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

TL;DR

This paper introduces semiparametric efficient estimators for average treatment effects using only data from treated and unlabeled units, addressing a novel causal inference scenario with missing treatment labels.

Contribution

It develops the first semiparametric efficient estimators for ATE in a positive and unlabeled data setting, extending causal inference methods to handle missing treatment information.

Findings

Derived the semiparametric efficiency bounds for the setting.

Constructed estimators that attain the efficiency bounds.

Contributed to causal inference with missing data and weak supervision.

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 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 (PU learning) and can be viewed as a special case of ATE estimation with missing data. For this setting, we derive the semiparametric efficiency bounds, which characterize the lowest achievable asymptotic variance for regular estimators. We then construct semiparametric efficient ATE estimators that attain these bounds. Our results contribute to the literature on causal inference with missing data and weakly supervised learning.