Learning U-Statistics with Active Inference
Authors: Xiaoning Wang, Yuyang Huo, Liuhua Peng et al.
Summary
The authors develop an active inference framework for U-statistics (a class of estimators central to many statistical tests) when labels are expensive. Instead of collecting all labels, they selectively query the most informative ones to improve estimation efficiency under a fixed budget while preserving valid statistical inference. The method uses augmented inverse probability weighting to account for the adaptive sampling rule and machine learning predictions, characterizes the optimal sampling rule that minimizes variance, and extends to empirical risk minimization based on U-statistics.
Main takeaways:
- U-statistics (estimators based on averaging over all subsets of data) are fundamental in statistics but often require expensive labels in modern applications.
- Active inference selectively queries labels to maximize information gain under a fixed labeling budget.
- The method uses augmented inverse probability weighting to incorporate the adaptive sampling rule and ML predictions, ensuring valid inference.
- The authors derive the variance-minimizing optimal sampling rule and provide practical sampling strategies.
- The framework extends to U-statistic-based empirical risk minimization (e.g., AUC optimization).
- Experiments show substantial efficiency gains over baseline methods while maintaining correct coverage.
Relevance
Not directly related to my persona/midtraining work—this is about active learning for U-statistics in classical statistical inference. Could be tangentially relevant if I'm thinking about efficient data collection during fine-tuning, but the connection is weak.
Abstract
arXiv:2605.11638v1 Announce Type: new 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.