提出一种基于神经网络的非参数两样本检验方法，提升检测分布差异的能力。
A nonparametric two-sample test using a parametric integral probability metric
- 用单节点神经网络设计判别器，构造新的积分概率度量
- 在有限样本下检验功效优于或相当于现有方法
- 理论保证一致性和渐近等价性，适合小样本场景
检测两个独立样本间的分布差异是统计学与机器学习中的基础问题。非参数两样本检验提供了一种不假设分布具体形式的严谨框架。本文提出一种基于新引入的积分概率度量（IPM）的两样本检验统计量，采用特制的单节点神经网络判别器类。我们证明所得统计量PReLU-IPM为非参数，并建立了相关检验程序PReLU-TST的理论保证，包括一致性及在正则条件下与非参数IPM基检验渐近等价。通过多个模拟和真实基准数据集分析，表明PReLU-TST在有限样本下对多种备择假设具有更高检验功效或表现相当。
原文摘要 · Abstract (English)
Detecting distributional differences between two independent samples is a fundamental problem in statistics and machine learning. Nonparametric two-sample testing provides a principled framework for determining whether two samples are drawn from the same underlying distribution, without assuming any specific parametric form for the distribution. In this study, we propose a new two-sample test statistic based on a newly introduced integral probability metric (IPM), using a specially designed parametric discriminator class with a single node of a neural network. We show that the resulting test statistic, called PReLU-IPM, is nonparametric and establish theoretical guarantees for the associated two-sample testing procedure, PReLU-TST, including its consistency and asymptotical equivalence to nonparametric IPM-based tests under regularity conditions. By analyzing multiple simulated and real benchmark datasets, we demonstrate that PReLU-TST achieves higher power across a range of alternatives or performs comparably to its competitors, for finite samples.
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