Consistent structure estimation of exponential-family random graph models with block structure
Consistent structure estimation of exponential-family random graph models with block structure
复制标题
DOI：
10.3150/19-bej1153
复制
发表时间：
2017-02
期刊：
影响因子：
1.5
通讯作者：
M. Schweinberger
中科院分区：
文献类型：
--
作者：
M. Schweinberger
我们考虑基于具有复杂相关性的随机图的单一观测的指数族随机图模型的统计推断的挑战性问题。为了便于统计推断，我们考虑了具有区块结构形式的附加结构的随机图。我们在其他地方已经证明，当区块结构已知时，它促进了具有复杂相关性(如传递性)的规范和曲线型指数族随机图模型的$M$-估计的一致性结果。在实践中，块结构在一些应用(例如，多级网络)中是已知的，但在其他应用中是未知的。当块结构未知时，首先也是最重要的问题是，基于具有复杂依赖关系的随机图的一次观察，它是否能够以高概率恢复。本文的主要相合性结果表明，在弱相依性和光滑性条件下，这是可能的。这些结果证实了具有区块结构的指数族随机图模型是统计网络分析的一个很有前途的方向。
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs with additional structure in the form of block structure. We have shown elsewhere that when the block structure is known, it facilitates consistency results for $M$-estimators of canonical and curved exponential-family random graph models with complex dependence, such as transitivity. In practice, the block structure is known in some applications (e.g., multilevel networks), but is unknown in others. When the block structure is unknown, the first and foremost question is whether it can be recovered with high probability based on a single observation of a random graph with complex dependence. The main consistency results of the paper show that it is possible to do so under weak dependence and smoothness conditions. These results confirm that exponential-family random graph models with block structure constitute a promising direction of statistical network analysis.