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

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  • Masahiro Kato
  • Fumiaki Kozai
  • Ryo Inokuchi

Abstract

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.

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  • Masahiro Kato & Fumiaki Kozai & Ryo Inokuchi, 2025. "PUATE: Semiparametric Efficient Average Treatment Effect Estimation from Treated (Positive) and Unlabeled Units," Papers 2501.19345, arXiv.org.
    • Handle: RePEc:arx:papers:2501.19345
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    1. Jaeil Ahn & Bhramar Mukherjee & Stephen B. Gruber & Samiran Sinha, 2011. "Missing Exposure Data in Stereotype Regression Model: Application to Matched Case–Control Study with Disease Subclassification," Biometrics, The International Biometric Society, vol. 67(2), pages 546-558, June.
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