PUATE: Efficient ATE Estimation from Treated (Positive) and Unlabeled Units
Masahiro Kato, Fumiaki Kozai, RYO INOKUCHI
The estimation of \emph{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 in a setting where only a treatment group and an unlabeled group—consisting of units whose treatment status is unknown—are observed. This scenario constitutes a variant of learning from positive and unlabeled data (\emph{PU learning}) and can be viewed as a special case of ATE estimation with missing data. For this setting, we derive the \emph{semiparametric efficiency bounds}, which characterize the lowest achievable asymptotic variance for regular estimators. We then construct semiparametric \emph{efficient ATE estimators} that attain these bounds. Our results contribute to the literature on causal inference with missing data and weakly supervised learning.