A1829
Title: Neural Wasserstein two-sample tests
Authors: Xiaoyu Hu - Xian Jiaotong University (China)
Zhenhua Lin - National University of Singapore (Singapore) [presenting]
Abstract: 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. A learning-assisted procedure based on the projection Wasserstein distance is developed, motivated by the observation that there often exists a low-dimensional projection under which the two high-dimensional distributions differ. In practice, the projection directions are learned via manifold optimization and a witness function using deep neural networks. To adapt to unknown projection dimensions and sparsity levels, a collection of candidate statistics is aggregated through a max-type construction, avoiding explicit tuning while potentially improving power. The validity and consistency of the proposed test are established, and a Berry-Esseen type bound for the Gaussian approximation is proved. 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.
