in expected outcomes between treatment and control groups, is a central topic in causal inference. This study develops semiparametric efficient estimators for ATE estimation in a setting where only a treatment group and an unknown group-comprising units for which it is unclear whether they received the treatment or control-are observable. This scenario represents a variant of learning from positive and unlabeled data (PU learning) and can be regarded as a special case of ATE estimation with missing data. For this setting, we derive semiparametric efficiency bounds, which provide lower bounds on the asymptotic variance of regular estimators. We then propose semiparametric efficient ATE estimators whose asymptotic variance aligns with these efficiency bounds. Our findings contribute to causal inference with missing data and weakly supervised learning.

Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices

This study designs an adaptive experiment for efficiently estimating average treatment effect (ATEs). We consider an adaptive experiment where an experimenter sequentially samples an experimental unit from a covariate density decided by the experimenter and assigns a treatment. After assigning a treatment, the experimenter observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using gathered samples. The objective of the experimenter is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed experiments that adaptively optimize the propensity score (treatment-assignment probability). As a generalization of such an approach, we propose a framework under which an experimenter optimizes the covariate density, as well as the propensity score, and find that optimizing both covariate density and propensity score reduces the asymptotic variance more than optimizing only the propensity score. Based on this idea, in each round of our experiment, the experimenter optimizes the covariate density and propensity score based on past observations. To design an adaptive experiment, we first derive the efficient covariate density and propensity score that minimizes the semiparametric efficiency bound, a lower bound for the asymptotic variance given a fixed covariate density and a fixed propensity score. Next, we design an adaptive experiment using the efficient covariate density and propensity score sequentially estimated during the experiment. Lastly, we propose an ATE estimator whose asymptotic variance aligns with the minimized semiparametric efficiency bound.