Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference

TL;DR

This paper develops efficient estimators for treatment effect estimation in semi-supervised settings, leveraging unlabeled covariates to improve inference accuracy in both one-sample and two-sample scenarios.

Contribution

It introduces a novel semi-supervised framework for causal inference that reduces estimator variance by incorporating auxiliary covariates.

Findings

Incorporating auxiliary covariates lowers the efficiency bound.

Proposed estimators achieve asymptotic variance smaller than traditional methods.

Framework applies to both one-sample and two-sample settings.

Abstract

This study investigates treatment effect estimation in the semi-supervised setting, also can be interpreted as prediction-powered inference. In our setting, we can use not only the standard triple of covariates, treatment indicator, and outcome, but also unlabeled auxiliary covariates. For this problem, we develop efficiency bounds and efficient estimators whose asymptotic variance aligns with the efficiency bound. In the analysis, we introduce two different data-generating processes: the one-sample setting and the two-sample setting. The one-sample setting considers the case where we can observe treatment indicators and outcomes for a part of the dataset, which is also called the censoring setting. In contrast, the two-sample setting considers two independent datasets with labeled and unlabeled data, which is also called the case-control setting or the stratified setting. In both settings, we find that by incorporating auxiliary covariates, we can lower the efficiency bound and obtain an estimator with an asymptotic variance smaller than that without such auxiliary covariates. We frame our framework as prediction-powered causal inference.