Spectral Estimation of Large Stochastic Blockmodels with Discrete Nodal Covariates
提出一种谱估计方法，用于估计离散协变量对网络链接概率的影响，该方法比标准算法更快，适用于大型网络，并在Facebook数据中发现了性别、角色和校园居住的同质性以及未观测社区。
In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. We show that a network model with discrete unobserved link heterogeneity and binary (or discrete) covariates corresponds to a stochastic blockmodel (SBM). We develop a spectral estimator for the effect of covariates on link probabilities, exploiting the correspondence of SBMs and generalized random dot product graphs (GRDPG). We show that computing our estimator is much faster than standard variational expectation–maximization algorithms and scales well for large networks. Monte Carlo experiments suggest that the estimator performs well under different data generating processes. Our application to Facebook data shows evidence of homophily in gender, role and campus-residence, while allowing us to discover unobserved communities. Finally, we establish asymptotic normality of our estimators.