论文标题
随机模块的估计和推断
Estimation and inference for stochastic blockmodels
论文作者
论文摘要
本文与加权随机块模型的非参数估计有关。我们首先表明该模型暗示了一组对某些子图的边缘的联合分布（以其最简单的形式）三重态和四个节点的四元组的限制。从这个方程系统中，模型的未知组件可以非参数恢复，直到通常的标记歧义。我们引入了一种简单且具有计算的方式来做到这一点。然后，估计器遵循类比原则。提供了极限理论。我们发现，组件分布及其功能及其密度函数（对于边缘权重连续的情况）都是可以在参数速率下估算的。报告了数值实验。
This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving (in its simplest form) triplets and quadruples of nodes. From this system of equations the unknown components of the model can be recovered nonparametrically, up to the usual labeling ambiguity. We introduce a simple and computationally-attractive manner to do this. Estimators then follow from the analogy principle. Limit theory is provided. We find that component distributions and their functionals, as well as their density functions (for the case where edge weights are continuous) are all estimable at the parametric rate. Numerical experiments are reported on.
