针对具有不同顶点数的图修正非参数双样本图假设检验及其在连接组学中的应用
Correcting a Nonparametric Two-sample Graph Hypothesis Test for Graphs with Different Numbers of Vertices with Applications to Connectomics
AI总结：
本文针对顶点数不等的双样本图假设检验失效问题，提出了基于ASE渐近分布采样的修正邻接谱嵌入（CASE）方法，使后续检验有效且一致，并成功应用于人类连接组学dMRI数据的生成分布等价性判定。
摘要：
随机图是具有许多应用的统计模型，应用范围从神经科学到社交网络分析。在某些应用中，特别令人感兴趣的是检验两个随机图的生成分布是否相等的问题。Tang等人（2017）提出了一种针对此设定的检验。该检验包括通过邻接谱嵌入（ASE）将图嵌入到低维空间中，随后使用基于最大均值差异的核双样本检验。然而，如果进行比较的两个图具有不相等的顶点数，Tang等人（2017）的检验可能无效。我们展示了这种无效性背后的直觉，并提出了一种修正方法，使得任何后续基于核或距离的检验都有效。我们的方法依赖于基于ASE的渐近分布进行采样。我们将这些改变后的嵌入称为修正邻接谱嵌入（CASE）。我们还表明，CASE弥补了原始检验的可交换性问题，并通过模拟研究证明了使用CASE的检验的有效性和一致性。最后，我们将提出的检验应用于确定在不同尺度下从扩散磁共振成像（dMRI）提取的人类连接组中生成分布等价性的问题。
英文摘要：
Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating distributions. Tang et al. (2017) propose a test for this setting. This test consists of embedding the graph into a low-dimensional space via the adjacency spectral embedding (ASE) and subsequently using a kernel two-sample test based on the maximum mean discrepancy. However, if the two graphs being compared have an unequal number of vertices, the test of Tang et al. (2017) may not be valid. We demonstrate the intuition behind this invalidity and propose a correction that makes any subsequent kernel- or distance-based test valid. Our method relies on sampling based on the asymptotic distribution for the ASE. We call these altered embeddings the corrected adjacency spectral embeddings (CASE). We also show that CASE remedies the exchangeability problem of the original test and demonstrate the validity and consistency of the test that uses CASE via a simulation study. Lastly, we apply our proposed test to the problem of determining equivalence of generating distributions in human connectomes extracted from diffusion magnetic resonance imaging (dMRI) at different scales.
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