Distribution-Free Multisample Test Based on Optimal Matching with Applications to Single Cell Genomics
Distribution-Free Multisample Test Based on Optimal Matching with Applications to Single Cell Genomics
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发表时间：
2019-06
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通讯作者：
Divyansh Agarwal;Somabha Mukherjee;B. Bhattacharya;N. Zhang
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作者：
Divyansh Agarwal;Somabha Mukherjee;B. Bhattacharya;N. Zhang
本文提出了一种基于最优匹配的非参数图检验方法，用于检验多个未知多元概率分布是否相等。我们的程序池的数据从不同的类创建一个图形的基础上最小的非二分匹配，然后利用边缘连接数据点的数量从不同的类来检查分布之间的接近度。所提出的测试是完全免费的分布（零分布不依赖于数据的分布），可以有效地应用于多变量以及非欧几里德数据，只要点间距离是明确定义的。我们证明了该检验是普适的，并证明了一般替代下检验统计量的分布极限定理。通过仿真研究，我们证明了它的上级性能对其他常见的和众所周知的多样本测试。在我们的测试表明跨类分布差异的情况下，我们还提出了一种方法来确定哪个类或组有助于这种整体差异。该方法适用于从患有肝细胞癌和非小细胞肺癌的人类受试者的外周血、癌组织和肿瘤相邻正常组织获得的单细胞转录组学数据。我们的方法揭示了在癌症环境中，生物化学代谢途径如何在免疫细胞中改变的模式，这取决于组织位置。本文描述的所有方法都在R包多交叉中实现。
In this paper we propose a nonparametric graphical test based on optimal matching, for assessing the equality of multiple unknown multivariate probability distributions. Our procedure pools the data from the different classes to create a graph based on the minimum non-bipartite matching, and then utilizes the number of edges connecting data points from different classes to examine the closeness between the distributions. The proposed test is exactly distribution-free (the null distribution does not depend on the distribution of the data) and can be efficiently applied to multivariate as well as non-Euclidean data, whenever the inter-point distances are well-defined. We show that the test is universally consistent, and prove a distributional limit theorem for the test statistic under general alternatives. Through simulation studies, we demonstrate its superior performance against other common and well-known multisample tests. In scenarios where our test suggests distributional differences across classes, we also propose an approach for identifying which class or group contributes to this overall difference. The method is applied to single cell transcriptomics data obtained from the peripheral blood, cancer tissue, and tumor-adjacent normal tissue of human subjects with hepatocellular carcinoma and non-small-cell lung cancer. Our method unveils patterns in how biochemical metabolic pathways are altered across immune cells in a cancer setting, depending on the tissue location. All of the methods described herein are implemented in the R package multicross.