# Semi-Supervised U-statistics

arXiv: https://arxiv.org/abs/2402.18921 · HTML: https://mlsanity.com/paper/2402.18921/

## Key facts

- Cited by 5 papers in the map (data through 7 Oct 2026).
- Builds on 12 of its 91 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [SODA10M: A Large-Scale 2D Self/Semi-Supervised Object Detection Dataset for Autonomous Driving](https://mlsanity.com/paper/2106.11118/) (2021)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [Doubly Robust Self-Training](https://mlsanity.com/paper/2306.00265/) (2023)
- [Debiased Machine Learning without Sample-Splitting for Stable Estimators](https://mlsanity.com/paper/2206.01825/) (2022)
- [Prediction De-Correlated Inference: A safe approach for post-prediction inference](https://mlsanity.com/paper/2312.06478/) (2023)
- [A General Framework for Treatment Effect Estimation in Semi-Supervised and High Dimensional Settings](https://mlsanity.com/paper/2201.00468/) (2022)
- [Semi-Supervised Quantile Estimation: Robust and Efficient Inference in High Dimensional Settings](https://mlsanity.com/paper/2201.10208/) (2022)
- [The correlation-assisted missing data estimator](https://mlsanity.com/paper/1911.01859/) (2019)
- [High Dimensional M-Estimation with Missing Outcomes: A Semi-Parametric Framework](https://mlsanity.com/paper/1911.11345/) (2019)
- [The Decaying Missing-at-Random Framework: Model Doubly Robust Causal Inference with Partially Labeled Data](https://mlsanity.com/paper/2305.12789/) (2023)

## Built on by (most cited first, 5 of 5)

- [Semi-Supervised Conformal Prediction With Unlabeled Nonconformity Score](https://mlsanity.com/paper/2505.21147/) (2025)
- [High-dimensional Semi-supervised Classification via the Fermat Distance](https://mlsanity.com/paper/2604.23573/) (2026)
- [Rescuing double robustness: safe estimation under complete misspecification](https://mlsanity.com/paper/2509.22446/) (2025)
- [Learning U-Statistics with Active Inference](https://mlsanity.com/paper/2605.11638/) (2026)
- [When a High Score Is an Illusion: Certifying Genuine versus Repackaged Forecasting Skill](https://mlsanity.com/paper/2609.19223/) (2026)

## Abstract (arXiv)

Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming. The prevalence of such datasets has consistently driven the demand for new tools and methods that exploit the potential of unlabeled data. Responding to this demand, we introduce semi-supervised U-statistics enhanced by the abundance of unlabeled data, and investigate their statistical properties. We show that the proposed approach is asymptotically Normal and exhibits notable efficiency gains over classical U-statistics by effectively integrating various powerful prediction tools into the framework. To understand the fundamental difficulty of the problem, we derive minimax lower bounds in semi-supervised settings and showcase that our procedure is semi-parametrically efficient under regularity conditions. Moreover, tailored to bivariate kernels, we propose a refined approach that outperforms the classical U-statistic across all degeneracy regimes, and demonstrate its optimality properties. Simulation studies are conducted to corroborate our findings and to further demonstrate our framework.