核投影Wasserstein距离的两样本检验
Two-sample Test with Kernel Projected Wasserstein Distance
摘要：
我们为双样本测试开发了一个核投影Wasserstein距离，这是统计学和机器学习中的一个重要组成部分：给定两组样本，以确定它们是否来自相同的分布。该方法通过在数据空间中找到使投影分布之间的距离最大化的非线性映射来操作。与现有的投影Wasserstein距离相比，该方法更有效地规避了维数灾难。我们提出了实用的算法来计算这个距离函数的非渐近不确定性量化的经验估计。数值例子验证了我们的理论结果，并表明所提出的方法具有良好的性能。
英文摘要：
We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method operates by finding the nonlinear mapping in the data space which maximizes the distance between projected distributions. In contrast to existing works about projected Wasserstein distance, the proposed method circumvents the curse of dimensionality more efficiently. We present practical algorithms for computing this distance function together with the non-asymptotic uncertainty quantification of empirical estimates. Numerical examples validate our theoretical results and demonstrate good performance of the proposed method.
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