标题： 通过多边缘最优传输的k-样本推断 显示英文标题

标题： k-Sample inference via Multimarginal Optimal Transport

摘要： 本文提出了一种多边缘最优传输（$MOT$）方法，用于同时比较支持在$\mathbb{R}^d$、$d \geq 1$的有限子集上的$k\geq 2$测度。我们推导了在所有$k$测度相同的原假设下以及至少有两个测度不同的备择假设下，经验$MOT$程序的最优值的渐近分布。我们利用这些结果构建了原假设的检验，并提供了此$k$-样本检验的一致性和功效保证。我们使用自助法一致估计渐近分布，并提出了一种低复杂度的线性规划来近似检验临界值。我们在合成数据和真实数据集上展示了我们方法的优势，包括美国2004-2020年的癌症真实数据。 显示英文摘要

摘要： This paper proposes a Multimarginal Optimal Transport ($MOT$) approach for simultaneously comparing $k\geq 2$ measures supported on finite subsets of $\mathbb{R}^d$, $d \geq 1$. We derive asymptotic distributions of the optimal value of the empirical $MOT$ program under the null hypothesis that all $k$ measures are same, and the alternative hypothesis that at least two measures are different. We use these results to construct the test of the null hypothesis and provide consistency and power guarantees of this $k$-sample test. We consistently estimate asymptotic distributions using bootstrap, and propose a low complexity linear program to approximate the test cut-off. We demonstrate the advantages of our approach on synthetic and real datasets, including the real data on cancers in the United States in 2004 - 2020.