arXiv:2606.08460stat.MLcs.LG2026-06

利用大量参考样本提升小样本检测能力,实现高效分布差异检验。

LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry

  • 用参考数据学习依赖参考的表征,捕捉分布关键结构
  • 在多种基准上表现优异,且保持类型I误差控制
  • 适合参考样本多、查询样本极少的场景,如异常检测

数据自适应的两样本检验通过从数据中学习差异度量(如基于核的特征表示)来判断两个样本是否来自同一分布。这类方法通常依赖数据划分以分离学习与检验过程,并控制第一类错误。然而,这种范式在严重样本量不平衡的少样本场景下表现不佳:参考样本充足,而查询样本仅寥寥几个。本文提出一种新方法,将这种不平衡转化为优势。利用丰富的参考数据,学习依赖参考的表征,总结参考分布的显著结构并提供检测偏离的有力信号。我们整合了捕获全局与局部结构的多种表征族,并仅使用参考样本通过不确定性引导原则自适应加权。理论上,我们建立了基于置换的类型I误差控制,并证明聚合检验的一致性:当表征集合包含至少一个一致表征时,随着样本量增大,检验功效收敛于1。实验表明,该聚合方法在多个基准上均表现强劲,同时保持类型I误差控制。

原文摘要 · Abstract (English)

Data-adaptive two-sample testing assesses if two samples come from the same distribution, using a discrepancy learned from the data (e.g., via kernel-based feature representations). Such methods typically rely on data splitting to decouple learning from testing and control type I error. However, this paradigm is ill-suited to few-shot settings with severe sample-size imbalance: abundant reference samples are available, while only a handful of query samples arrive. In this paper, we show how this imbalance can be leveraged constructively. Using abundant reference data, we learn reference-dependent representations that summarize salient structure of the reference distribution and provide informative signals for detecting departures. We incorporate a collection of representation families that capture both global and local structure, and adaptively weight them using only reference samples via an uncertainty-guided principle. Theoretically, we establish permutation-based type I error control and show consistency of the aggregated test: as the sample sizes grow, the test power converges to one whenever the representation set contains at least one consistent representation. Empirically, our aggregation achieves strong performance across a range of benchmarks while retaining type I error control.

两样本检验少样本学习分布检测参考样本

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