|| Two-sample Test using Projected Wasserstein Distance
||Jie Wang, Georgia Institute of Technology, United States; Rui Gao, University of Texas at Austin, United States; Yao Xie, Georgia Institute of Technology, United States|
||Tuesday, 20 July, 23:40 - 00:00
||Wednesday, 21 July, 00:00 - 00:20
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to circumvent the curse of dimensionality in Wasserstein distance: when the dimension is high, it has diminishing testing power, which is inherently due to the slow concentration property of Wasserstein metrics in the high dimension space. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions. We characterize theoretical properties of the two-sample convergence rate on IPMs and this new distance. Numerical examples validate our theoretical results.