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

arXiv: https://arxiv.org/abs/2511.08303 · HTML: https://mlsanity.com/paper/2511.08303/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 54 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 20 of 20)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Off-Policy Evaluation and Learning for External Validity under a Covariate Shift](https://mlsanity.com/paper/2002.11642/) (2020)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Prediction-powered Generalization of Causal Inferences](https://mlsanity.com/paper/2406.02873/) (2024)
- [Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices](https://mlsanity.com/paper/2403.03589/) (2024)
- [Efficient nonparametric causal inference with missing exposure information](https://mlsanity.com/paper/1802.08952/) (2018)
- [Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation](https://mlsanity.com/paper/2509.22122/) (2025)
- [Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression](https://mlsanity.com/paper/2510.24433/) (2025)
- [RieszBoost: Gradient Boosting for Riesz Regression](https://mlsanity.com/paper/2501.04871/) (2025)
- [Direct Debiased Machine Learning via Bregman Divergence Minimization](https://mlsanity.com/paper/2510.23534/) (2025)
- [A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression](https://mlsanity.com/paper/2510.26783/) (2025)

## Built on by (most cited first, 1 of 1)

- [Prediction-Powered Causal Inference by Automatic Debiased Machine Learning and Semi-Supervised Riesz Regression](https://mlsanity.com/paper/2606.12892/) (2026)

## Abstract (arXiv)

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.