# A Unified Framework for Semiparametrically Efficient Semi-Supervised Learning

arXiv: https://arxiv.org/abs/2502.17741 · HTML: https://mlsanity.com/paper/2502.17741/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2025.

## Built on by (most cited first, 14 of 14)

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- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Generalized Prediction-Powered Inference, with Application to Binary Classifier Evaluation](https://mlsanity.com/paper/2602.10332/) (2026)
- [Spatially Robust Inference with Predicted and Missing at Random Labels](https://mlsanity.com/paper/2603.11368/) (2026)
- [Prediction-powered Inference by Mixture of Experts](https://mlsanity.com/paper/2604.27892/) (2026)
- [Optimized Labeling Resource Allocation for Prediction-Assisted Inference via OPAL](https://mlsanity.com/paper/2606.03211/) (2026)
- [Rescuing double robustness: safe estimation under complete misspecification](https://mlsanity.com/paper/2509.22446/) (2025)
- [Generation-Powered Inference for Distribution-Valued Outcomes](https://mlsanity.com/paper/2608.14542/) (2026)

## Abstract (arXiv)

We consider statistical inference under a semi-supervised setting where we have access to both a labeled dataset consisting of pairs Xi, Yi i=1n and an unlabeled dataset  Xi i=n+1n+N. We ask the question: under what circumstances, and by how much, can incorporating the unlabeled dataset improve upon inference using the labeled data? To answer this question, we investigate semi-supervised learning through the lens of semiparametric efficiency theory. We characterize the efficiency lower bound under the semi-supervised setting for an arbitrary inferential problem, and show that incorporating unlabeled data can potentially improve efficiency if the parameter is not well-specified. We then propose two types of semi-supervised estimators: a safe estimator that imposes minimal assumptions, is simple to compute, and is guaranteed to be at least as efficient as the initial supervised estimator; and an efficient estimator, which -- under stronger assumptions -- achieves the semiparametric efficiency bound. Our findings unify existing semiparametric efficiency results for particular special cases, and extend these results to a much more general class of problems. Moreover, we show that our estimators can flexibly incorporate predicted outcomes arising from ``black-box" machine learning models, and thereby achieve the same goal as prediction-powered inference (PPI), but with superior theoretical guarantees. We also provide a complete understanding of the theoretical basis for the existing set of PPI methods. Finally, we apply the theoretical framework developed to derive and analyze efficient semi-supervised estimators in a number of settings, including M-estimation, U-statistics, and average treatment effect estimation, and demonstrate the performance of the proposed estimators via simulations.