标题： 神经 Wasserstein 两样本检验 显示英文标题

标题： Neural Wasserstein Two-Sample Tests

摘要： 两样本同质性检验问题在统计学中是基础性的，在高维情况下尤其具有挑战性，其中经典检验可能会出现显著的效力损失。 我们开发了一种基于投影1-Wasserstein距离的学习辅助过程，我们称之为神经Wasserstein检验。 该方法的提出是基于这样一个观察：通常存在一个低维投影，使得两个高维分布在此投影下有所差异。 在实际操作中，我们通过流形优化和使用深度神经网络的见证函数来学习投影方向。 为了适应未知的投影维度和稀疏水平，我们通过一种最大值型构造对一组候选统计量进行聚合，避免了显式的调参，同时可能提高效力。 我们建立了所提出检验的有效性和一致性，并证明了高斯近似的Berry--Esseen型界。 特别是，在原假设下，聚合统计量收敛于标准高斯向量的绝对最大值，从而得到一种渐近枢轴（分布无关）的校准方法，避免了重采样。 模拟研究和一个真实数据例子展示了所提出方法的强大有限样本性能。 显示英文摘要

摘要： The two-sample homogeneity testing problem is fundamental in statistics and becomes particularly challenging in high dimensions, where classical tests can suffer substantial power loss. We develop a learning-assisted procedure based on the projection 1-Wasserstein distance, which we call the neural Wasserstein test. The method is motivated by the observation that there often exists a low-dimensional projection under which the two high-dimensional distributions differ. In practice, we learn the projection directions via manifold optimization and a witness function using deep neural networks. To adapt to unknown projection dimensions and sparsity levels, we aggregate a collection of candidate statistics through a max-type construction, avoiding explicit tuning while potentially improving power. We establish the validity and consistency of the proposed test and prove a Berry--Esseen type bound for the Gaussian approximation. In particular, under the null hypothesis, the aggregated statistic converges to the absolute maximum of a standard Gaussian vector, yielding an asymptotically pivotal (distribution-free) calibration that bypasses resampling. Simulation studies and a real-data example demonstrate the strong finite-sample performance of the proposed method.