论文标题
非参数两样本假设检验，用于具有负和重复特征值的随机图
Nonparametric Two-Sample Hypothesis Testing for Random Graphs with Negative and Repeated Eigenvalues
论文作者
论文摘要
我们为低级别，有条件独立的边缘随机图提出了一个非参数的两样本测试统计统计，其边缘概率矩阵具有负特征值和任意关闭特征值。我们提出的测试统计量涉及使用适用于图形嵌入的适当旋转行的最大平均差异，其中使用最佳传输估算了旋转。我们表明，我们的测试统计量（适当缩放）对于足够致密的图是一致的，并且我们研究了其在不同的稀疏状态下的收敛性。此外，我们还提供了经验证据，表明我们的新型对齐程序可以比在幼稚的对齐中假定eigengap的实践中的幼稚对齐能力更好。
We propose a nonparametric two-sample test statistic for low-rank, conditionally independent edge random graphs whose edge probability matrices have negative eigenvalues and arbitrarily close eigenvalues. Our proposed test statistic involves using the maximum mean discrepancy applied to suitably rotated rows of a graph embedding, where the rotation is estimated using optimal transport. We show that our test statistic, appropriately scaled, is consistent for sufficiently dense graphs, and we study its convergence under different sparsity regimes. In addition, we provide empirical evidence suggesting that our novel alignment procedure can perform better than the naïve alignment in practice, where the naïve alignment assumes an eigengap.
