Skip to content
DraconiticResearch
Search Sources API
190,860 studies31 sourcesUpdated 57 min ago
PreprintarXiv licencearXiv

Learning U-Statistics with Active Inference

  • Xiaoning Wang
  • Yuyang Huo
  • Liuhua Peng
  • Changliang Zou
Open at sourcePDFDOICite

Abstract

U-statistics play a central role in statistical inference. In many modern applications, however, acquiring the labels required for U-statistics is costly. Motivated by recent advances in active inference, we develop an active inference framework for U-statistics that selectively queries informative labels to improve estimation efficiency under a fixed labeling budget, while preserving valid statistical inference. Our approach is built on the augmented inverse probability weighting U-statistic, which is designed to incorporate the sampling rule and machine learning predictions. We characterize the optimal sampling rule that minimizes its variance and design practical sampling strategies. We further extend the framework to U-statistic-based empirical risk minimization. Experiments on real datasets demonstrate substantial gains in estimation efficiency over baseline methods, while maintaining target coverage.

Related

  1. Nonparametric Inference Based on Expected Order Statistics
    Tommaso Lando, Lorenzo Tedesco
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  2. Martingalized U-statistics-based sequential inference: a blessing of degeneracy
    Weijia Li, Leheng Cai, Qirui Hu
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. High-Dimensional Two-Sample Inference via Marginal Likelihood-Ratio Rank Statistics
    Xiaoxu Zhang, Long Feng
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  4. Neural Estimation of Summary Statistics for Simulation-Based Inference with Non-Asymptotic Guarantees
    Rui Li, Rong Tang
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  5. Tree statistics improve neural simulation-based inference of epidemiological parameters over case counts alone
    Zena Lapp, Emma E. Goldberg, John R. Tipton +3
    arXivPreprintCC BY-NC-SA 4.0Full textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026learning,
  title = {{Learning U-Statistics with Active Inference}},
  author = {Xiaoning Wang and Yuyang Huo and Liuhua Peng and Changliang Zou},
  howpublished = {arXiv},
  year = {2026},
  month = may,
  doi = {10.48550/arxiv.2605.11638},
  eprint = {2605.11638},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.11638},
}
RIS
TY  - UNPB
TI  - Learning U-Statistics with Active Inference
AU  - Xiaoning Wang
AU  - Yuyang Huo
AU  - Liuhua Peng
AU  - Changliang Zou
PY  - 2026
DA  - 2026/05/12
PB  - arXiv
DO  - 10.48550/arxiv.2605.11638
UR  - https://arxiv.org/abs/2605.11638
AB  - U-statistics play a central role in statistical inference. In many modern applications, however, acquiring the labels required for U-statistics is costly. Motivated by recent advances in active inference, we develop an active inference framework for U-statistics that selectively queries informative labels to improve estimation efficiency under a fixed labeling budget, while preserving valid statistical inference. Our approach is built on the augmented inverse probability weighting U-statistic, which is designed to incorporate the sampling rule and machine learning predictions. We characterize the optimal sampling rule that minimizes its variance and design practical sampling strategies. We further extend the framework to U-statistic-based empirical risk minimization. Experiments on real datasets demonstrate substantial gains in estimation efficiency over baseline methods, while maintaining target coverage.
ER  -