检验节点特征与网络结构相关性，提出四种高效新方法。
Testing for correlation between network structure and high-dimensional node covariates
- 基于线性模型或典型相关分析，不依赖复杂假设。
- 在低秩潜空间模型下有理论保证，支持高维特征。
- 计算更高效，适合真实网络数据验证相关性。
在多个应用领域中，网络常伴随节点级特征被观测。一个常见问题是判断节点协变量是否与网络结构本身相关。本文提出四种新方法：两种基于节点特征与驱动网络结构的潜变量之间的线性模型；另两种采用典型相关分析直接关联节点特征与网络结构，避免线性假设。我们在低秩潜空间模型框架下为所有方法提供理论保障，该模型允许节点协变量为高维。相比以往方法，本工作计算成本更低、建模假设更少。通过模拟数据和真实网络数据，验证并比较了所提方法的性能。
原文摘要 · Abstract (English)
In many application domains, networks are observed with node-level features. In such settings, a common problem is to assess whether or not nodal covariates are correlated with the network structure itself. Here, we present four novel methods for addressing this problem. Two of these are based on a linear model relating node-level covariates to latent node-level variables that drive network structure. The other two are based on applying canonical correlation analysis to the node features and network structure, avoiding the linear modeling assumptions. We provide theoretical guarantees for all four methods when the observed network is generated according to a low-rank latent space model endowed with node-level covariates, which we allow to be high-dimensional. Our methods are computationally cheaper and require fewer modeling assumptions than previous approaches to network dependency testing. We demonstrate and compare the performance of our novel methods on both simulated and real-world data.
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