Spectral Inference for Large Stochastic Blockmodels With Nodal Covariates
Spectral Inference for Large Stochastic Blockmodels With Nodal Covariates
复制标题
具有节点协变量的大型随机块模型的谱推断
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
C. Priebe
中科院分区：
文献类型：
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作者：
A. Mele;Lingxin Hao;Joshua Cape;C. Priebe
在网络分析的许多应用中，区分影响网络结构的可观测因素和未观测因素是很重要的。为此，我们给出了随机分块模型中未观测分块和协变量影响的谱估计。我们的主要策略是将随机分块模型估计问题转化为广义随机点积图中潜在位置的恢复问题。在理论方面，我们建立了估计量的渐近正态，以便于后续的推断。在应用方面，我们证明了我们的估计器的计算速度比标准的变分期望最大化算法要快得多，并且在大型网络中具有很好的伸缩性。本文的结果为估计网络中观察到的协变量和未观察到的潜在社区结构对链路形成概率的影响提供了基础。
In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. To this end, we develop spectral estimators for both unobserved blocks and the effect of covariates in stochastic blockmodels. Our main strategy is to reformulate the stochastic blockmodel estimation problem as recovery of latent positions in a generalized random dot product graph. On the theoretical side, we establish asymptotic normality of our estimators for the subsequent purpose of performing inference. On the applied side, we show that computing our estimator is much faster than standard variational expectation--maximization algorithms and scales well for large networks. The results in this paper provide a foundation to estimate the effect of observed covariates as well as unobserved latent community structure on the probability of link formation in networks.