具有有向网络异质度差异性的标注图模型
An Annotated Graph Model with Differential Degree Heterogeneity for Directed Networks
AI总结：
针对有向网络中存在上下文信息与度异质性时缺乏适用推断模型的问题，提出一种标注图模型，通过引入稀疏假设与 $\ell_1$-正则化的惩罚似然方法克服维数灾难，实现估计与选择一致性，且对协变量参数推断无需去偏处理。
摘要：
有向网络通常被方便地表示为图，其中有序边编码了顶点间的交互。尽管其广泛可用，但在存在上下文信息和度异质性的情况下，仍缺乏适用于推断的统计模型。本文提出了一种标注图模型，其参数显式地考虑了这些特征。为克服由度异质性建模导致的维数灾难，我们引入了稀疏性假设，并提出了一种带有 $\ell_1$-正则化的惩罚似然方法进行参数估计。我们在稀疏网络假设下研究了该方法的估计和选择一致性，并表明对协变量参数的推断是直接的，从而无需在 $\ell_1$-惩罚似然估计中采用常见的去偏处理。模拟与数据分析证实了我们的理论发现。
英文摘要：
Directed networks are conveniently represented as graphs in which ordered edges encode interactions between vertices. Despite their wide availability, there is a shortage of statistical models amenable for inference, specially when contextual information and degree heterogeneity are present. This paper presents an annotated graph model with parameters explicitly accounting for these features. To overcome the curse of dimensionality due to modelling degree heterogeneity, we introduce a sparsity assumption and propose a penalized likelihood approach with $\ell_1$-regularization for parameter estimation. We study the estimation and selection consistency of this approach under a sparse network assumption, and show that inference on the covariate parameter is straightforward, thus bypassing the need for the kind of debiasing commonly employed in $\ell_1$-penalized likelihood estimation. Simulation and data analysis corroborate our theoretical findings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
