论文标题
高维独立性测试通过最大和平均距离相关性
High-Dimensional Independence Testing via Maximum and Average Distance Correlations
论文作者
论文摘要
本文研究了多元独立性测试的最大和平均距离相关性的利用。我们表征了它们在高维设置中相对于略有依赖性维度的数量的一致性属性，比较每个测试统计量的优势，检查其各自的空分布，并提供基于卡方的快速测试程序。所得的测试是非参数，并且适用于欧几里得距离和高斯内核作为基础度量。为了更好地了解所提出的测试的实际用例，我们评估了最大距离相关性，平均距离相关性以及各种多变量依赖性场景的原始距离相关性的经验性能，并进行了真实的数据实验，以测试人类质量中各种癌症类型和肽水平的存在。
This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally dependent dimensions, compare the advantages of each test statistic, examine their respective null distributions, and present a fast chi-square-based testing procedure. The resulting tests are non-parametric and applicable to both Euclidean distance and the Gaussian kernel as the underlying metric. To better understand the practical use cases of the proposed tests, we evaluate the empirical performance of the maximum distance correlation, average distance correlation, and the original distance correlation across various multivariate dependence scenarios, as well as conduct a real data experiment to test the presence of various cancer types and peptide levels in human plasma.
