Learning U-Statistics with Active Inference
$U$-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 strat...
| Authors | Xiaoning Wang, Yuyang Huo, Liuhua Peng et al. |
|---|---|
| Primary category | stat.ML |
| Published | 12 May 2026 |
| Last updated at source | 12 May 2026 |
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